IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


1.0 


I.I 


12.5 


lii|21 

m  m 

£   1^   12.0 

lit 


^^^■ 


V 


FhobgraphJc 

Sciences 

Corporalion 


•S5 


4^"^^ 


33  WIST  MAM  STRHT 

WnSTILN.Y.  145M 

(7U)t7a-4S03 


i\ 


A* 


CIHM/ICMH 

Microfiche 

Series. 


CIHM/ICMH 
Collection  de 
microfiches. 


Canadian  Instituta  for  Historical  IMicroraproductiont  /  Inttitut  Canadian  da  microraproductions  historiquas 


^> 


<v 


Tachnical  and  Bibliographic  Notaa/Notas  tachniquaa  at  bibliographiquaa 

Tha  Instituta  hat  attamptad  to  obtain  tha  baat 
original  copy  availabia  for  filming.  Faaturaa  of  thia 
copy  which  may  ba  bibliographically  uniqua, 
which  may  altar  any  of  tha  imagaa  in  tha 
raproduction,  or  which  may  aignificantly  changa 
tha  uaual  mathod  of  filming,  ara  chackad  balow. 

L'Institut  a  microfilm*  la  meilleur  exemplaire 
qu'll  lui  a  4t*  possible  de  se  procurer.  Les  details 
da  cat  exemplaire  qui  aont  paut-Atre  uniques  du 
point  de  vue  bibliographique,  qui  peuvent  modifier 
une  image  reproduite.  ou  qui  peuvent  sxiger  une 
modification  dans  la  mAthoda  normale  de  f ilmage 
sont  indiqute  ci-dessous. 

Coloured  covars/ 
Couvartura  da  coulaur 

1 

Coloured  pages/ 
Pages  de  couleur 

Covars  damagad/ 
L 1   Couvartura  andommagte 

_i. 

Pages  damaged/ 
Pages  endommagAas 

Covars  rastorad  and/or  laminatad/ 
Couvartura  raataurte  at/ou  palliculAa 

"'^-- 

Pages  restored  and/or  laminated/ 
Pages  reataurias  at/ou  pellicultes 

1 — 1   Covar  title  missing/ 

Le  titre  de  couverture  manque 

y 

Pages  discoloured  stained  or  foxed/ 
Pages  dAcolorAes,  tachat^es  ou  piquAas 

p  1    Coloured  maps/ 
...    Cartes  gAographiques  en  couleur 



Pages  detached/ 
Pages  dAtachtas 

Tha  I 
toth 


The 
poaa 
of  til 
filmi 


Origl 
bagii 
thai 
sion, 
otha 
first 
sion, 
Drill 


□   Coloured  ink  (i.e.  other  than  blue  or  black)/ 
Encra  de  couleur  (i.e.  autre  que  bleue  ou  noire) 

I     I   Coloured  plates  and/or  illustrations/ 


rjl   Showthrough/ 


D 


D 


D 


Planches  et/ou  illustrations  w\  couleur 

Bound  with  other  material/ 
Rail*  avac  d'autras  documents 

Tight  binding  may  cause  shadows  or  distortion 
along  interior  margin/ 

La  re  liure  serrie  peut  causer  de  I'ombre  ou  de  la 
distortion  le  long  de  la  marge  intArieure 

Blank  leaves  added  during  restoration  may 
appear  within  the  text.  Whenever  poaaibla.  these 
have  been  omitted  from  filming/ 
II  se  peut  que  certainas  pages  blanches  ajouttea 
lore  d'una  restauration  apparaiaaant  dana  la  texte, 
mais.  lorsqua  cela  Atait  possible,  ces  pages  n'ont 
pas  hxh  filmiaa. 

Additional  comments:/ 
Commentaires  supplAmentaires; 


Transparence 

Quality  of  prir 

Quality  InAgala  de  I'impression 

Includes  supplementary  materii 
Comprend  du  material  suppMmentaira 

Only  edition  available/ 
Seule  Mition  disponible 


I     I   Quality  of  print  varies/ 

I     I   Includes  supplementary  material/ 

I — I   Only  edition  available/ 


0 


Pagea  wholly  or  piHrtiaily  obscured  by  errata 
slips,  tissues,  etc.,  have  ba«n  raf limed  to 
enaura  the  best  possible  image/ 
Les  pages  totalamant  ou  partiaiiement 
obacurcies  par  un  fauillat  d'errata.  une  pelure, 
etc..  ont  M  filmAes  A  nouveau  da  faqon  A 
obtanir  la  mailleure  image  possible. 


Th« 
Shan 
TlNl 
whic 

Map 
diffa 
amir 
bagii 
right 
raqu 
m«tl 


This  item  is  filmed  at  tha  reduction  ratio  checked  below/ 

Ca  document  est  filmA  au  taux  de  riduction  indlqu*  ci'dessous. 

10X  14X  18X  22X 


2SX 


aox 


7 

12X 


16X 


aox 


MX 


28X 


32X 


Th«  copy  film«d  h«r«  haa  been  raproductd  thanks 
to  th«  g«n«roaity  of: 

Dana  Portar  Am  Library 
Univtrsity  of  Watarioo 

Tbo  imogoo  appooring  hara  ara  tlia  baat  quality 
poaaibia  eonaidaring  tha  condition  and  lagibiiity 
of  tlw  original  copy  and  in  icaaping  wMi  tha 
filming  contract  apacif icationa. 


Original  copiaa  in  printad  papar  covara  ara  filmad 
baginning  with  tha  front  cover  and  anding  on 
tha  laat  paga  with  a  printad  or  illuatratad  impraa- 
aion,  or  tha  back  cover  whan  appropriate.  All 
othar  original  copiaa  ara  filmad  beginning  on  the 
first  pege  with  a  printed  or  illuatratad  imprae- 
aion,  and  anding  on  the  laat  page  with  e  printed 
or  illuatrated  impreeaton. 


L'axampiaira  f  ilm4  f  ut  reproduit  grice  i  la 
gAnArosit*  da: 

Dana  Portar  Arts  Library 
Univartity  of  Watarioo 

Lea  images  suivantas  ont  Ati  raproduitas  avac  la 
plua  grand  soin.  compta  tonu  da  la  condition  at 
da  la  nattet*  da  i'axemplaira  film*,  at  an 
conformftA  avac  lea  conditiona  du  eontrat  de 
filmege. 

Lee  exempleirea  originaux  dont  la  couvarture  an 
papier  est  imprimie  sent  filmte  en  commanpant 
par  la  premier  plat  at  an  tarminent  soit  par  la 
darnlAre  pege  qui  eomporte  une  amprainte 
d'impraaaion  ou  d'illuatration,  soit  par  la  second 
plat,  salon  la  caa.  Toua  las  autres  axamplairaa 
originaux  aont  flimAa  an  commenpant  par  la 
pramlAre  page  qui  eomporte  une  empreinte 
d'impreeaion  ou  d'illuatration  at  en  terminant  par 
la  derniAre  pege  qui  eomporte  une  telle 
amprainte. 


The  laet  recorded  frame  on  eech  microfiche 
ahaN  contain  the  aymbd  •-»>  (meening  "CON< 
TINUEO").  or  the  aymbol  ▼  (meening  "END"), 
whichever  eppliee. 


Un  dee  symboles  suivents  sppereftra  sur  la 
derni^re  imege  de  cheque  microfiche,  seion  le 
caa:  le  symbols  — »-  signifie  "A  SUIVRE",  le 
symbols  ▼  signifie  "FIM". 


ptotee,  charts,  ste..  mey  be  filmed  et 
different  reduction  rettoe.  Thoee  too  lerge  to  be 
entirely  included  in  one  exposure  ere  filmed 
beginning  in  the  upper  left  hend  comer,  left  to 
right  and  top  to  bottom,  aa  many  framee  ae 
required.  The  following  diagrame  illuatrate  the 
method: 


Lee  cartaa.  planchea.  tableeux.  etc..  pauvent  Atra 
filmAa  i  dee  taux  de  rMuction  diff Arents. 
Lorsque  le  document  est  trop  grend  pour  Atre 
reproduit  en  un  soul  clich*.  il  est  film*  A  partir 
de  Tangle  supArieur  geuche,  de  gauche  i  droite, 
et  de  haut  en  baa.  an  prenant  le  nombre 
d'imegee  n^ceaaaire.  Lea  diagrammas  suivents 
illustrent  le  mAthode. 


1  2  3 


32X 


1 

2 

3 

4 

5 

6 

OUTLINES 


w 


ASTRONOMY, 


IP 


1 


i 


/ 


£/ 


,'.?5, 


t 

1 

.*i 

1 

t 

9 

2 

3 

i*< 

^ 

'•i 

> 

A 

I 

s 

t 

r 

" 

0 

0 

t 

c 

"  ■*                 [ 

\ 

*      ,  ,       - 

.  "    .     ~~'" 

I 

'ik 


'Klfe 


'^. 


P^ai'e 


7io2 


F^2. 


Fl^.4. 


^/V/ 


I 


\/t^2. 


ID 


I 

8 


5 


M4.4. 


\ 


VSfW' 


-;,»■'■ 


UA 


•/ 


n 


OUTLINES 


ASTRONOMY: 


'/ 


e 


•r 

SIR  JOHN  F.  W.  HERSCHEL,  BART.  K.H. 

M.A.  D.C.L.  F.K.8.L.  k  E.  IIox.  5I.U.I.A.  F.Il.A.S.  P.Q.a.  M.C.U.P.8. 

Corrgipondent  or  Honorary  Member  of  the  Imperial,  Royal,  and  National,  Academiei  of  Selenett 

o(  Berlin,  Druiielt,  Copenhagen,  Onttingen,  Kaarlrni,  Maitarhiiaetti  (U.  S.),  Modena, 

N'aplet,  Parii,  I'etertburit,  Stockholm,  Turin,  Viejina,  and  Waibin|ton  (U.  S); 

the  Italian  and  Helvetic  Societlea) 

(lie  Academiei,  Inilltutei,  Ac,  of  Albany  (U.  !<.>,  Rnlogna,  Catania,  Dijon,  Lauianne, 

Nantei,  I'adua,  I'alermo,  Konic,  Venice,  Utrecht,  and  Wilna; 

th*  rbliomilhic  Society  of  I'arii ;  Aiiatic  Society  of  nengal  j  South  African  Lit.  and  Phil.  Society ; 

Literary  and  Iliitorical  Society  of  Quebec  ;  Iliitorical  Society  of  New  York ; 

Royal  Midico-Chirurgical  Soc.,and  Init.  of  Civil  Engineer!,  Londoa; 

Geographical  Soe.  of  Berlin ;  Aitronoroical  lod 

Meteorological  Soc.  of  Briliib  Oulaoa] 

fee.  &e.  &c. 


as 


A   NEW   EDITION. 


If 


WITH  NUMEROUS  PLATES  AND  WOOD-CUTS. 


\ 
S 

! 

0 

\ 


PHILADELPHIA: 
BLANC  HARD   &   LEA. 
1853. 
PR09MIV  Of 

MIKISITY  If  WHTH 


16102 


l^*^^^*^^^^^^^^^^^»*^*^<^*w^*N#w»»^«<fc»^ 


Printed  by  T.  K  &  P.  G.  CoUini. 


?0  YTiF;^«iOR<l 


NOTE 

TO 

THE    FOURTH    EDITION. 


Several  alterations  and  additions  are  made  in  this  Edition,  be- 
sides what  have  been  introduced  into  tho  Third,  to  bring  it  up 
to  tho  actual  state  of  astronomical  discovery.  The  elements  of 
four  new  planets  (Parthcnopo,  Egeria,  Victoria,  and  Irene)  have 
been  added,  and  improved  elements  of  Iris,  Metis,  Hebe,  and 
Hygeia,  substituted  for  the  provisional  elements  before  given. 
Tho  remarkable  discovery  of  an  additional  ring  of  Saturn,  and 
the  curious  researches  of  M.  Peters  on  the  proper  motion  of 
Sirius,  with  several  minor  features,  are  noticed.  Wlif^re  such 
additions  aro  introduced  in  tho  text,  they  are  indicated  by  being 
enclosed  in  brackets  [    ]. 


J.  F.  W.  Herschel. 


London,  4ug.  5,  1851. 


H9B4 


i 


S 


0 

11 

i 

0 


(V) 


5 

i 


■w 


PREFACE. 


The  work  here  offered  to  the  Public  is  based  upon  and  may  be 
considered  as  an  extension,  and,  it  is  hoped,  an  improvement  of 
a  treatise  on  the  same  subject,  forming  Part  43,  of  the  Cabinet 
Cyclopaedia,  published  in  the  year  1833.  Its  object  and  general 
character  are  suflRciently  stated  in  the  introductory  chapter  of 
that  volume,  here  reprinted  with  little  alteration ;  but  an  oppor- 
tunity having  been  afforded  me  by  the  Proprietors,  preparatory 
to  its  re-appearance  in  a  form  of  more  pretension,  I  have  gladly 
availed  myself  of  it,  not  only  to  correct  some  errors  which,  to 
my  regret,  subsisted  in  the  former  volume,  but  to  remodel  it  alto- 
gether (though  in  complete  accordance  with  its  original  design  as 
a  work  of  explanation)]  to  introduce  much  new  matter  in  the 
earlier  portions  of  it ;  to  re-write,  upon  a  far  more  matured  and 
comprehensive  plan,  the  part  relating  to  the  lunar  and  planetary 
perturbations,  and  to  bring  the  subjects  of  sidereal  and  nebular 
astronomy  to  the  level  of  the  present  state  of  our  knowledge  in 
those  departments. 

The  chief  novelty  iu  the  volume,  as  it  now  stands,  will  be  found 
in  the  manner  in  which  the  subject  of  Perturbations  is  treated. 
It  is  not  —  it  cannot  be  made  elementary^  in  the  sense  in  which 
that  word  is  understood  in  these  days  of  light  reading.  The 
chapters  devoted  to  it  must,  therefore,  be  considered  as  addressed 
to  a  class  of  readers  in  possession  of  somewhat  more  mathematical 
knowledge  than  those  who  will  find  the  rest  of  the  work  readily 

(vii) 


0 

5 

I 

0 

C 

I 


VIU 


PREFACE. 


If 


and  easily  accessible;  to  readers  desirous  of  preparing  them- 
selves, by  the  possession  of  a  sort  of  carte  du  pays,  for  a  cam- 
paign in  the  most  difficult,  but  at  the  same  time  the  most  attract- 
ive and  the  most  remunerative  of  all  the  applications  of  modern 
geometry.  More  especially  they  may  be  considered  as  addressed 
to  students  in  that  university,  where  the  "  Principia"  of  Newton 
is  not,  nor  ever  will  be,  put  aside  as  an  obsolete  book,  behind  the 
age;  and  where  the  grand,  though  rude  outlines  of  the  lunar 
theory,  as  delivered  in  the  eleventh  section  of  that  immortal 
work,  are  studied  less  for  the  sake  of  the  theory  itself  than  for 
the  spirit  of  far-reaching  thought,  superior  to  and  disencumbered 
of  technical  aids,  which  distinguishes  that  beyond  any  other  pro- 
duction of  the  human  intellect. 

In  delivering  a  rational  as  distinguished  from  a  technical  expo- 
sition of  this  subject,  however,  the  course  pursued  by  Newton  in 
the  section  of  the  Principia  alluded  to,  has  by  no  means  been 
servilely  followed.  As  regards  the  perturbations  of  the  nodes 
and  inclinations,  indeed,  nothing  equally  luminous  can  ever  be 
substituted  for  his  explanation.  But  as  resp'  3ts  the  other  dis- 
turbances, the  point  of  view  chosen  by  Newton  has  been  aban- 
doned for  another,  which  it  is  somewhat  difficult  to  perceive  why 
he  did  not,  himself,  select.  By  a  different  resolution  of  the  dis- 
turbing forces  from  that  adopted  by  him,  and  by  the  aid  of  a  few 
obvious  conclusions  from  the  laws  of  elliptic  motion  which  would 
have  found  their  place,  naturally  and  consecutively,  as  corollaries 
of  the  seventeenth  proposition  of  his  first  book  (a  proposition 
which  seems  almost  to  have  been  prepared  with  a  special  view  to 
this  application),  the  momentary  change  of  place  of  the  upper 
focus  ji  the  disturbed  ellipse  is  brought  distinctly  under  inspec- 
tion ;  and  a  clearness  of  conception  introduced  into  the  pertur- 
bations of  the  excentricities,  perihelia,  and  epochs,  which  the 
author  does  not  think  it  presumption  to  believe  can  be  obtained 
by  no  other  method,  and  which  certainly  is  not  obtained  by  that 
from  which  it  is  a  departure.  It  would  be  out  of  keeping  with 
the  rest  of  the  work  to  have  introduced  into  this  part  of  it  any 
algebraic  investigations ;  else  it  would  have  been  easy  to  show 
that  the  mode  of  procedure  here  followed  leads  direct,  and  by 


from 


m 


PREFACE. 


IX 


ig  them- 
r  a  cam- 
;  attract- 

raodern 
ddressed 

Newton 
hind  the 
le  lunar 
immortal 
than  for 
umbered 
;her  pro- 


jal  expo- 
ewton  in 
ins  been 
le  nodes 
ever  be 
ther  dig- 
)n  aban- 
nve  why 
the  dis- 
of  a  few 
jh  would 
rollaries 
)position 

view  to 
}  upper 
•  inspec- 

pertur- 
lich  the 
obtained 

by  that 
ng  with 
f  it  any 
to  show 

and  by 


steps  (for  the  subject)  of  the  most  elementary  character,  to  the 
general  formuUe  for  these  perturbations,  delivered  by  Laplace 

in  the  Mecanique  Celeste.' 

f 

The  reader  will  find  one  class  of  the  lunar  and  planetary  in- 
equalities handled  in  a  very  different  manner  from  that  in  which 
their  explanation  is  usually  presented.  It  comprehends  those 
which  are  characterized  as  incident  on  the  epoch,  the  principal 
among  them  being  the  annual  and  secular  equations  of  the  moon, 
and  that  very  delicate  and  obscure  part  of  the  perturbational 
theory  (so  little  satisfactory  in  the  manner  in  whi«h  it  emerges 
from  the  analytical  treatment  of  the  subject),  the  constant  or 
permanent  effect  of  the  disturbing  force  in  altering  the  disturbed 
orbit.  I  will  venture  to  hope  that  what  is  here  stated  will  tend 
to  remove  some  rather  generally  diffused  misapprehensions  as 
to  the  true  bearings  of  Newton's  explanation  of  the  annual 
equation.^ 

If  proof  were  wanted  of  the  inexhaustible  fertility  of  astro- 
nomiciil  science  in  points  of  novelty  and  interest,  it  would  suffice 
to  adduce  the  addition  to  the  list  of  members  of  our  system  of 
no  less  than  eight  new  planets  and  satellites  during  the  prepara- 
tion of  these  sheets  for  the  press.  Among  them  is  one  whose 
discovery  must  ever  be  regarded  as  one  of  the  noblest  triumphs 
of  theory.  In  the  account  here  given  of  this  discovery,  I  trust 
to  have  expressed  myself  with  complete  impartiality ;  and  in  the 
exposition  of  the  perturbative  action  on  Uranus,  by  which  the 
existence  and  situation  of  the  disturbing  planet  became  revealed 
to  us,  I  have  endeavoured,  in  pursuance  of  the  general  plan  of 
tliis  work,  rather  to  exhibit  a  rational  view  of  the  dynamical 
action,  than  to  convey  the  slightest  idea  of  the  conduct  of  those 
masterpieces  of  analytical  skill  which  the  researches  of  Messrs. 
Lcverrier  and  Adams  exhibit. 

To  the  latter  of  these  eminent  geometers,  as  well  as  to  my 
excellent  and  esteemed  friend  the  Astronomer  Royal,  I  have  to 

'  Livre  ii.  chop.  viii.  art.  07. 

»  Principia,  lib.  i.  prop.  G6,  cor.  6. 


f 

V 

(I 
< 

0 


I 

0 

X 

0 


5 


PREFACE. 


I 


; » 


return  my  best  thanks  for  communications  which  would  have 
effectually  relieved  some  doubts  I  at  one  period  entertained,  had 
I  not  succeeded  in  the  interim  in  getting  clear  of  them,  as  to  the 
compatibility  of  my  views  on  the  subject  of  the  annual  equation 
already  alluded  to,  with  the  tenor  of  Newton's  account  of  it.  To 
my  valued  friend,  Professor  De  Morgan,  I  am  indebted  for  some 
most  ingenious  suggestions  on  the  subject  of  the  mistakes  com- 
mitted in  the  early  working  of  the  Julian  reformation  of  the 
calendar,  of  which  I  should  have  availed  myself,  had  it  not  ap- 
peared preferable,  on  mature  consideration,  to  present  the  sub- 
ject in  its  ^simplest  form,  avoiding  altogether  entering  into  mi- 
nutiae of  chronological  discussion. 

J.  F.  W.  Herschel. 


CoUingwood,  April  12,  1849. 


lid  have 
ined,  had 
as  to  the 

equation 
bfit.    To 

for  some 
kes  cora- 
•n  of  the 
t  not  ap- 

the  sub- 

into  mi- 


SCHEL. 


CONTENTS. 


Frefacb Page  vii — x 

Introduction 17 

PART  I. 

CHAPTER  I. 

General  notions.  Apparent  and  real  motions.  Shape  and  size  of  the  Earth. 
The  horizon  and  its  dip.  The  atmosphere.  Refraction.  Twilight.  Appear- 
ances resulting  from  diurnal  motion.  From  change  of  station  in  general. 
Parallactic  motions.  Terrestrial  parallax.  That  of  the  stars  insensible. 
First  step  towards  forming  an  idea  of  the  distance  of  the  stars.  Copernican 
view  of  the  Earth's  motion.  Relative  motion.'  Motions  partly  real,  partly 
apparent.  Geocentric  astronomy,  or  ideal  reference  of  phocnomena  to  the 
Earth's  centre  as  a  common  conventional  station 24 


! 

3 
< 

0 


CHAPTER  II. 

Terminology  and  elementary  geometrical  conceptions  and  relations.  Termino- 
logy relating  to  the  globe  of  the  Earth  —  to  the  celestial  sphere.  Celestial 
perspective C2 

CHAPTER  III. 

Of  the  nature  of  astronomical  instruments  and  observations  in  general.  Of 
sidereal  and  solar  time.  Of  the  measurements  of  time.  Clocks,  chronome- 
ters. Of  astronomical  measurements.  Principle  of  telescopic  sights  to 
increase  the  accuracy  of  pointing.  Simplest  application  of  this  principle. 
The  transit  instrument.  Of  the  measurement  of  angular  intervals.  Methods 
of  increasing  the  accuracy  of  reading.  Tlie  vernier.  The  microscope.  Of 
the  mural  circle.  The  Meridian  circle.  Fixation  of  polar  and  horizontal 
points.  The  level,  plumb-line,  artificial  horizon.  Principle  of  collimation. 
Collimators  of  Rittenhouse,  Eater,  and  Benzenberg.  Of  compound  instru- 
ments with  co-ordinate  circles.  The  equatorial,  altitude,  and  azimuth  instru- 
ment. Theodolite.  Of  the  sextant  and  reflecting  circle.  Principle  of  repe- 
tition. Of  micrometers.  Parallel  wire  micrometer.  Principle  of  the  dupli- 
cation of  images.  The  heliometer.  Double  refracting  eye-piece.  Variable 
pi-ism  micrometer.     Of  the  position  miorometer 70 


I 

0 


\ 


J 


xu 


CONTENTS. 


CHAPTER  IV. 


OF    GEOOUAPHT. 


Of  tho  figure  of  the  Enrth.  Its  exact  (limcnsioiis.  Its  form  that  of  oquilibmim 
modified  hy  centrifugal  force.  Variation  of  gravity  on  its  surface.  Statical 
and  dynamical  measures  of  gravity.  The  pendulum.  Gravity  to  a  spheroid. 
Other  eflFects  of  tho  Eartli's  rotation.  Trade  winds.  Determination  of  geo- 
graphical positions — of  latitudes — of  longitudes.  Conduct  of  a  trigonometri- 
cal survey.  Of  maps.  Projections  of  the  sphere.  Measurement  of  heights 
by  the  barometer 118 

CIIAl'TER  V. 

OF    UnANOORAPHT. 

Construction  of  celestial  maps  and  globes  by  observations  of  right  ascension  and 
declination.  Celestial  objects  distinguished  into  fixed  and  erratic.  Of  the 
constellations.  Natural  n-gions  in  the  heavens.  The  Milky  AVay.  The  Zo- 
diac. Of  the  ecliptic.  Celestial  latitudes  and  longitudes.  Precession  of  the 
equinoxes.  Nutation.  Aberration.  Refraction.  Parallax.  Summary  view 
of  tho  uranographical  concctions IGl 


CHAPTER  VI. 

^  ,  OF     THE     sun's     MOTION. 

Apparent  motion  of  Ihe  sun  not  uniform.  Its  apparent  diameter  also  variable. 
Variation  of  its  disi  ince  concluded.  Its  apparent  orbit  an  ellipse  about  tho 
focus.  Law  of  the  angular  velocity.  Equable  description  of  areas.  Parallax 
of  the  Sun.  Its  distance  and  magnitude.  Copernican  explanation  of  the 
Sun's  apparent  motion.  Parallelism  of  the  Earth's  axis.  The  seasons.  Hent 
received  from  the  Sun  in  different  parts  of  the  orbit.  Mean  and  true  longi- 
tudes of  the  Sun.  Equation  of  the  centre.  Sidereal,  tropical,  and  anoma- 
listic years.  Physical  constitution  of  the  Sun.  Its  spots.  Faculm.  Probable 
nature  and  cause  of  the  spots.  Atmosphere  of  tho  Sun.  Its  supposed  clouds. 
Temperature  at  its  surface.  Its  expenditure  of  heat.  Terrestrial  effects  of 
solar  radiation 185 


rence. 
ficial  f( 
Climate 
Librati( 


Of  terrcst 
tiles,  ap 
diminut 
accordai 
Density 
Sun  on 


Apparent  i 
their  nai 
Dimensii 
planets, 
tion.  E 
place, 
tune, 
of  the  p 


'1 


Of  the  Mo 
their  pri 
the  prim! 
Kepler's 
eclipses, 
Saturn — 


CHAPTER  VII. 

Of  the  Moon.  Its  sidereal  period.  Its  apparent  diameter.  Its  parallax,  dis- 
tance, and  real  diameter.  First  approximation  to  its  orbit.  An  ellipse  about 
the  Earth  in  the  focus.  Its  excentricity  and  inclination.  Motion  of  its  nodes 
and  apsides.  Of  occultations  and  solar  eclipses  generally.  Limits  within 
which  they  are  possible.  They  prove  the  Moon  to  bo  an  opaque  solid.  Its 
light  derived  from  the  Sun.  Its  phases.  Synodic  revolution  or  lunar  month. 
Of  ecjipses  more  particularly.    Their  phenomena.    Their  periodical  recur- 


Great  numl 
much  gre 
more  thai 
conforma 
return  of 

2 


CONTENTS. 


XIU 


rence.  Physical  constitution  of  tiie  Moon.  Its  mountains  and  other  super- 
ficial features.  Indications  of  former  volcanic  activity.  Its  atmospiiere. 
Climate.  Radiation  of  heat  from  its  surface.  Rotation  on  its  ovrn  axis. 
Libration.     Appearance  of  the  Earth  from  it 213 


CHAPTER  VIII. 

Of  terrestrial  gi'avity.  Of  the  law  of  universal  gravitation.  Paths  of  projec- 
tiles, apparent,  real.  The  Moon  retained  in  her  orbit  by  gravity.  Its  law  of 
diminution.  Laws  of  elliptic  motion.  Orbit  of  the  Earth  round  the  Sun  in 
accordance  with  these  laws.  Masses  of  the  Earth  and  Sun  compared. 
Density  of  the  Sun.  Force  of  gravity  at  its  surface.  Disturbing  eflfect  of  the 
Sun  on  the  Moon's  motion 283 


CHAPTER  IX. 

OFTHESOLARSTSTEM. 

Apparent  motions  of  the  planets.  Their  stations  and  retrogradations.  The  Sun 
their  natural  centre  of  motion.  Inferior  planets.  Their  phases,  periods,  etc. 
Dimensions  and  form  of  their  orbits.  Transits  across  the  Sun.  Superior 
planets.  Their  distances,  periods,  etc.  Kepler's  laws  and  their  interpreta- 
tion. Elliptic  elements  of  a  planet's  orbit.  Its  heliocentric  and  geocentric 
place.  Empirical  law  of  planetary  distances ;  violated  in  the  case  of  Nep- 
tune. The  ultra-zodiacal  planets.  Physical  peculiarities  observable  in  each 
of  the  planets 24!^ 


CHAPTER  X. 

OF    THE    SATELLITES. 

Of  the  Moon,  as  a  satellite  of  the  Earth.  General  proximity  of  satellites  to 
their  primaries,  and  consequent  subordination  of  their  motions.  Masses  of 
U»e  primaries  concluded  from  the  periods  of  their  satellites.  Maintenance  of 
Kepler's  laws  in  the  secondary  systems.  Of  Jupiter's  satellites.  Their 
eclipses,  etc.  Velocity  of  light  discovered  by  their  means.  Satellites  of 
Saturn — of  Uranus — of  Neptune 282 

CHAPTER  XI. 

OF   COMETS.  V 

Great  number  of  recorded  comets.  The  number  of  those  unrecorded  probably 
much  greater.  General  description  of  a  comet.  Comets  without  tails,  or  with 
more  than  one.  Their  extreme  tenuity.  Their  probable  structure.  Motions 
conformable  to  the  law  of  gravity.  Actual  dimensions  of  comets.  Periodical 
return  of  several.  Halley's  comet.  Other  ancient  comets  probably  periodic 
2 


! 

V 

ID 
< 

0 

i 

5 

0 

I 

3 


XIV 


CONTENTS. 


Encke's  comet  —  Biela's — Fnyc's  —  Lcxcirt)  —  De  Vice's — Brorsen's — Peter's. 
Great  comet  of  1848.  Its  probftblo  identity  witii  several  oltler  comets.  Great 
interest  at  present  attaclicd  to  cometury  astronomy,  and  its  reasons.  Ile- 
marlis  on  cometary  orbits  in  general 205 


:  TART  II. 

f        '  • 

OF  THE  rLANETARY   PERTURBATIONS. 
CIIAriEU  XII. 

Subject  propounded.  Problem  of  tliree  bodies.  Superposition  of  small  motions. 
Estimation  of  the  disturbing  force.  Its  geometrical  representation.  Nume- 
rical estimation  in  particular  cases.  Kesolutiou  into  rectangular  components. 
Radial,  transversal,  and  orthogonal  disturbing  forces.  Normal  and  tangential. 
Their  characteristic  effects.  Elfects  of  tl>e  ortliogonal  force.  Motion  of  the 
nodes.  Conditions  of  their  advance  and  recess.  Coses  of  nn  exterior  planet 
disturbed  by  an  interior.  The  reverse  case.  In  every  case  the  node  of  the 
disturbed  orbit  recedes  on  the  plane  of  tlie  disturbing  on  an  average.  Com- 
bined effect  of  many  such  disturbances.  Motion  of  the  Moon's  nodes. 
Cliauge  of  inclination.  Conditions  of  its  increase  and  diminution.  Average 
effect  in  a  whole  revolution.  Compensation  in  a  complete  revolution  of  the 
nodes.  Lagrange's  theorem  of  the  stability  of  the  inclinations  of  the  plane- 
tary orbits.  Change  of  obliquity  of  the  ecliptic.  Precession  of  the  equinoxes 
explained.     Nutation.     Principle  of  forced  vibrations 326 

CHAPTER  XIII. 

THEORY  OF   THE   AXES,    PERIHELIA,    AND   EXCENTRICITIES. 

Variation  of  elements  in  general.  Distinction  between  periodic  and  secular 
variations.  Geometrical  expression  of  tangential  and  normal  forces.  Varia- 
tion of  the  M.ijor  Axis  produced  only  by  the  tangential  force.  Lagrange's 
theorem  of  the  conservation  of  the  mean  distances  and  periods.  Theory  of 
the  Perihelia  and  Excentricities.  Geometrical  representation  of  their  mo- 
mentary variations.  Estimation  of  the  disturbing  forces  in  nearly  circular 
orbits.  Application  to  the  case  of  the  Moon.  Theory  of  the  lunar  apsides 
and  excentricity.  Experimental  illustration.  Application  of  the  foregoing 
principles  to  the  jilanetary  theory.  Compensation  in  orbits  very  nearly  cir- 
cular. Effects  of  ellipticity.  General  results.  Lagrange's  theorem  of  the 
stability  of  the  excentricities  354 


CHAPTER  XIV. 

Of  the  inequalities  independent  of  the  excentricities.     The  Moon's  variation  and 
parallactic  inequality.     Analogous  planetary  inequalities.     Three  oases  of 


Variable 
their 
Ancient 
classific 
each  ot 
Elemeni 
double 
Proper 
Situatio 
giving 
motion 
of  the 
and  abe 
of  a  bin 


CONTENTS. 


tf 


s— Peter's, 
jts.  Great 
sons.  Re- 
295 


lall  motions, 
on.     Nume- 
componcnts. 
[1  tangential, 
lotion  of  the 
terior  planet 
node  of  the 
rage.     Cora- 
oon's  nodes. 
)n.     Average 
ilution  of  the 
jf  the  plane- 
he  equinoxes 
326 


and  secular 

irces.     Varia- 

Lagrange's 

.     Theory  of 

of  their  mo- 
early  circular 
lunar  apsides 
the  foregoing 
iry  nearly  cir- 
icorem  of  the 
364 


;  variation  and 
hree  oases  of 


planetary  perturbation  distinguished.  Of  inequalities  dependent  on  the  exccn- 
tricities.  Long  inequality  of  Jupiter  and  Saturn.  Law  of  reciprocity  between 
the  periodical  variations  of  tlio  clfnicnts  of  both  planets.  Long  inequality  of 
the  Earth  and  Venus.  Variation  of  the  epoch.  Inequalities  incident  on  the 
epoch  affecting  tlie  mean  motion.  Interpretation  of  the  constant  part  of  these 
inequalities.  Annual  equation  of  the  Moon.  Her  secular  acceleration.  Lunar 
inequalities  due  to  the  action  of  Venus.  Effect  of  the  spheroidal  figure  of  the 
Earth  and  other  planets  on  the  motions  of  their  satellites.  Of  the  tides. 
Masses  of  disturbing  bodies  deducible  from  the  perturbations  they  produce. 
Mass  of  the  Moon,  and  of  Jupiter's  satellites,  how  ascertained.  Perturbations 
of  Uranus  resulting  in  the  discovery  of  Neptune 887 

PART  III. 

OP   SIDEREAL   ASTRONOMY. 

CHAPTER  XV. 

Of  the  fixed  stars.  Their  classification  by  magnitudes.  Photometric  scale  of 
magnitudes.  Conventional  or  vulgar  scale.  Photometric  comparison  of  stars. 
Distribution  of  stars  over  the  heavens.  Of  the  Milky  Way  or  galaxy.  Its 
Bupposod  form  that  of  a  flat  stratum  partially  subdivided.  Its  visible  course 
among  the  constellations.  Its  internal  structure.  Its  apparently  indefinite 
extent  in  certain  directions.  Of  the  distance  of  the  fixed  stars.  Their 
annual  parallax.  Parallactic  unit  of  sidereal  distance.  Eflfect  of  parallax 
analogous  to  that  of  aberration.  How  distinguished  from  it.  Detection  of 
parallax  by  meridional  observations.  Henderson's  application  to  o  Centauri. 
Dy  differential  observations.  Discoveries  of  Bessel  and  Struve.  List  of  stars 
in  which  parallax  has  been  detected.  Of  the  real  magnitudes  of  the  stars. 
Comparison  of  their  lights  with  that  of  the  Sun 439 

CHAPTER  XVL 

Variable  and  periodical  stars.  List  of  those  already  known.  Irregularities  in 
their  periods  and  lustre  when  brightest.  Irregular  and  temporary  stars. 
Ancient  Chinese  records  of  several.  Missing  stars.  Double  stars.  Their 
classification.  Specimens  of  each  class.  Binary  systems.  Revolution  round 
each  other.  Describe  elliptic  orbits  under  the  Newtonian  law  of  gravity. 
Elements  of  orbits  of  several.  Actual  dimensions  of  their  orbits.  Coloured 
double  stars.  Phoonomenon  of  complementary  colours.  Sanguine  stars. 
Proper  motion  of  the  stars.  Partly  accounted  for  by  a  real  motion  of  the  Sun. 
Situation  of  the  solar  apex.  Agreement  of  southern  and  northern  stars  in 
giving  the  same  result.  Principles  on  which  the  investigation  of  the  solar 
motion  depends.  Absolute  velocity  of  the  Sun's  motion.  Supposed  revolution 
of  the  whole  sidereal  system  round  a  common  centre.  Systematic  parallax 
and  aberration.  Effect  of  the  motion  of  light  in  altering  the  apparent  period 
of  a  binary  star  4G7 


\ 

'i 


\ 


5 


f 


XVI 


CONTENTS. 


CIIAriER  XVII. 


i, 


OF  CLUSTERS   OF   BTAItS   AND   NEnUI..!!. 

Of  clustering  groups  of  stars.  Globular  clusters.  Their  stability  dynntnically 
possible.  List  of  the  most  rctnnrknble.  Cliissifiention  of  nebulu)  and  clusters. 
Their  distribution  over  tlio  heavens.  Irregular  clusters,  llesolvnbility  of 
nebuliD.  Theory  of  the  formation  of  clusters  by  nebulous  subsidence.  Of 
elliptic  nebuhc.  That  of  Andromeda.  Annular  and  planetary  nebulio. 
Double  nebulic.  Nebulous  stars.  Connection  of  nobuho  with  double  stars. 
Insulated  ncbulie  of  forms  not  wholly  irregular.  Of  amorphous  ncbulio. 
Their  law  of  distribution  nmrks  them  as  outliers  of  the  galaxy.  Nebnliu  and 
nebulous  group  of  Orion — of  Argo — of  Sagittarius — of  Cygnus,  The  Magel- 
lanic clouds.  Singular  nebula  in  the  greater  of  them.  The  zodiacal  light. 
Shooting  stars 4'J8 


I'M 


f-. 


V^ 


it 


-     PART  IV. 

OP    THE    ACCOUNT    OF    TIME. 

CHAPTER  XVIII. 

Natural  imits  of  time.  Relation  of  the  sidereal  to  the  solar  day  affected  by 
precession.  Incommensurability  of  the  day  and  year.  Its  inconvenience. 
How  obviated.  The  Julian  Calendar.  Irregularities  at  its  first  introduction. 
Reformed  by  Augustus.  Gregorian  reformation.  Solar  and  lunar  cycles. 
Indiction.  Julian  period.  Table  of  chronological  eras.  Rules  for  calculating 
the  days  elapsed  between  given  dates.     Equinoctial  time G-3 

APPENDIX. 

I.  Lists  of  Northern  and  Southern  Stars,  with  their  approximate  Magni- 
tudes, on  the  Vulgar  and  Photometric  Scales 541 

II.  Synoptic  Table  of  the  Elements  of  the  Planetary  System 543 

III.  Synoptic  Table  of  the  Elements  of  the  Orbits  of  the  Satellites,  so  far 

as  they  are  known  645 

IV.  Elements  of  Periodical  Comets  at  their  last  appearance 548 

Index 549 


/ 


(1.)  E\ 
at  a  somo^ 
much  to  le 
are  far  fror 
those  conn^ 
which  com 
reason  to  i 
constitute  i 
apprehendc 
osoaped  his 
only  so,  bu 
the  genera 
for  the  cou 
crude  and 
thing  of  ai 
conclusion 
logical  argi 
may  have 
tion,  on  th( 
of  that  inU 
of  all  scien 
mental  pui 
moral  beai 
rue"  with 
contemplat 
2 


OUTLINES 


or 


I* 


ASTEONOMY. 


'WN»X"V>^;'\^/^^^^^^^V 


INTRODUCTION. 


(1.)  Every  student  who  enters  upon  a  scientific  pursuit,  especially  if 
at  a  somewhat  advanced  period  of  life,  will  find  not  only  that  he  has 
much  to  learn,  but  much  also  to  unlearn.  Familiar  objects  and  events 
are  far  from  presenting  themselves  to  our  senses  in  that  aspect  and  with 
those  connections  under  which  science  requires  them  to  be  viewed,  and 
which  constitute  their  rational  explanation.  There  is,  therefore,  every 
reason  to  expect  that  those  objects  and  relations  which,  taken  together, 
constitute  the  subject  he  is  about  to  enter  upon  will  have  been  previously 
apprehended  by  him,  at  least  imperfectly,  because  much  has  hitherto 
escaped  his  notice  which  is  essential  to  its  right  understanding :  and  not 
only  so,  but  too  often  also  erroneously,  owing  to  mistaken  antdogies,  and 
the  general  prevalence  of  vulgar  errors.  As  a  first  preparation,  therefore, 
for  the  course  he  is  about  to  commence,  he  must  loosen  his  hold  on  all 
crude  and  hastily  adopted  notions,  and  must  strengthen  himself,  by  some- 
thing of  an  efibrt  and  a  resolve,  for  the  unprejudiced  admission  of  any 
conclusion  which  shall  appear  to  be  supported  by  careful  observation  and 
logical  argument,  even  should  it  prove  of  a  nature  adverse  to  notions  he 
may  have  previously  formed  for  himself,  or  taken  up,  without  examina- 
tion, on  the  credit  of  others.  Such  an  effort  is,  in  fact,  a  commencement 
of  that  intellectual  discipline  which  forms  one  of  the  most  important  ends 
of  all  science.  It  is  the  first  movement  of  approach  toward<«  that  state  of 
mental  purity  which  alone  can  fit  us  for  a  full  and  steady  perception  of 
moral  beauty  as  well  as  physical  adaptation.  It  is  the  "  euphrasy  and 
rue"  with  which  we  must  "  purge  our  sight"  before  we  can  receive  and 
contemplate  as  they  are  the  lineaments  of  truth  and  nature. 

2  (17) 


! 

I 
III 

3 


0 

s 

I 

0 
0 


\ 


5 


18 


OUTLINES   OF   ASTRONOMY. 


'1; 


i 


II 


(2.)  There  is  no  science  whicli,  more  than  nstroiioniy,  stiuulu  in  need 
of  sucli  a  preparation,  or  drawa  more  largcily  on  that  intellectual  'iloraliiy 
which  is  ready  to  adopt  whatever  is  demonstrated,  or  concede  wliutever  is 
rendered  highly  probable,  however  new  and  uneonnnon  the  points  of  view 
may  bo  in  which  objects  the  most  familiar  may  thereby  become  placed. 
Almost  all  its  conclusions  stand  in  open  and  striking  contradiction  with 
those  of  superficial  and  vulgar  observation,  and  with  what  appears  to 
every  one,  until  ho  has  understood  and  weighed  the  proofs  to  Iho  con- 
trary, the  most  positive  evidence  of  his  senses.  Thus,  the  earth  on  which 
bo  stands,  and  which  has  served  for  ages  as  the  unshaken  foundation  of 
tho  firmest  structures,  either  of  art  or  nature,  is  divested  by  th(  astn 
Domer  of  its  attribute  of  fixity,  and  conceived  by  him  as  turning  swiin) 
on  its  centre,  and  at  tho  samo  time  moving  onwards  through  .pace  with 
great  rapidity.  Tho  sun  and  the  moon,  which  appear  to  uTitaught  eyes 
round  bodies  of  no  very  eonsiderablo  size,  becomo  enlarged  iu  his  imagi- 
nation into  vast  globes,  —  the  one  approaching  in  magnitude  to  tho  earth 
itself,  the  other  immensely  surpassing  it.  The  planets,  which  a}>pcar 
only  as  stars  somewhat  brighter  than  the  rest,  are  to  him  spacious,  elabo- 
rate, and  habitable  worlds ;  several  of  them  much  greater  and  far  more 
curiously  furnished  than  the  oarth  ho  inhabits,  as  there  are  also  others 
less  so;  and  the  stars  them.sdves,  properly  so  culled,  which  to  ordinary 
apprehension  present  only  luuid  sparks  or  brilliant  atoms,  are  to  bim  suns 
of  various  and  transcendent  glory  —  effulgent  centres  of  life  and  light  to 
myriads  of  unseen  worlds.  So  that  when,  after  dilating  his  thoughts  to 
comprehend  the  gi'andeur  of  those  ideas  his  calculations  have  called  up, 
and  exhausting  his  imagination  and  the  powers  of  his  language  to  devise 
similes  and  metaphors  illustrative  of  the  immensity  of  the  scale  on  which 
his  universe  is  constructed,  he  shrinks  back  to  his  native  sphere ;  he  finds 
It,  in  comparison,  a  mere  point ;  so  lost  —  even  in  tho  minute  system  to 
which  it  belongs  —  as  to  be  invisible  and  unsusp  .teJ  I'on-  some  of  its 
principal  and  remoter  member.- . 

(3.)  There  is  hardly  any  thing  which  sets  in  a  ihoiigar  iight  the  inhe- 
rent power  of  truth  over  the  mind  of  man,  when  opposed  by  no  motives 
of  fnterest  or  passion,  than  the  perfect  readiness  with  which  all  these  con- 
clusions are  assented  to  as  soon  as  their  evidence  is  clearly  apprehended, 
and  t'.<5  tenacious  h^ld  they  acquire  over  our  belief  when  once  admitted. 
In  thii  tu!"1uc\  therefor",  of  this  volume,  I  shall  take  it  for  granted  that 
the  rcador  in  more  desirous  to  Ic  rn  the  system  which  it  is  its  object  to 
teucb  as  it  now  stands,  than  to  raise  or  revive  objections  against  it;  and 
that,  in  short,  he  comes  to  the  task  with  a  willing  mind ;  an  assumption 
which  will  not  only  save  the  trouble  of  piling  argument  on  argument  to 


convince 
much  as 
tho  outsi 
aside,  iuv 
only  torn 

(4.)T 
stri.  ily  tl; 
L^.K,  .  it 
po:aiiion. 
u."K  r  the 
are  all  tlu 
The  mode 
tho  ucccss 
copious  in 
churacter 
eligible, 
in  astrouoi 
advanced 
our  statem 
cither  in  c 
slow  and  ii 
advantagec 
on  him  a 
phenomeni 
then,  rejec 
our  objects 
Writing  oi 
in  as  little 
comm  unlet 
aft' ctation. 

(5.)  W^ 
of  the  woi 
affords  of  i 
student  wi 
stration  or 
tant  remai 
sustinente 

'  "  The  c 
which,  like 
coherent  wl 
inductions. 


i^} 


INTROIHTTIUN. 


19 


h  in  nood 
'  'iboraliiy 
luitovcr  is 
ita  of  view 
110  phictid. 
ction  with 
[tppcura  to 
)  Iho  con- 
1  on  which 
ndution  of 
th(   astit 
irig  swill  1) 
sjaco  with 
aught  eyes 
hia  iinngi- 
Q  the  earth 
ich  a]>pc!ir 
,ou.s,  elabo- 
i  fur  moro 
also  others 
|o  ordinary 
lim  suns 
light  to 
loughts  to 
called  up, 
to  devise 
on  which 
he  finds 
system  to 
imo  of  its 

the  inhe- 
inotives 
these  con- 
rchcnded, 
admitted, 
nted  that 
object  to 
t  it ;  and 
sumption 
ament  to 


convince  the  sceptical,  but  will  ^'n  ally  facilif-'^  his  actual  progress;  inas- 
much us  ho  will  find  it  at  onco  casKi  and  moro  ^itistiictiTy  to  i>ursuo  from 
tho  outset  a  straight  and  dcfinito  path,  than  to  bo  constautty  stepping 
aside,  involving  himself  in  perplexities  and  circuits,  which,  after  all,  cati 
only  terminate  m  finding  himself  compelled  to  adopt  tho  same  road. 

(4.)  Tho  method,  therefore,  we  propose  to  follow  in  this  work  is  neither 
strit  ily  the  analytic  nor  tho  synthetic,  but  rather  such  a  combinatio^a  of 
IritJi,  ,  it.    » leaning  to  tho  latter,  as  may  best  suit  with  a  didactu  om- 
posiiion.     Its  object  is  not  to  convince  or  refute  opponents,  nor  to  inquire, 
u  .'K  r  the  semblance  of  an  assumed  ignorance,  for  principles  of  which  we 
arc  all  tho  timo  in  full  possession  —  but  simply  to  teach  what  is  known. 
The  moderate  limit  of  a  single  volume,  to  which  it  will  be  confined,  and 
tho  necessity  of  being  on  every  point,  within  that  limit,  rather  difi'u.so  and 
copious  in  explanation,  as  well  as  the  eminently  matured  and  ascert  mcd 
character  of  tho  science  itself,  render  this  course  both  practicabk   and 
eligible.    Practicable,  because  there  is  now  no  danger  of  any  rovolu'ion 
in  astronomy,  like  those  which  are  daily  changing  the  features  of  tho  .  ess 
advanced  sciences,  supervening,  to  destroy  all  our  hypotheses,  and  thiow 
our  statements  into  confusion.     Eligible,  because  the  space  to  be  bestowed, 
cither  in  combating  refuted  systems,  or  in  leading  tho  reader  forward  by 
slow  and  measured  steps  from  the  known  to  the  unknown,  may  be  more 
advantageously  devoted  to  such  explanatory  illustrations  as  will  impress 
on  him  a  familiar  and,  as  it  were,  u  practical  sense  of  tho  sequence  of 
phenomena,  and  the  manner  in  which  they  are  produced.     We  shall  not, 
then,  reject  tho  analytic  course  where  it  leads  moro  easily  and  directly  to 
our  objects,  or  in  any  way  fetter  ourselves  by  a  rigid  adherence  to  method. 
Writing  only  to  be  understood,  and  to  communicate  as  much  information 
in  as  little  space  as  possible,  consistently  with  its  distinct  and  effectual 
communication,  no  sacrifice  can  be  afforded  to  system,  to  form,  or  to 
aft.  ctation. 

(5.)  We  shall  take  for  granted,  from  tho  outset,  the  Copernican  system 
of  the  world;  relying  on  the  easy,  obvious,  and  natural  explanation  it 
affords  of  all  the  phenomena  as  they  come  to  be  described,  to  impress  the 
student  with  a  sense  ttf  its  truth,  without  either  the  formality  of  demon- 
stration or  the  superfluous  tedium  of  eulogy,  calling  to  mind  that  impor- 
tant remark  of  Bacon  :  —  "  Theoriarum  vires,  areta  et  quasi  so  mutuo 
sustinente  paruum  adaptationc,  qua  quasi  in  orbem  cohaerent,  firman tur'j" 

'  "  The  confirmation  of  theories  relies  on  the  compact  adaptation  of  their  parts,  by 
which,  liite  those  of  an  arch  or  dome  they  mutually  sustain  each  other,  and  form  a 
coherent  whole."  This  is  what  Dr.  Whewell  exprussively  terms  the  contilienee  of 
inductions. 


e 

in 

5 

< 

0 

i 
E 

0 

C 


20 


OUTLINES   OF   ASTRONOMY. 


not  failing,  however,  to  point  out  to  the  reader,  as  occasion  offers,  the 
contrast  which  its  superior  simplicity  offers  to  the  complication  of  other 
hypotheses. 

(6.)  The  preliminary  knowledge  which  it  is  desirable  that  the  student 
should  possess,  in  order  for  the  more  advantageous  perusal  of  the  following 
pages,  consists  in  the  familiar  practice  of  decimal  and  sexagesimal  arith- 
metic; some  moderate  acquaintance  with  geometry  and  trigonometry, 
both  plane  and  spherical ;  the  elementary  principles  of  mechanics ;  and 
enough  of  optics  to  understand  the  construction  and  use  of  the  telescope, 
and  some  other  of  the  simpler  instruments.  Of  course,  the  more  of  such 
knowledge  he  brings  to  the  perusal,  the  easier  will  be  his  progress,  and 
the  more  co^nplete  the  information  gained;  but  we  shall  endeavour  in 
every  case,  as  far  as  it  can  be  done  without  a  sacrifice  of  clearness,  and  of 
that  useful  brevity  which  consists  in  the  absence  of  prolixity  and  epi- 
sode, to  render  what  we  have  to  say  as  independent  of  other  books  as 
possible. 

(7.)  After  all,  I  must  distinctly  caution  such  of  my  readers  as  may 
commence  and  terminate  their  astronomical  studies  with  the  present  work 
(though  of  such,  —  at  least  in  the  latter  predicament,  —  I  trust  the  num- 
ber will  be  few),  that  its  utmost  pretension  is  to  place  them  on  the 
threshold  of  this  particular  wing  of  the  temple  of  Science,  or  rather  on 
an  eminence  exterior  to  it,  whence  they  may  obtain  something  like  a 
general  notion  of  its  structure ;  or,  at  most,  to  give  those  who  may  wish 
to  enter  a  ground-plan  of  its  accesses,  and  put  them  in  possession  of  the 
pass-word.  Admission  to  its  sanctuary,  and  to  the  privileges  and  feelings 
of  a  votary,  is  only  to  be  gained  by  one  means,  —  sound  and  sufficient 
knoidedge  of  mathematics,  Ihe  great  instrument  of  all  exact  inquiry, 
without  which  no  man  can  ever  make  such  advances  in  this  or  any  other 
of  the  higher  departments  of  science  as  can  entitle  him  to  form  an  inde- 
pendent opinion  on  any  subject  of  discussion  within  their  range.  It  is 
not  without  an  effort  that  those  who  possess  this  knowledge  can  commu- 
nicate on  such  subjects  with  those  who  do  not,  and  adapt  their  language 
and  their  illustrations  to  the  necessities  of  such  an  intercourse.  Proposi- 
tions which  to  the  one  are  almost  identical,  are  theorems  of  import  and 
difficulty  to  the  other ;  nor  is  their  evidence  presented  in  the  same  way  to 
the  mind  of  each.  In  teaching  such  propositions,  under  such  circum- 
stances, the  appeal  has  to  be  made,  not  to  the  pure  and  abstract  reason, 
but  to  the  sense  of  analogy  —  to  practice  and  experience  :  principles  and 
modes  of  action  have  to  be  established  not  by  direct  argument  from 
acknowledged  axioms,  but  by  continually  recurring  to  the  sources  from 
which  the  axioms  themselves  have  been  drawn ;  viz.  examples ;  that  is  to 


say,  by  bri 
which  the 
place :  thu 
tion,  and  ( 
exigencies, 
traversed  c 
way;  that 
understood 
tion,  or  a  d 
plex  cases 
own  end  b^ 
which  I  sh 
(8.)  On 
road  of  mo 
ble  of  it,  ar 
by  the  way 
that  those 
knowledge 
incompatibl 
account  in 
present  anj 
different  li^ 
to  strike  n 
because  no 
their  notio 
happen,  th: 
placed  not 
satisfactory 
some  inwai 
may  lead 
unknown  I 
the  preseni 
selected  fro 
the  author' 
which,  of  c 
them  beyoi 
(0.)  Besi 
with  which 
data  are  be 
problems  a 
||  bis  lines  m 


INTRODUCTION. 


21 


offers,  the 
n  of  other 

he  student 
e  following 
imal  arith- 
jonometry, 
anics;  and 
I  telescope, 
3re  of  such 
ogress,  and 
deavour  in 
ess,  and  of 
ty  and  epi- 
r  books  as 

srs  as  may 
resent  vrork 
3t  the  num- 
icm  on  the 
^r  rather  on 
ping  like  a 
0  may  wish 
ision  of  the 
md  feelings 
d  sufficient 
ict  inquiry, 
r  any  other 
rm  an  inde- 
re.     It  is 
jan  commu- 
lir  language 
Proposi- 
import  and 
amo  way  to 
ich  circum- 
ract  reason, 
nciples  and 
iraent  from 
Durces  from 
that  is  to 


say,  by  bringing  forward  and  dwelling  on  simple  and  familiar  instances  in 
which  the  same  principles  and  the  same  or  similar  modes  of  action  take 
place :  thus  erecting,  as  it  were,  in  each  particular  case,  a  separate  induc- 
tion, and  constructing  at  each  step  a  little  body  of  science  to  meet  its 
exigencies.  The  difference  is  that  of  pioneering  a  road  through  an  un- 
traversed  country  and  advancing  at  case  along  a  broad  and  beaten  high- 
way ;  that  is  to  say,  if  we  are  determined  to  make  ourselves  distinctly 
understood,  and  will  appeal  to  reason  at  all.  As  for  the  method  of  asser- 
tion, or  a  direct  demand  on  the  faith  of  the  student  (though  in  some  com- 
plex cases  indispensable,  where  illustrative  explanation  would  defeat  its 
own  end  by  becoming  tedious  and  burdensome  to  both  parties),  it  is  one 
which  I  shall  neither  willingly  adopt  nor  would  recommend  to  others. 

(8.)  On  the  other  hand,  although  it  is  something  new  to  abandon  the 
road  of  mathematical  demonstration  in  the  treatment  of  subjects  suscepti- 
ble of  it,  and  to  teach  any  considerable  branch  of  science  entirely  or  chiefly 
by  the  way  of  illustration  and  familiar  parallels,  it  is  yet  not  impossible 
that  those  who  are  already  well  acquainted  with  our  subject,  and  whose 
knowledge  has  been  acquired  by  that  confessedly  higher  practice  which  is 
incompatible  with  the  avowed  objects  of  the  present  work,  may  yet  find  their 
account  in  its  perusal,  —  for  this  reason,  that  it  is  always  of  advantage  to 
present  any  given  body  of  knowledge  to  the  mind  in  as  great  a  variety  of 
different  lights  as  possible.  It  is  a  property  of  illustrations  of  this  kind 
to  strike  no  two  minds  in  the  same  manner,  or  with  the  same  force; 
because  no  two  minds  are  stored  with  the  same  images,  or  have  acquired 
their  notions  of  them  by  similar  liubits.  Accordingly,  it  may  very  well 
happen,  that  a  proposition,  even  to  one  best  acquainted  with  it,  may  be 
placed  not  merely  in  a  new  and  uncommon,  but  in  a  more  impressive  and 
satisfactory  light  by  such  a  course  —  some  obscurity  may  be  dissipated, 
some  inward  misgivings  cleared  up,  or  even  some  links  supplied  which 
may  lead  to  the  perception  of  connections  and  deductions  altogether 
unknown  before.  And  the  probability  of  this  is  increased  when,  as  in 
the  present  instance,  the  illustrations  chosen  have  not  been  studiously 
selected  from  books,  but  are  such  as  have  presented  themselves  freely  to 
the  author's  mind  as  being  most  in  harmony  with  his  own  views ;  by 
which,  of  course,  he  means  to  lay  no  claim  to  originality  in  all  or  any  of 
them  beyond  what  they  may  really  possess. 

(0.)  Besides,  there  are  cases  in  the  application  of  mechanical  principles 

with  which  the  mathematical  student  is  but  too  familiar,  where,  when  the 

data  arc  before  him,  and  the  numerical  and  geometrical  relations  of  his 

problems  all  clear  to  his  conception, — when  his  forces  are  estimated  and 

i]  his  lines  measured,  —  nay,  when  even  he  has  followed  up  the  application 


fX 


V 

3 
< 

i 


S 


C 

9 

I 

i 


/ 


OUTLINES   OF   ASTRONOMY. 


I 


Klil-i 


t    « 


of  his  technical  processes,  and  fairly  arrived  at  his  conclusion,  —  there  is 
still  something  wanting  in  his  mind  —  not  in  the  evidence,  for  he  has 
examined  each  link,  and  finds  the  chain  complete  —  not  in  the  principleSj 
for  those  ho  well  knows  are  too  firmly  established  to  be  shaken  —  but  pre- 
cisely in  the  mode  of  action.  He  has  followed  out  a  train  of  reasoning 
by  logical  and  technical  rules,  but  the  signs  he  has  employed  are  not 
pictures  of  nature,  or  have  lost  their  original  meaning  as  such  to  his 
mind :  he  has  not  seen,  as  it  were,  the  process  of  nature  passing  under 
his  eye  in  an  instant  of  time,  and  presented  as  a  consecutive  whole  to  his 
imagination.  A  familiar  parallel,  or  an  illustration  drawn  from  some 
artificial  or  natural  process,  of  which  he  has  that  direct  and  individual 
impression  which  gives  it  a  reality  and  associates  it  with  a  name,  will,  in 
almost  every  such  case,  supply  in  a  moment  this  deficient  feature,  will 
convert  all  his  symbols  into  real  pictures,  and  infuse  an  animated  meaning 
into  what  was  before  a  lifeless  succession  of  words  and  signs.  I  cannot, 
indeed,  always  promise  myself  to  attain  this  degree  of  vividness  of  illus- 
tration, nor  are  the  points  to  be  elucidated  themselves  always  capable  of 
being  so  paraphrased  (if  I  may  use  the  expression)  by  any  single  in- 
stance adducible  in  the  ordinary  course  of  experience ;  but  the  object  will 
at  least  be  kept  in  view ;  and,  as  I  am  very  conscious  of  having,  in  making 
such  attempts,  gained  for  myself  much  clearer  views  of  several  of  the 
more  concealed  efifects  of  planetary  perturbation  than  I  had  acquired  by 
their  mathematical  investigation  in  detail,  it  may  reasonably  be  hoped 
that  the  endeavour  will  not  always  be  unattended  with  a  similar  success 
in  others. 

(10.)  From  what  has  been  said,  it  will  be  evident  that  our  aim  is  not 
to  ofler  to  the  public  a  technical  treatise,  in  which  the  student  of  practical 
or  theoretical  astronomy  shall  find  consigned  the  minute  description  of 
methods  of  observation,  or  the  formulae  he  requires  prepared  to  his  hand, 
or  their  demonstrations  drawn  out  in  detail.  In  all  these  the  present 
work  will  be  found  meagre,  and  quite  inadequate  to  his  wants.  Its  aim 
ie  entirely  difierent;  being  to  present  in  each  case  the  mere  ultimate 
rationale  of  facts,  arguments,  and  processes ;  and,  in  all  cases  of  mathe- 
matical application,  avoiding  whatever  would  tend  to  encumber  its  pages 
with  algebraic  or  geometrical  symbols,  to  place  under  his  inspection  that 
central  thread  of  common  sense  on  which  the  pearls  of  analytical  research 
are  invariably  strung;  but  which,  by  the  attention  the  latter  claim  for 
themselves,  is  often  concealed  from  the  eye  of  the  gazer,  and  not  always 
disposed  in  the  straightest  and  most  convenient  form  to  follow  by  those 
who  string  them.  This  is  no  fault  of  those  who  have  conducted  the 
inquiries  to  which  we  allude.     The  contention  of  mind  for  which  they  call 


13  enormoi 
little  can  1 
sion,  by  m 
to  pay  moi 
success,  - 
those  whic 
reason,  - 
which  is  o 
still  more 
atmosphen 
render  goo 
in  our  pov 
tored  com 
attain. 


INTRODUCTION. 


23 


-  there  is 
)r  he  has 
•rinciples, 

-  but  pre- 
reasoning 
i  are  not 
ch  to  his 
ng  under 
olc  to  his 
•om  some 
individual 
B,  will,  in 
Lture,  wil) 
i  meaning 
I  cannot, 
3  of  illus- 
apahle  of 
single  in- 
>bject  will 
n  making 
al  of  the 
luired  by 
}e  hoped 
ir  success 

im  is  not 
practical 
iption  of 
his  hand, 
5  present 

Its  aim 

ultimate 

if  mathe- 

its  pages 

!tion  that 

research 
jlaim  for 
)t  always 
by  those 
icted  the 
they  call 


is  enormous;  and  it  may,  perhaps,  be  owing  to  their  experience  of  how 
little  can  be  accomplished  in  carrying  such  processes  on  to  their  conclu- 
sion, by  mere  ordinary  clearness  of  liead ;  and  how  necessary  it  often  is 
to  pay  more  attention  to  the  purely  mathematical  conditions  which  ensure 
success,  —  the  hooks-and-eyes  of  their  equations  and  series,  —  than  to 
those  which  enchain  causes  with  their  effects,  and  both  with  the  human 
reason,  —  that  we  must  attribute  something  of  that  indistinctness  of  view 
which  is  often  complained  of  as  a  grievance  by  the  earnest  student,  and 
still  more  commonly  ascribed  ironically  to  the  native  cloudiness  of  an 
atmosphere  too  sublime  for  vulgar  comprehension.  We  think  we  shall 
render  good  service  to  both  classes  of  readers,  by  dissipating,  so  far  as  lies 
in  our  power,  that  accidental  obscurity,  and  by  showing  ordinary  untu- 
tored comprehension  clearly  what  it  can,  and  what  it  cannot,  hope  to 
attain.  .  .  ,    . 


I 
f 


5 


g 

•■i 

s 

I 

0 
0 

s 


2 


,   Sis.  ...r  -       -i 


24 


OUTLINES  OF  ASTRONOMY. 


i*"  : 


CHAPTER  I. 

GENERAL  NOTIONS. — APPARENT  AND  REAL  MOTIONS.  —  SHAPE  AND 
SIZE  OP  THE  EARTH.  —  THE  HORIZON  AND  ITS  DIP.  —  THE  ATMO- 
SPHERE. —  REFRACTION.  —  TWILIGHT.  —  APPEARANCES  RESULTING 
FROM  DIURNAL  MOTION.  —  FROM  CHANGE  OP  STATION  IN  GENERAL. 
—  PARALLACTIC  MOTIONS.  —  TERRESTRIAL  PARALLAX. — THAT  OP 
THE  STARS  INSENSIBLE.  —  FIRST  STEP  TOWARDS  FORMING  AN  IDEA 
OF  THE  DISTANCE  OF  THE  STARS. — COPERNICAN  VIEW  OF  THE 
earth's  MOTION. — RELATIVE  MOTION. — MOTIONS  PARTLY  REAL, 
PARTLY  APPARENT.— GEOCENTRIC  ASTRONOMY,  OR  IDEAL  REFERENCE 
OF  PHENOMENA  TO  THE  EARTH's  CENTRE  AS  A  COMMON  CONVEN- 
TIONAL  STATION. 

m 

(11.)  The  magDitudes,  distances,  arrangement,  and  motions  of  the 
great  bodies  which  make  up  the  visible  universe,  their  constitution  and 
physical  condition,  so  far  as  they  can  be  known  to  us,  with  their  mutuj^l 
influences  and  actions  on  each  other,  so  far  as  they  can  be  traced  by  t  j 
effects  produced,  and  established  by  legitimate  reasoning,  form  the  assem- 
blage of  objects  to  which  the  intention  of  the  astronomer  is  directed. 
The  term  astronomy'  itself,  which  denotes  the  law  or  rule  of  the  aslra  (by 
which  the  ancients  understood  not  only  the  stars  properly  so  called,  but 
the  sun,  the  moon,  and  all  the  visible  constituents  o^  the  heavens),  suffi- 
ciently indicates  this )  and,  although  the  term  astrology,  which  denotes  the 
reason,  theortf^  or  interpretation  of  the  stars,*  has  become  degraded  in  its 
application,  and  confined  to  superstitious  and  delusive  attempts  to  divine 
future  events  by  their  dependence  on  pretended  planetary  influences,  the 
same  meaning  originally  attached  itself  to  that  epithet. 

(12.)  But,  besides  the  stars  and  other  celestial  bodies,  the  earth  itself, 
regarded  as  an  individual  body,  is  one  principal  object  of  the  astronomer's 
consideration,  and  indeed,  the  chief  of  all.     It  derives  its  importance,  in 

*  Aorrip,  a  Star  ;  vonof,  a  law  ;  or  ve/iccv,  to  tend,  as  a  shepherd,  his  flock ;  so  that 
avrpovu/io;  means  "  shepherd  of  the  stars."  The  two  two  etymologies  are,  however, 
coincident, 

'  Aoyof,  reason,  or  a  word,  the  vehicle  of  reason ;  the  interpreter  of  thought. 


a  practical : 
its  relation 
our  wants,  1 
only  one  an 
determinate 
situation,  or 

(13.)  To 
astronomy, 
heavenly  bo 
apparently  s 
ent  than  th( 
stars  ?    Tht 
brilliant, 
tinual  chan^ 
night,  or  at 
or  two  of  th 
community 
movements 
cepted  the  p 
is  going  on  i 
ventions,  ast 
must  be  lim 
attempt  to  a 
to  a  certain 
sequence,  an 
get  rid  of  t 
knowledge  o 
effort  toward 
familiarize  h 
but  a  great  e 
tations  and  i 

(14.)  It  i 
in  space,  of 
but  of  whicl 
ing  their  ev( 
instance,  wh 
station  from 
immediately 
if  BO,  of  wh 
of  objects,  a 
will  of  couri 


GENERAL  NOTIONS. 


a  practical  as  well  as  theoretical  sense,  not  only  from  its  proximity,  and 
its  relation  to  us  as  animated  beings,  who  draw  from  it  the  supply  of  all 
our  wants,  but  as  the  station  from  which  we  see  all  the  rest,  and  as  the 
only  one  among  them  to  which  we  can,  in  the  first  instance,  refer  for  any 
determinate  mark  ^  and  measures  by  which  to  recognize  their  changes  of 
situation,  or  with  which  to  compare  their  distances. 

(13.)  To  the  reader  who  now  for  the  first  time  takes  up  a  book  on 
astronomy,  it  will  no  doubt  seem  strange  to  class  the  earth  with  the 
heavenly  bodies,  and  to  assume  any  community  of  nature  among  things 
apparently  so  different.  For  what,  in  fact,  can  be  more  apparently  differ- 
ent than  the  vast  and  seemingly  immeasurable  extent  of  the  earth,  and  the 
stars  ?  The  earth  is  a  dark  and  opaque,  while  the  celestial  bodies  are 
brilliant.  We  perceive  in  it  no  motion,  while  in  them  we  observe  a  con-„ 
tlnual  change  of  place,  as  we  view  them  at  different  hours  of  the  day  or 
night,  or  at  different  seasons  of  the  year.  The  ancients,  accordingly,  one 
or  two  of  the  more  enlightened  of  them  only  excepted,  admitted  no  such 
community  of  nature ;  and,  by  thus  placing  the  heavenly  bodies  and  their 
movements  without  the  pale  of  analogy  and  experience,  effectually  inter- 
cepted the  progress  of  all  reasoning  from  what  passes  here  below,  to  what 
is  going  on  in  the  regions  where  they  exist  and  move.  Under  such  con- 
ventions, astronomy,  as  a  science  of  cause  and  effect,  could  not  exist,  but 
must  be  limited  to  a  mere  registry  of  appearances,  unconnected  with  any 
attempt  to  account  for  them  on  reasonable  principles,  however  successful 
to  a  certain  extent  might  bo  the  attempt  to  follow  out  their  order  of 
sequence,  and  to  establish  empirical  laws  expressive  of  this  order.  To 
get  rid  of  this  prejudice,  therefore,  is  the  first  step  towards  acquiring  a 
knowledge  of  what  is  really  the  case ;  and  the  student  has  made  his  first 
effort  towards  the  acquisition  of  sound  knowledge,  when  he  has  learnt  to 
familiarize  himself  with  the  idea  that  the  earth,  after  all,  may  be  nothing 
but  a  great  star.  How  correct  such  an  idea  may  be,  and  with  what  limi- 
tations and  modifications  it  is  to  be  admitted,  we  shall  see  presently. 

(14.)  It  is  evident,  that,  to  form  any  just  notions  of  the  arrangement, 
in  space,  of  a  number  of  objects  which  we  cannot  approach  and  examine, 
but  of  which  all  the  information  we  can  gain  is  by  sitting  still  and  watch- 
ing their  evolutions,  it  must  be  very  important  for  us  to  know,  in  the  first 
instance,  whether  what  we  call  sitting  still  is  really  such :  whether  the 
station  from  which  we  view  them,  with  ourselves,  and  all  objects  which 
immediately  surround  us,  be  not  itself  in  motion,  unperceived  by  us ;  and 
if  so,  of  what  nature  that  motion  is.  The  apparent  places  of  a  number 
of  objects,  and  their  apparent  arrangement  with  respect  to  each  other, 
will  of  course  be  materially  dependent  on  the  situation  of  the  spectator 


I, 


3 


% 


ii' 


II 


I 


OUTLINES   OP  ASTRONOMY. 

among  tbem ;  and  if  this  situation  bo  liable  to  change,  unknown  to  the 
spectator  himself,  an  appearance  of  change  in  the  respective  situations  of 
the  objects  will  arise,  without  the  reality.  If,  then,  such  be  actually  the 
case,  it  will  follow  that  all  the  movements  we  think  we  perceive  among 
the  stars  will  not  be  real  movements,  but  that  some  part,  at  least,  of 
whatever  changes  of  relative  place  we  perceive  among  them  must  bo 
merely  apparent,  the  results  of  the  shifting  of  our  own  point  of  view ; 
and  that,  if  we  would  ever  arrive  at  a  knowledge  of  their  real  motions,  it 
can  only  be  by  first  investigating  our  own,  and  making  due  allowance  for 
its  effects.  Thu>:,  the  question  whether  the  earth  is  in  motion  or  at  rest, 
and  if  in  motion,  what  that  motion  is,  is  no  idle  inquiry,  but  one  on  which 
depends  our  only  chance  of  arriving  at  true  conclusions  respecting  the 
constitution  of  the  universe. 

(15.)  Nor  let  it  be  thought  strange  that  we  should  speak  of  a  motion 
existing  in  the  earth,  unperceived  by  its  inhabitants ;  we  must  remember 
that  it  is  of  the  earth  as  a  whole,  with  all  that  it  holds  within  its  substance 
or  sustains  on  its  surface,  that  we  are  speaking ;  of  a  motion  common  to 
the  solid  mass  beneath,  to  the  ocean  which  flows  around  it,  the  air  that 
rests  upon  it,  and  the  clouds  which  float  above  it  in  the  air.  Such  a 
motion,  which  should  displace  no  terrestrial  object  from  its  relative  situa- 
tion among  others,  interfere  with  no  natural  processes,  and  produce  no 
sensations  of  shocks  or  jerks,  might,  it  is  very  evident,  subsist  undetected 
by  us.  There  is  no  peculiar  sensation  which  advertises  us  that  we  are  in 
motion.  We  perceive  jerks,  or  shocks,  it  is  true,  because  these  are  sud- 
den changes  of  motion,  produced,  as  the  laws  of  mechanics  teach  us,  by 
sudden  and  powerful  forces  acting  during  short  times ;  and  these  forces, 
applied  to  our  bodies,  are  what  we  feel.  When,  for  example,  we  are 
carried  along  in  a  carriage  with  the  blinds  down,  or  with  our  eyes  closed 
(to  keep  us  from  seeing  external  objects),  we  perceive  a  tremor  arising  from 
inequalities  in  the  road,  over  which  the  carriage  is  successively  lifted  and 
let  fall,  but  we  have  no  sense  of  progress.  As  the  road  is  smoother,  our 
sense  of  motion  is  diminished,  though  our  rate  of  travelling  is  accelerated. 
Railway  travelling,  especially  by  night,  or  in  a  tunnel,  has  familiarized 
every  one  with  this  remark.  Those  who  have  made  aeronautic  voyages 
testify  that  with  closed  eyes,  and  under  the  influence  of  a  steady  breeze 
communicating  no  oscillatory  or  revolving  motion  to  the  car,  the  sensation 
is  that  of  perfect  rest,  however  rapid  the  transfer  from  place  to  place. 

(16.)  But  it  is  on  shipboard,  where  a  great  system  is  maintained  in 
motion,  and  where  we  are  surrounded  with  a  multitude  of  objects  which 
participate  with  ourselves  and  each  other  in  the  common  progress  of  the 
whole  mass,  that  we  feel  most  satisfactorily  the  identity  of  ponsation 


between  a 
heavy  vess( 
a  canal,  not 
We  read,  s 
land.  If  ' 
we  drop  it, 
air;  and  s 
ment  on  sh 
different;  1 
other  light 
the  opposit 
remain  at  i 
so  far  as  ni 
complete; 
our  own  m( 
external,  tL 


(17.)  In 
form  to  ou 
cannot  hav 
nite  outline 
other  bodie 
form  of  the 
tions  from 
below,  to  ai 
got  rid  of, 
easier  to  ric 
inactivity, 
thing  we 
large;  and 
unduly  inte 
lies  the  oth 
and  rise  ag 
see  after  a 
solid  mattei 
the  earth, 
subterranco 
for  many  k 
stantly  sliif 
the  moon 


APPARENT   AND   REAL  MOTIONS. 


27 


between  a  state  of  motion  and  one  of  rest.  In  the  cabin  of  a  large  and 
heavy  vessel,  going  smoothly  before  the  wind  in  still  water,  or  drawn  along 
a  canal,  not  the  smallest  indication  acquaints  us  with  the  way  it  is  making. 
We  read,  sit,  walk,  and  perform  every  customary  action  as  if  we  were  on 
land.  If  we  throw  a  ball  into  the  air,  it  falls  back  into  our  hand ;  or  if 
we  drop  it,  it  alights  at  our  feet.  Insects  buzz  around  us  as  in  the  free 
air;  and  smoke  ascends  in  the  same  manner  as  it  would  do  in  an  apart- 
ment on  shore.  If,  indeed,  we  come  on  deck,  the  case  is,  in  some  respects, 
diflferent ;  the  air,  not  being  carried  along  with  us,  drifts  away  smoke  and 
other  light  bodies  —  such  as  feathers  abandoned  to  it  —  apparently,  in 
the  opposite  direction  to  that  of  the  ship's  progress ;  but,  in  reality,  Ihey 
remain  at  rest,  and  we  leave  them  behind  in  the  air.  Still,  the  illusion, 
so  far  as  massive  objects  and  our  own  movements  are  concerned,  remains 
complete ;  and  when  we  look  at  the  shore,  we  then  perceive  the  effect  of 
our  own  motion  transferred,  in  a  contrary  direction,  to  external  objects  — 
exUrnal,  that  is,  to  the  system  of  which  we  form  a  part. 

"  Provehimur,  portu,  tcrrnque  urbesque  recedunt. 

(17.)  In  order,  however,  to  conceive  the  earth  as  in  motion,  we  must 
form  to  ourselves  a  conception  of  its  shape  and  size.  Now,  an  object 
cannot  have  shape  and  size  unless  it  is  limited  on  all  sides  by  some  defi- 
nite outline,  so  Jas  to  admit  of  our  imagining  it,  at  least,  disconnected  from 
other  bodies,  and  existing  insulated  in  space.  The  first  rude  notion  we 
form  of  the  earth  is  that  of  a  flat  surface,  of  indefinite  extent  in  all  direc- 
tions from  the  spot  where  we  stand,  above  which  are  the  air  and  sky ; 
below,  to  an  indefinite  profundity,  solid  matter.  This  is  a  prejudice  to  be 
got  rid  of,  like  that  of  the  earth's  immobility  j  —  but  it  is  one  much 
easier  to  rid  ourselves  of,  inasmuch  a"  it  originates  only  in  our  own  montal 
inactivity,  in  not  questioning  ourselves  ivhere  we  will  place  a  limit  to  a 
thing  we  have  been  accustomed  from  infancy  to  regard  as  immensely 
large ;  and  does  not,  like  that,  originate  in  the  testimony  of  our  senses 
unduly  interpreted.  On  the  contrary,  the  direct  testimony  of  our  senses 
lies  the  other  way.  When  we  see  the  sun  set  in  the  evening  in  the  west, 
and  rise  again  in  the  east,  as  we  cannot  doubt  that  it  is  the  same  sun  we 
see  after  a  temporary  absence,  we  must  do  violence  to  all  our  notions  of 
solid  matter,  to  suppose  it  to  have  made  its  way  through  the  substance  of 
the  earth.  It  must,  tlierefore,  have  gone  under  it,  and  that  not  by  a  mere 
subterraneous  channel ;  for  if  we  notice  the  points  where  it  sets  and  rises 
for  many  successive  days,  or  for  a  whole  year,  we  shall  find  them  con- 
stantly shifting,  round  a  very  large  extent  of  the  horizon;  and,  besides, 
the  moon  and  stars  also  set  and  rise  again  in  all  points  of  the  visible 


I 

5' 

2 

\-^ 

km 

s 

G 

0 


2 


28 


OUTLINES  OP  ASTRONOMY. 


horizon.  The  conclusion  is  plain  :  the  earth  cannot  extend  indefinitely 
in  depth  downwards,  nor  indefinitely  in  surface  laterally ;  it  must  have  not 
only  bounds  in  a  horizontal  direction,  but  also  an  under  side  round  which 
the  sun,  moon,  and  stars  can  pass ;  and  that  side  must,  at  least,  be  so  far 
like  what  we  see,  that  it  must  have  a  sky  and  sunshine,  and  a  day  when 
it  is  night  to  us,  and  vice  versd ;  where,  in  short, 


— "  redit  il  nobis  Aurora,  diemque  reducit. 
Nosque  ubi  primus  equis  oriens  afflavit  anhelis, 
Illic  sera  rubens  accendit  lumina  Vesper. 


Georg. 


(18.)  As  soon  as  we  have  familiarized  ourselves  with  the  conception  of 
an  earth  without  foundations  or  fixed  supports  —  existing  insulated  in 
space  from  contact  of  every  thing  external,  it  becomes  easy  to  imagine  it 
in  motion  —  or,  rather,  difficult  to  imagine  it  otherwise :  for,  since  there 
is  nothing  to  retain  it  in  one  place,  should  any  causes  of  motion  exist,  or 
VLuy  forces  act  upon  it,  it  roust  obey  their  impulse.  Let  us  next  sec  \^hat 
obvious  circumstances  there  are  to  help  us  to  a  knowledge  of  the  shape 
of  the  earth. 

(19.)  Let  us  first  examine  what  we  can  actually  see  of  its  shape.  Now, 
it  is  not  on  land  (unless,  indeed,  on  uncommonly  level  and  extensive 
plains),  that  we  can  see  any  thing  of  the  general  figure  of  the  earth ;  — 
the  hills,  trees,  and  other  objects  which  roughen  its  surface,  and  break 
and  elevate  the  line  of  the  horizon,  though  obviously  bearing  a  most  mi- 
nute proportion  to  the  whole  earth,  are  yet  too  considerable  with  respect 
to  ourselves  and  to  that  small  portion  of  it  which  we  can  see  at  a  single 
view,  to  allow  of  our  forming  any  judgment  of  the  form  of  the  whole,  from 
that  of  a  part  so  disfigured.  But  with  the  surface  of  the  sea  or  any  vastly 
extended  level  plain,  the  case  is  otherwise.  If  we  sail  out  of  sight  of 
land,  whether  we  stand  on  the  deck  of  the  ship  or  climb  the  mast,  we  see 
the  surface  of  the  sea  —  not  losing  itself  in  distance  and  mist,  but  termi- 
nated by  a  sharp,  clear,  well-defined  line  or  offing  as  it  is  called,  which 
runs  all  round  us  in  a  circle,  having  our  station  for  its  centre.  That  this 
line  is  really  a  circle,  we  conclude,  first,  from  the  perfect  apparent  similar- 
ity of  all  its  parts;  and,  secondly,  from  the  fact  of  all  its  parts  appearing 
at  the  same  distance  from  us,  and  that,  evidently,  a  moderate  one ;  and 
thirdly,  from  this,  that  its  apparent  diameter,  measured  with  an  instru- 
ment called  the  dip  sector,  is  the  same  (except  under  some  singular  atmos- 
pheric circumstances,  which  produce  a  temporary  distortion  of  the  outline), 
in  whatever  direction  the  measure  is  taken, —  properties  which  belong  only 
to  the  circle  among  geometrical  figures.     If  we  ascend  a  high  eminence 


on  a  plain 
good. 

(20.)  Mi 
trifling  emi 
riiFe,  Mown 
of  the  who! 
few  and  rar 
real  boundi 
same  appeal 
that  the  an^ 
tor,  is  matei 
apparent  si 
from  its  sun 
increased. 

(21.)  Th 
the  earth's 
however  see 
globe. 

(22.)  A  ( 
sented  by  tl 
tions  at  difie 


THE   HORIZON  AND   ITS   DIP. 


on  a  plain  (for  instance,  one  of  the  Egyptian  pyramids;)  the  same  holds 
good. 

(20.)  Masts  of  ships,  however,  and  the  edifices  erected  by  man,  are 
trifling  eminences  compared  to  what  nature  itself  affords;  iBtna,  Tene- 
riife,  Mowna  lloa,  are  eminences  from  which  no  contemptible  aliquot  part 
of  the  whole  earth's  surface  can  be  seen ;  but  from  these  again — in  those 
few  and  rare  occasions  when  the  transparency  of  the  air  will  permit  the 
real  boundary  of  the  horizon,  the  true  sea-line,  to  be  seen — the  very 
same  appearances  are  witnessed,  but  with  this  remarkable  addition,  viz., 
that  the  angular  diameter  of  the  visible  area,  as  measured  by  the  dip  sec- 
tor, is  materially  less  than  at  a  lower  level ;  or,  in  other  words,  that  the 
apparent  size  of  the  earth  has  sensibly  diminished  as  we  have  receded 
from  its  surface,  while  yet  the  absolute  quantity  of  it  seen  at  once  has  been 
increased. 

(21.)  The  same  appearances  are  observed  universally,  in  every  part  of 
the  earth's  surface  visited  by  man.  Now,  the  figure  of  a  body  which, 
however  seen,  appears  always  circular,  can  be  no  other  than  a  sphere  or 
globe. 

(22.)  A  diagram  will  elucidate  this.  Suppose  the  earth  to  be  repre- 
sented by  the  sphere  LHNQ,  whose  centre  is  C,  and  let  A,  G,  M  be  sta- 
tions at  different  elevations  above  various  points  of  its  surface,  represented 

Fig.  1. 


I 


S 

0 

\ 


30 


OUTLINES   OF   ASTRONOMY. 


% 


■^  M 


^y  °t  S)  *"  respectively.  From  each  of  tliom  (as  from  M)  let  a  lino  bo 
drawn,  as  MNn,  a  tangent  to  the  surface  at  N,  then  will  this  line  represent 
the  visual  ray  along  which  the  spectator  at  M  will  see  the  visible  horizon  ; 
and  as  this  tangent  sweeps  round  M,  and  comes  successively  into  tlie  posi- 
tions 3IOo,  3IPp,  MQq,  the  point  of  contact  N  will  mark  out  on  the  sur- 
face the  circle  NOPQ.  The  area  of  the  spherical  surface  comprehended 
within  this  circle  is  the  portion  of  the  earth's  surface  visible  to  a  spectator 
at  M,  and  the  angle  NMQ  included  between  the  two  extreme  visual  rays 
is  the  measure  of  its  apparent  angular  diameter.  Leaving,  at  present,  out 
of  consideration  the  eflfect  of  refraction  in  the  air  below  M,  of  which  more 
hereafter,  and  which  always  tends,  in  some  degree,  to  increase  that  angle, 
or  render  it  more  obtuse,  this  is  the  angle  measured  by  the  dip  sector. 
Now,  it  is  evident,  1st,  that  as  the  point  M  is  more  elevated  above  m,  the 
point  immediately  below  it  on  the  sphere,  the  visible  area,  i.  e.  the  spher- 
ical segment  or  slice  NOPQ,  increases ;  2dly,  that  the  distauce  of  the  vis- 
ible horizon^  or  boundary  of  our  view  from  the  eye,  viz.  the  lino  MN, 
increases ;  and,  3dly,  that  the  angle  NMQ  becomes  less  obtuse,  or,  in  other 
words,  the  apparent  angular  diameter  of  the  earth  diminishes,  being  no- 
where so  great  as  180°,  or  two  right  angles,  but  falling  short  of  it  by 
gome  sensible  quantity,  and  that  more  and  more  the  higher  we  ascend. 
The  figure  exhibits  three  states  or  stages  of  elevation,  with  the  horizon, 
&c.,  corresponding  to  each,  a  glance  at  which  will  explain  our  meaning: 
or,  limiting  ourselves  to  the  larger  and  more  distinct,  MNOPQ,  let  the 
reader  iujagine  wNM,  MQ^^  to  be  the  two  legs  of  a  ruler  jointed  at  M,  and 
kept  extended  by  the  globe  NwjQ  between  them.  It  is  clear,  that  as  the 
joint  M  is  urged  home  towards  the  surface,  the  legs  will  open,  and  the  ruler 
will  become  more  nearly  straight,  but  will  not  attain  perfect  .ntraightness 
till  M  is  brought  fairly  up  to  contact  with  the  surface  at  m,  in  which  case 
its  whole  length  will  become  a  tangent  to  the  sphere  at  m,  as  is  the  line 
xy. 

(23.)  This  explains  what  is  meant  by  the  dip  of  the  horizon.  3Im, 
which  is  perpendicular  to  the  general  surface  of  the  sphere  at  m,  is  also 
the  direction  in  which  a  plumb-line'  would  hang;  for  it  is  an  observed 
fact,  that  in  all  situations,  in  every  part  of  the  earth,  the  direction  of  a 
plumb-line  is  exactly  perpendicular  to  the  surface  of  still  water;  and, 
moreover,  that  it  is  also  exactly  perpendicular  to  a  line  or  surface  truly 
adjusted  by  a  spirit-level.'  Suppose,  then,  that  at  our  station  M  we  were 
to  adjust  a  line  (a  wooden  ruler  for  instance)  by  a  spirit-level,  with  perfect 
exactness;  then,  if  we  suppose  the  direction  of  this  line  indefinitely  pro- 

' '  Ofii^w,  to  terminate. 

''See  these  insiruminis  described  in  Chap.  Ill, 


longed  bot 
M  w,  and 
spectator 
above  this 
between  >k 
sphere  by 
zone  —  the 
below  the 
It  is  a  con 

(l>4.) 
figure  of  tl 
tion)  is  thi 
which,  wh 
irrcgulariti 
as  trifling 
consider  ar 
That  the  a 
of  the  cur\ 
the  eye  to 
tinctness. 
acquired  ii 
observation 
test,  and  a 
of  the  cart 

(25.)  Ir 
at  the  sea-! 
offing  or  vi 
upper  parti 
hid  from  vi 
them  and  ( 
from  our 
spectator,  I 
of  the  shi| 
As  it  recec 
is  seen  do 
But  as  soo 
tion  still  C( 
disappear  I 
certain  dis 
and  sails  : 
things,  the 


THE   HORIZON   AND   ITS   DIP. 


31 


longed  both  wnys,  as  XMY,  the  lino  so  drawn  will  bo  at  right  angles  to 
Mw»,  and  thcreforo  purallcl  to  xmy,  the  tungoiit  to  the  sphere  at  m.  A 
spectator  i)liiccd  at  M  will  thorofore  see  not  only  all  the  vault  of  the  sky 
above,  this  lino,  as  X/V,  but  also  that  portion  or  zone  of  it  which  lies 
between  XN  and  YQ;  in  other  words,  his  sky  will  bo  more  than  a  hemi- 
sphere by  the  zone  YQXN.  It  is  the  angular  breadth  of  this  redundant 
zone  —  the  angle  YMQ,  by  which  the  visible  horizon  appears  depressed 
below  the  direction  of  a  spirit-level  —  that  is  called  the  dip  of  the  horizon. 
It  is  a  correction  of  constant  use  in  nautical  astronomy. 

(24.)  From  the  foregoing  explanations  it  appears,  1st,  That  the  general 
figure  of  the  earth  (so  far  as  it  can  be  gathered  from  this  kind  of  observa- 
tion) is  that  of  ii  sphere  or  globe.  In  this  wo  also  include  that  of  the  sea, 
which,  wherever  it  extends,  covers  and  fills  in  those  inequalities  and  local 
irregularities  which  exist  on  land,  but  which  can  of  course  only  be  regarded 
as  trifling  deviations  from  the  general  outline  of  the  whole  mass,  as  we 
consider  an  orange  not  the  less  round  for  the  roughness  on  its  rind.  2dly, 
That  the  appearance  of  a  visible  horizon,  or  sca-ofBng,  is  a  consequence 
of  the  curvature  of  the  surface,  and  docs  not  arise  from  the  inability  of 
the  eye  to  follow  objects  to  a  greater  distance,  or  from  atmospheric  indis- 
tinctness. It  will  be  worth  while  to  pursue  the  general  notion  thus 
acquired  into  some  of  its  coLsequcnces,  by  which  its  consistency  with 
observations  of  a  different  kind,  and  on  a  larger  scale,  will  be  put  to  the 
test,  and  a  clear  conception  be  formed  of  the  manner  in  which  the  parts 
of  the  earth  are  related  to  each  other,  and  held  together  as  a  whole. 

(25.)  In  the  first  place,  then,  every  one  who  has  passed  a  little  while 
at  the  sea-side  is  aware  that  objects  may  be  seen  perfectly  well  beyond  the 
offing  or  visible  horizon  —  but  not  the  whole  of  them.  We  only  see  their 
upper  parts.  Their  bases  where  they  rest  on,  or  rise  out  of  the  water,  are 
hid  from  view  by  the  spherical  surface  of  the  sea,  which  protrudes  between 
them  and  ourselves.  Suppose  a  ship,  for  instance,  to  sail  directly  away 
from  our  station ;  —  at  first,  when  the  distance  of  the  ship  is  small,  a 
spectator,  S,  situated  at  some  certain  height  above  the  sea,  sees  the  whole 
of  the  ship,  even  to  the  water  line  where  it  rests  on  the  sea,  as  at  A. 
As  it  recedes  it  diuilnisues,  it  is  true,  in  apparent  size,  but  still  the  whole 
is  seen  down  to  the  water  line,  till  it  reaches  the  visible  horizon  at  B. 
But  as  soon  as  it  has  passed  this  distance,  not  only  does  the  visible  por- 
tion still  continue  to  diminish  in  apparent  size,  but  the  hull  begins  to 
disappear  bodily,  as  if  sunk  below  the  surface.  When  Ic  has  reached  a 
certain  distance,  as  at  C,  its  hull  has  entirely  vanished,  but  the  masts 
and  sails  remain,  presenting  the  appearance  c.  But  if,  in  this  state  of 
things,  the  spectator  quickly  ascends  to  a  higher  station,  T,  whose  visible 


I 

< 

0 

E 

0 
0 

% 

\ 


OUTLINES  OF  ASTRONOMY. 


I  t 


horizon  is  at  D,  tho  hull  comes  agam  in  sight ;  and,  whun  ho  duscends 
again  he  loses  it.     Tho  ship  still  receding,  tho  lower  sails  seem  to  sink 

Fig.  2. 


and  b  B,  th( 
B,  —  data  \ 


below  the  water,  as  at  d,  and  at  length  the  whole  disappears :  while  yet 
tho  distinctness  with  which  the  last  portion  of  the  sail  d  is  seen  is  such 
as  to  satisfy  us  that  were  it  not  for  the  interposed  segment  of  the  sea, 
ABODE,  the  distance  TE  is  not  so  great  as  to  have  prevented  an  equally 
perfect  view  of  the  whole. 

(26.)  The  history  of  aeronautic  adventure  affords  a  curious  illustration 
of  tho  same  principle.  The  late  Mr.  Sadler,  the  celebrated  aeronaut, 
a&oondcd  on  one  occasion  in  a  balloon  from  Dublin,  and  was  wafted  across 
tho  Irish  Channel,  when,  on  his  approach  to  the  Welsh  coast,  the  balloon 
descended  nearly  to  the  surface  of  the  sea.  By  this  time  the  sun  was 
set,  and  the  shades  of  evening  began  to  close  in.  He  threw  out  nearly 
all  his  ballast,  and  suddenly  sprang  upwards  to  a  great  height,  and  by  so 
doing  brought  his  horizon  to  dip  below  the  sun,  producing  the  whole 
phenomenon  of  a  western  sunrise.  Subsequently  descending  in  Wales, 
he  of  course  witnessed  a  second  sunset  on  the  same  evening. 

(27.)  If  we  could  measure  the  heights  and  exact  distance  of  two  sta- 
tions which  could  barely  be  discerned  from  each  other  over  the  edge  of 
the  horizon,  we  could  ascertain  the  actual  size  of  the  earth  itself:  and,  in 
fact,  were  it  not  for  the  effect  of  refraction,  by  which  we  are  enabled  to 
sec  in  some  small  degree  round  the  interposed  segment  (as  will  be  here- 
after explained),  this  would  bo  a  tolerably  good  method  of  ascertaining 
it.  Suppose  A  and  B  to  be  two  eminences,  whose  perpendicular  heights 
A  a  and  B  b  (which,  for  simplicity,  we  will  suppose  to  be  exactly  equal) 
arc  known,  as  well  as  their  exact  horizontal  interval  aDi,  by  measure- 
ment; then  it  is  clear  that  D,  the  visible  horizon  of  both,  will  lie  just 
half-way  between  them,  and  if  we  suppose  aJ)b  to  be  the  sphere  of  the 
earth,  and  C  its  centre  in  the  figure  C  D  6  B,  we  know  D  b,  the  length  of 
the  arch  of  the  circle  between  D  and  b, — viz.  half  the  measured  interval, 


us  to  find  tb 
pose  both  tl 
parisou  with 
the  followiuj 
The  eart 
visible  hori: 
eye  above  th 
When  th( 
complicated. 
(28.)  Alt 
this  from  b( 
earth,  yet  it 
of  use  in  tl 
many  just  ( 
tion  in  num 
ten  feet  abo 
water,  and  ii 
miles.     But 
or  4  miles,  i 
in  the  same 
It  must,  the 
about  8000 
(29.)  Sue 
earth's  magi 
to  compare  i 
size,  so  OS  to 
dimension, 
face,  arising 
on  the  rind 
3 


^IZE   OF  THE   EARTH. 


and  &B,  the  excess  of  its  g^«ant  above  its  radius — which  is  tho  height  of 
B;  —  data  which,  by  the  solution  of  an  easy  geometrical  problem,  euable 


us  to  find  the  length  of  the  radius  D  C.  If,  as  is  really  the  case,  we  sup- 
pose both  the  heights  and  distance  of  the  stations  inconsiderable  in  com- 
parison with  tho  size  of  tho  earth,  the  solution  alluded  to  is  contained  in 
the  following  proposition :  — 

The  earth's  diameter  bears  the  same  proportion  to  the  distance  of  the 
visible  horizon  from  the  eye  as  that  distance  does  to  the  height  of  the 
eye  above  the  sea  level. 

When  the  stations  are  unequal  in  height,  the  problem  is  a  little  more 
complicated. 

(28.)  Although,  as  we  have  observed,  the  efiect  of  refraction  prevents 
this  from  being  an  exact  method  of  ascertaining  the  dimensions  of  the 
earth,  yet  it  will  suffice  to  afibrd  such  an  approximation  to  it  as  shall  be 
of  use  in  the  present  stage  of  the  reader's  knowledge,  and  help  him  to 
many  just  conceptions,  on  which  account  we  shall  exemplify  its  applica- 
tion in  numbers.  Now,  it  appears  by  observation,  that  two  points,  each 
ten  feet  above  the  surface,  cease  to  be  visible  from  each  other  over  still 
water,  and  in  average  atmospheric  circumstances,  at  a  distance  of  about  8 
miles.  But  10  feet  is  the  528th  part  of  a  mile,  so  that  half  their  distance, 
or  4  miles,  is  to  the  height  of  each  as  4  X  528  or  2112  : 1,  and  therefore 
in  the  same  proportion  to  4  miles  is  the  length  of  the  earth's  diameter. 
It  must,  therefore,  be  equal  to  4  x  2112  =  8448,  or,  in  round  numbers, 
about  8000  miles,  which  is  not  very  far  from  the  truth. 

(29.)  Such  is  the  first  rough  result  of  an  attempt  to  ascertain  the 
earth's  magnitude ;  and  it  will  not  be  amiss,  if  we  take  advantage  of  it 
to  compare  it  with  objects  we  have  been  accustomed  to  consider  as  of  vast 
size,  so  as  to  interpose  a  few  steps  between  it  and  our  ordinary  ideas  of 
dimension.  We  have  before  likened  the  inequalities  on  the  earth's  sur- 
face, arising  from  mountains,  valleys,  buildings,  &c.  to  the  roughnesses 
on  the  rind  of  an  orange,  compared  with  its  general  mass.  The  compari- 
3 


I 

< 


0 

s 

0 
0 

% 

I 

2 


34 


OUTLINES   OF  ASTRONOMY. 


son  is  quite  free  from  exaggeration.  The  highest  mountain  known  hardly 
exceeds  five  miles  in  perpendicular  elevation :  this  is  only  one  1000th 
part  of  the  earth's  diameter;  consequently,  on  a  globe  of  sixteen  inches 
in  diameter,  such  a  mountain  would  be  represented  by  a  protuberance  of 
no  more  than  one  hundredth  part  of  an  inch,  which  is  about  the  thickness 
of  ordinary  drawing-paper,  ^ow,  as  there  is  no  entire  continent,  or  even 
any  very  extensive  tract  of  land,  known,  whose  general  elevation  above 
the  sea  is  any  thing  like  half  this  quantity,  it  follows,  that  if  we  would 
construct  a  correct  model  of  our  earth,  with  its  seas,  continents,  and 
mountains,  on  a  globe  sixteen  inches  in  diameter,  the  whole  of  the  land, 
with  the  exception  of  a  few  prominent  points  and  ridges,  must  be  com- 
prised on  it  within  the  thickness  of  thin  writing-paper;  and  the  highest 
bills  would  be  represented  by  the  smallest  visible  grains  of  sand. 

(30.)  The  deepest  mine  existing  does  not  penetrate  half  a  mile  below 
the  surface :  a  scratch,  or  pin-hole,  duly  representing  it,  on  the  surface  of 
such  a  globe  as  our  model,  would  be  imperceptible  without  a  magnifier. 

(31.)  The  greatest  depth  of  sea,  probably,  does  not  very  much  exceed 
the  greatest  elevation  of  the  continents ;  and  would,  of  course,  be  repre- 
sented by  an  excavation,  in  about  the  same  proportion,  into  the  substance 
of  the  globe :  so  that  the  ocean  comes  to  be  conceived  as  a  mere  film  of 
liquid,  such  as,  on  our  model,  would  be  left  by  a  brush  dipped  in  colour, 
and  drawn  over  those  parts  intended  to  represent  the  sea :  only,  in  so  con- 
ceiving it,  we  must  bear  in  mind  that  the  resemblance  extends  no  farther 
than  to  proportion  in  point  of  quantity.  The  mechanical  laws  which 
would  regulate  the  distribution  and  movements  of  such  a  film,  and  its 
adhesion  to  the  surface,  are  altogether  different  from  those  which  govern 
the  phenomena  of  the  sea. 

(32.)  Lastly,  the  greatest  extent  of  the  earth's  surface  which  has 
ever  been  seen  at  once  by  man,  was  that  exposed  to  the  view  of  MM. 
Biot  and  Gay-Lussac,  in  their  celebrated  aeronautic  expedition  to  the 
enormous  height  of  25,000  feet,  or  rather  less  than  five  miles.  To  esti- 
mate the  proportion  of  the  area  visible  from  this  elevation  to  the  whole 
earth's  surface,  we  must  have  recourse  to  tiie  geometry  of  the  sphere, 
which  informs  us  that  the  convex  surface  of  a  spherical  segment  is  to  the 
whole  surface  of  the  sphere  to  which  it  belongs  as  the  versed  sine  or  thick- 
ness of  the  segment  is  to  the  diameter  of  the  sphere ;  and  further,  that 
this  thickness,  in  the  case  we  are  considering,  is  almost  exactly  equal  to 
the  perpendicukr  elevation  of  the  point  of  sight  above  the  surface.  The 
proportion,  therefore,  of  the  visible  area,  in  this  case,  to  the  whole  earth's 
surface,  is  that  of  five  miles  to  8000,  or  1  to  1600.  The  portion  visible 
from  Mtna,  the  Peak  of  Teneriffe,  or  Mowna  Roa,  is  about  one  4000th. 


(33.)  Wl 

surface  of  t 

aware,  by  n 

barometer, 

bent  on  a  g 

a  direct  me: 

given  space 

we  learn, th 

left  below  u 

that  at  10,( 

that  of  the 

and  at  18,0 

the  material 

earth's  surfa 

priori,  from 

ble  of  being 

the  incumbe 

higher,  we  s! 

relieve  ourse 

upon  us,  yet 

tity  of  air  su 

tional  height 

calculation,  b 

perties  of  air 

compression, 

the  earth  not 

or  rarefaction 

could  not  su 

delicate  meai 

would  fail  to 

(34.)  Layi 

tions  as  to  t 

beyond  whicl 

clear,  that,  foi 

are  more  dist 

diameter  as  v 

visible  vapou 

dering  it  turl 

*  Tlio  lieight 
measurement  o 
10,872  English 


THE    ATMOSPHERE. 


85 


^n  hardly 
!  IGOOth 
in  inches 
ranee  of 
thickness 
;,  or  even 
on  above 
we  would 
cnts,  and 
the  land, 
be  com- 
ic highest 

ile  below 
surface  of 
ignifier. 
ch  exceed 
be  reprc- 
substance 
re  film  of 
in  colour, 
in  so  con- 
10  farther 
ws  which 
and  its 
h  govern 

hich  has 
of  MM. 

)n  to  the 
To  esti- 

he  whole 

}  sphere, 
is  to  the 
or  thick- 
her,  that 
equal  to 
■ce.  The 
e  earth's 
n  visible 
4000th. 


(33.)  When  we  ascend  to  any  very  considerable  elevation  above  the 
surface  of  the  earth,  either  in  a  balloon,  or  on  mountains,  fve  are  made 
aware,  by  many  uneasy  sensations,  of  an  insufficient  supply  of  air.  The 
barometer,  an  instrument  which  informs  us  of  the  weight  of  air  incum- 
bent on  a  given  horizontal  surface,  confirms  this  impression,  and  affords 
a  direct  measure  of  the  rate  of  diminution  of  the  quantity  of  air  which  a 
given  space  includes  as  we  recede  from  the  surface.  From  its  indications 
we  learn,  that  when  we  ha'-e  ascended  to  the  height  of  1000  feet,  we  have 
left  below  us  about  one-thirtieth  of  the  whole  mass  of  the  atmosphere : — 
that  at  10,600  feet  of  perpendicular  elevation  (which  is  rather  less  than 
that  of  the  summit  of  ^tna')  we  have  ascended  through  about  one-third; 
and  at  18,000  feet  (which  is  nearly  that  of  Cotopaxi)  through  one-half 
the  material,  or,  at  least,  the  ponderable  body  of  air  incumbent  on  the 
earth's  surface.  From  the  progression  of  these  numbers,  as  well  as  d 
priori,  from  the  nature  of  the  air  itself,  which  is  compressible,  i.  e.  capa- 
ble of  being  condensed  or  crowded  into  a  smaller  space  in  proportion  to 
the  incumbent  pressure,  it  is  easy  to  see  that,  although  by  rising  still 
higher,  we  should  continually  get  above  more  and  more  of  the  air,  and  so 
relieve  ourselves  more  and  more  from  the  pressure  with  which  it  weighs 
upon  us,  yet  the  amount  of  this  additional  relief,  or  the  ponderable  quan- 
tity of  air  surmounted,  would  be  by  no  means  in  proportion  to  the  addi- 
tional height  ascended,  but  in  a  constantly  decreasing  ratio.  An  easy 
calculation,  however,  founded  on  our  experimental  knowledge  of  the  pro- 
perties of  air,  and  the  mechanical  laws  which  regulate  its  dilatation  and 
compression,  is  sufficient  to  show  that,  at  an  altitude  above  the  surface  of 
the  earth  not  exceeding  the  hundredth  part  of  its  diameter,  the  tenuity, 
or  rarefaction,  of  the  air  must  be  so  excessive,  that  not  only  animal  life 
could  not  subsist,  or  combustion  be  maintained  in  it,  but  that  the  most 
delicate  means  we  possess  of  ascertaining  the  existence  of  any  air  at  all 
would  fail  to  affi)rd  the  slightest  perceptible  indications  of  its  presence. 

(34.)  Laying  out  of  consideration,  therefore,  at  present,  all  nice  ques- 
tions as  to  the  probable  existence  of  a  definite  limit  to  the  atmosphere, 
beyond  which  there  is,  absolutely  and  rigorously  speaking,  no  air,  it  is 
clear,  that,  for  all  practical  purposes,  we  may  speak  of  those  regions  which 
are  more  distant  above  the  earth's  surface  than  the  hundredth  part  of  its 
diameter  as  void  of  air,  and  of  course  of  clouds  (which  are  nothing  but 
visible  vapours,  diffused  and  floating  in  the  air,  sustained  by  it,  and  ren- 
dering it  turbid  as  mud  docs  water).     It  seems  probable,  from  many  indi- 

'  The  height  of  uEtna  above  the  Mediterranean  (as  it  results  from  a  barometrical 
measurement  of  my  own,  mode  in  July,  1824,  under  very  favourable  circumstances)  is 
10,872  English  kc\.--Author. 


s 

s 


\4 

s 

ffl 
f 

0 

i 

2 


36 

cations,  that  the 
exceed  ten  miles 


OUTLINES   OF   AS'mOXO.MY. 

greatest  height  at  which  visible  clouds  ever  exist  does  not 
I  which  height  the  density  of  the  air  is  about  an  eighth 


part  of  what  it  is  at  the  level  of  the  sea. 

(35.)  We  are  thus  led  to  regard  the  atmosphere  of  air,  with  the  clouds 
it  supports,  as  constituting  a  coating  of  equable  or  nearly  equable  thick- 
ness, enveloping  our  globe  on  all  sides ;  or  rather  as  an  aerial  ocean,  of 
Tvbich  the  surface  of  the  sea  and  land  constitutes  the  bed,  and  whose  infe- 
rior portions  or  strata,  within  a  few  miles  of  the  earth,  contain  by  far  the 
greater  part  of  the  whole  mass,  the  density  diminishing  with  extreme 
rapidity  as  we  recede  upwards,  till,  within  a  very  moderate  distance  (such 
as  would  be  represented  by  the  sixth  of  an  inch  on  the  model  we  have 
before  spoken  of,  and  which  is  not  more  in  proportion  to  the  globe  on 
which  it  rests,  than  the  downy  skin  of  a  peach  in  comparison  with  the 
fruit  within  it),  all  sensible  trace  of  the  existence  of  air  disappears. 

(36.)  Arguments,  however,  are  not  wanting  to  render  it,  if  not  abso- 
lutely certain,  at  least  in  the  highest  degree  probable,  that  the  surface  of 
the  aerial,  like  that  of  the  aqueous  ocean,  has  a  real  and  definite  limit,  as 
above  hinted  at ;  beyond  which  there  is  positively  no  air,  and  above  which 
a  fresh  quantity  of  air,  could  li.  be  added  from  without,  or  carried  aloft 
from  below,  instead  of  dilating  itself  indefinitely  upwards,  would,  after  a 
certain  very  enormous  but  still  finite  enlargement  of  volume,  sink  and 
merge,  as  water  poured  into  the  sea,  and  distribute  itself  among  the  mass 
beneath.  With  the  truth  of  this  conclusion,  however,  astronomy  has 
little  concern ;  all  the  effects  of  the  atmosphere  in  modifying  astronomical 
phenomena  being  the  same,  whether  it  be  supposed  of  definite  extent  or 
not. 

(37.)  Moreover,  whichever  idea  we  adopt,  within  those  limits  in  which 
it  possesses  any  appreciable  density  its  constitution  is  the  same  over  all 
points  of  the  earth's  surface ;  that  is  to  say,  on  the  great  scale,  and  leaving 
out  of  consideration  temporary  and  local  causes  of  derangement,  such  as 
winds,  and  great  fluctuations,  of  the  nature  of  waves,  which  prevail  in  it 
to  an  immense  extent.  In  other  words,  the  law  of  diminution  of  the 
air's  density  as  we  recede  upwards  from  the  level  of  the  sea  is  the  same 
in  every  column  into  which  we  may  conceive  it  divided,  or  from  whatever 
point  of  the  surfiice  we  may  set  out.  It  may  therefore  be  considered  as 
consisting  of  successively  superposed  strata  or  layers,  each  of  the  form  of 
a  spherical  shell,  concentric  with  the  general  surface  of  the  sea  and  land, 
and  each  of  which  is  rarer,  or  specifically  lighter,  than  that  immediately 
beneath  it;  and  denser,  or  specifically  heavier,  than  that  immediately 
above  it.  This,  at  least,  is  the  kind  of  distribution  which  alone  would  be 
consistent  with  the  laws  of  the  equilibrium  of  fluids.     Inasmuch,  however, 


as  the  atmo 
state  of  circ 
over  that  at 
of  this  law 
that  even 
strata,  b-lov 
of  considera 
must  be  obs 
inequalities 
hardly  more 
inequalities 
of  its  surfac 
effect  in  giv 
constituting 
sweep  over 
disturb  the 

(38.)  It 
parent  medi 
their  straigh 
atmosphere  : 
seen  oblique 
same  spectai 
false  impress 
taining  the  i 
duced  on  ea( 
in  which  the 

(39.)  Sui 
K  A  k;  anc 
of  decreasin; 
divided,  and 
surface.  Le 
most  limit  o1 
would  see  it 
when  the  ra' 
by  the  laws 
direction,  as 
the  extreme 
wards,  the  i 
undergo  grcj 
instead  of  pu 
b  a,  continuj 


THE   ATMOSPHERE. 


37 


si  does  not 
t  an  eighth 

the  clouda 
able  thick- 
l  ocean,  of 
vhose  infe- 
by  far  the 
h  extreme 
ance  (such 
j1  we  have 
e  globe  on 
a  with  the 
ears. 

not  abso- 
surface  of 
te  limit,  as 
bove  which 
Tried  aloft 
lid,  after  a 
,  sink  and 
g  the  mass 
)nomy  has 
tronomical 
i  extent  or 

s  in  which 
le  over  all 
nd  leaving 
it,  such  as 
revail  in  it 
ion  of  the 
I  the  same 
\  whatever 
sidered  as 
10  form  of 
nnd  land, 
imediately 
imediately 
3  would  be 
1,  however, 


as  the  atmosphere  is  not  in  perfect  equilibrium,  being  clwaya  kept  in  a 
state  of  circulation,  owing  to  the  excess  of  heat  in  its  equatorial  regions 
over  that  at  the  poles,  some  slight  deviation  from  the  rigorous  expression 
of  this  law  takes  place,  and  in  peculiar  localities  there  is  reason  to  believe 
that  even  considerable  permanent  depressions  of  the  contours  of  these 
strata,  b^low  their  general  or  spherical  level,  subsist.  But  these  are  points 
of  consideration  rather  for  the  meteorologist  than  the  astronomer.  It 
must  be  observed,  moreover,  that  with  this  distribution  of  its  strata  the 
inequalities  of  mountains  and  valleys  have  little  concern.  These  exercise 
hardly  more  influence  in  modifying  their  general  spherical  figure  than  the 
inequalities  at  the  bottom  of  the  sea  interfere  with  the  general  sphericity 
of  its  surface.  They  would  exercise  absolutely  none  were  it  not  for  their 
eflfect  in  giving  another  than  horizontal  direction  to  the  currents  of  air 
constituting  winds,  as  shoals  in  the  ocean  throw  up  the  currents  which 
sweep  over  them  towards  the  surface,  and  so  in  some  small  deg-ee  tend  to 
disturb  the  perfect  level  of  that  surface. 

(38.)  It  is  the  power  which  air  possesses,  in  common  with  all  trans- 
parent media,  of  refracting  the  rays  of  light,  or  bending  them  out  of 
their  straight  course,  which  renders  a  knowledge  of  the  constitution  of  the 
atmosphere  important  to  the  astronomer.  Owing  to  this  property,  objects 
seen  obliquely  through  it  appear  otherwise  situated  than  they  would  to  the 
same  spectator,  had  the  atmosphere  no  existence.  It  thus  produces  a 
false  impression  respecting  their  places,  which  must  be  rectified  by  ascer- 
taining the  amount  and  direction  of  the  displacement  so  apparently  pro- 
duced on  each,  before  we  can  come  at  a  knowledge  of  the  true  directions 
in  which  they  are  situated  from  us  at  any  assigned  moment. 

(39.)  Suppose  a  spectator  placed  at  A,  any  point  of  the  earth's  surface 
K  A  k',  and  let  L  /,  M  m,  N  n,  represent  the  successive  strata  or  layers, 
of  decreasing  density,  into  which  we  may  conceive  the  atmosphere  to  be 
divided,  and  which  are  spherical  surfaces  concentiic  with  K  fc,  the  earth's 
surface.  Let  S  represent  a  star,  or  other  heavenly  body,  beyond  the  ut- 
most limit  of  the  atmosphere.  Then,  if  the  air  were  away,  the  spectator 
would  see  it  in  the  direction  of  the  straight  line  A  S.  But,  in  reality, 
when  the  ray  of  light  S  A  reaches  the  atmosphere,  suppose  at  d,  it  will, 
by  the  laws  of  optics,  begin  to  bend  downwards,  and  take  a  more  inclined 
direction,  as  d  c.  This  bending  will  at  first  be  imperceptible,  owing  to 
the  extreme  tenuity  of  the  uppermost  strata;  but  as  it  advances  down- 
wards, the  strata  continually  increasing  in  density,  it  will  continually 
undergo  greater  and  greater  refraction  in  the  same  direction;  and  thus, 
instead  of  pursuing  the  straight  line  8  (2  A,  it  will  describe  a  curve  S  (2  c 
h  a,  continually  more  and  more  concave  downwards,  and  will  reach  the 


f 

V 

C3 


\4 

Km. 

s 

E 
I 

0 
0 


7 


38 


OUTLINES   OF   ASTRONOMY. 


m 


earth,  not  at  A,  but  at  a  certain  point  a,  nearer  to  S.  This  ray,  conse- 
quently, will  not  reach  the  spectator's  eye.  The  ray  by  which  he  will  see 
the  st,Tr  is,  therefore,  not  S  d  A,  but  another  ray  which,  had  there  been 
no  atmosphere,  would  have  struck  the  earth  at  K,  a  point  behind  the 
spectator ;  but  which,  being  bent  by  the  air  into  the  curve  S  D  C  B  A, 
actually  strikes  on  A.  Now,  it  is  a  law  of  optics,  that  an  object  is  seen 
in  the  direction  which  the  visual  ray  has  at  the  instant  of  arriving  at  the 
eycj  without  regard  to  what  may  have  been  otherwise  its  course  between 
the  object  and  the  eye.  Hence  the  star  S  will  be  seen,  not  in  the  direc- 
tion A  S,  but  in  that  of  A  5,  a  tangent  to  the  curve  S  D  C  B  A,  at  A. 

Fig.  4. 


But  because  the  curve  described  by  the  refracted  ray  is  concave  down- 
wards, the  tangent  A  s  will  lie  above  A  S,  the  unrefracted  ray :  conse- 
quently the  object  S  will  appear  more  elevated  above  the  horizon  A  H, 
when  seen  through  the  refracting  atmosphere,  than  it  would  appear  were 
there  no  such  atmosphere.  Since,  however,  the  disposition  of  the  strata 
is  the  same  in  all  directions  around  A,  the  visual  ray  will  not  be  made  to 
deviate  laterally,  but  will  remain  constantly  in  the  same  vertical  plane, 
S  A  C,  passing  through  the  eye,  the  object,  and  the  earth's  centre. 

(40.)  The  efiFect  of  the  air's  refraction,  then,  is  to  raise  all  the  heavenly 
bodies  higher  above  the  horizon  in  appearance  than  they  are  in  reality. 
Any  such  body,  situated  actually  in  the  true  horizon,  will  appear  above  it, 
or  will  have  some  certain  apparent  altitude  (as  it  is  called).  Nay,  even 
some  of  those  actually  below  the  horizon,  and  which  would  therefore  be 
invisible  but  for  the  efiFect  of  refraction,  ai'c,  by  that  eflPect,  raised  above  it 
and  brought  into  sight.   Thus,  the  sun,  when  situated  at  P  below  the  true 


horizon,  A 
p,  by  the  r 
(41.)  Tl 
the  strict  d 
any  assign  c 
is,  unfortuc 
which  geoi 
the  subject^ 
that  the  d 
depends)  is 
by  its  temj. 
we  recede  f 
diminishing 
is  not  yet  fi 
ceptibly  afiFi 
part  of  an  i 
distribution 
introduce  a 
the  araoun< 
our  knowlc 
Tlie  uncert 
narrow  lim 
delicate  inc 
present. 

(42.)  A 
amount  of 
or  in  every 
or  point  of 
circumstanc 
which  may 
pensable  of 
table  we  art 
all  our  noti 
ingly,  const 
of  astronoE 
admit  of  th 
selves  here 
especially  d 


REFRACTION. 


89 


ay,  conse- 
le  vrill  see 
lere  been 
ehind  the 
DCBA, 
ct  is  seen 
ing  at  the 
B  between 
the  direc- 
t  A;  at  A. 


1 


ave  down- 
ly:  conse- 
izon  A  H, 
ppear  were 
the  strata 
)e  made  to 
ical  plane, 
sntre. 

e  heavenly 
in  reality, 
ir  above  it. 
Nay,  even 
lerefore  be 
ed  above  it 
)W  the  true 


horizon,  A  H,  of  the  spectator,  beoomea  visible  to  him,  as  if  it  stood  at 
p,  by  the  refracted  ray  F  q  r  t  A,  to  which  A  p  is  a  tangent. 

(41.)  The  exact  estimation  of  the  amount  of  atmospheric  refraction,  or 
the  strict  determination  of  the  angle  S  A  s,  by  which  a  celestial  object  at 
any  assigned  altitude,  H  A  S,  is  raised  in  appearance  above  its  true  place, 
is,  unfortunately,  a  very  difficult  subject  of  physical  inquiry,  and  one  on 
which  geometers  (from  whom  alone  we  can  look  for  any  information  on 
the  subject)  are  not  yet  entirely  agreed.     The  difficulty  arises  from  this, 
that  the  dennty  of  any  stratum  of  air  (on  which  its  refracting  power 
depends)  is  affected  not  merely  by  the  superincumbent  pressure,  but  also 
by  its  temperature  or  degree  of  heat.     Now,  although  we  know  that  as 
we  recede  from  the  earth's  surface  the  temperature  of  the  air  is  constantly 
diminishing,  yet  the  law^  or  amount  of  this  diminution  at  different  heights, 
is  not  yet  fully  ascertained.     Moreover,  the  refracting  power  of  air  is  per- 
ceptibly affected  by  its  moisture ;  and  this,  too,  is  not  the  same  in  every 
part  of  an  aerial  column ;  neither  are  we  acquainted  with  the  laws  of  its 
distribution.     The  consequence  of  our  ignorance  on  these  points  is  to 
introduce  a  corresponding  degree  of  uncertainty  into  the  determination  of 
the  amount  of  refraction,  which  affects,  to  a  certain  appreciable  extent, 
our  knowledge  of  several  of  the  most  important  data  of  astronomy. 
The  uncertainty  thus  induced,  is,  however,  confined  within  such  very 
uuiTow  limits  as  to  be  no  cause  of  embarrassment,  except  in  the  most 
delicate  inquiries,  and  to  call  for  no  further  allusion  in  a  treatise  like  the 
present. 

(42.)  A  "  Table  of  Refraction,"  as  it  is  called,  or  a  statement  of  the 
amount  of  apparent  displacement  arising  from  this  cause,  at  all  altitui^os, 
or  in  every  situation  of  a  heavenly  body,  from  the  horizon  to  the  zenith,^ 
or  point  of  the  sky  vertically  above  the  spectator,  and,  under  all  the 
circumstances  in  which  astronomical  observations  are  usually  performed 
which  may  influence  the  result,  is  one  of  the  most  important  and  indis- 
pensable of  all  astronomical  tables,  since  it  is  only  by  the  use  of  such  a 
table  we  are  enabled  to  get  rid  cf  an  illusion  which  must  otherwise  pervert 
all  our  notions  respecting  the  celestial  motions.  Such  have  been,  accord- 
ingly, constructed  with  great  care,  and  are  to  be  found  in  every  collection 
of  astronomical  tables.  Our  design,  in  the  present  treatise,  will  not 
admit  of  the  introduction  of  tables;  and  we  must,  therefore,  content  our- 
selves here,  and  in  similar  cases,  with  referring  the  reader  to  works 
especially  destined  to  furnish  these  useful  aids  to  calculation.    It  is,  how- 


c 

I 

\ 

3 
< 

0 

Is  IV 

pi 

% 

0 

\ 

i 


'  From  an  Arabic  word  of  this  signification. 
Chap.  II. 


See  this  term  technically  defined  in 


40 


OUTLINES   OP  ASTRONOMY. 


ever,  desirable  that  he  should  bear  in  mind  the  following  general  notions 
of  its  amount,  and  law  of  variations. 

(43.)  1st.  In  the  zsnith  there  is  no  refraction.  A  celestial  object, 
situated  vertically  over-head,  is  seen  in  its  true  direction,  as  if  there  were 
no  atmosphere,  at  least  if  the  air  be  tranquil. 

2dly.  In  descending  from  the  zenith  to  the  horizon,  the  refraction  con- 
tinually increases.  Objects  near  the  horizon  appear  more  elevated  by  it 
above  their  true  directions  tL  ya.  those  at  a  high  altitude. 

3dly.  The  rate  of  its  increase  is  nearly  in  proportion  to  the  tangent  of 
the  apparent  angular  distance  of  the  object  from  the  zenith.  But  this 
rule,  which  is  not  far  from  the  truth,  at  moderate  zenith  distances,  ceases 
to  give  correct  results  in  the  vicinity  of  the  horizon,  where  the  law 
becomes  much  more  complicated  in  its  expression. 

4thly.  The  average  amount  of  refraction,  for  an  object  half-way  between 
the  zenith  and  the  horizon,  or  at  an  apparent  altitude  of  45°,  is  about  1' 
(more  exactly  5V"),  a  quantity  hardly  sensible  to  the  naked  eye ;  but  at 
the  visible  horizon  it  amounts  to  no  less  a  quantity  than  33',  which  is 
rather  more  than  the  greatest  apparent  diameter  of  either  the  sun  or  the 
moon.  Hence  it  follows,  that  when  we  see  the  lower  edge  of  the  sun  or 
moon  just  apparently  resting  on  the  horizon,  its  whole  disk  is  in  reality 
below  it,  and  would  be  entirely  out  of  sight  and  concealed  by  the  con- 
vexity of  the  earth,  but  for  the  bending  round  it,  which  the  rays  of  light 
have  undergone  in  their  passage  through  the  air,  as  alluded  to  in  art.  40. 

5thly.  That  when  the  barometer  is  higher  than  its  average  or  mean 
state,  the  amount  of  refraction  is  greater  than  its  mean  amount ;  when 
lower,  less;  and, 

6thly.  That  in  one  and  the  same  state  of  the  barometer  the  refrac- 
tion is  greater,  the  colder  the  air.  The  variation,  owing  to  these  two 
causes,  from  its  mean  amount  (at  temp.  55°,  pressure  30  inches),  are 
about  one  420th  part  of  that  amount  for  each  degree  of  the  thermometer 
of  Fahrenheit,  and  one  300th  for  each  tenth  of  an  inch  in  the  height  of 
the  barometer. 

(44.)  It  follows  from  this,  that  one  obvious  effect  of  refraction  must  be 
to  shorten  the  duration  of  night  and  darkness,  by  actually  prolonging  the 
stay  of  the  sun  and  moon  above  the  horizon.  But  even  after  they  are  set, 
the  influence  of  the  atmosphere  still  continues  to  send  us  a  portion  of  their 
light;  not,  indeed,  by  direct  transmission,  bat  by  reflection  upon  the  va- 
pours, and  minute  solid  particles  which  float  in  it,  aud,  perhaps,  also  on 
the  actual  material  atoms  of  the  air  itself  To  understand  how  this  takes 
place,  we  must  recollect,  that  it  is  not  only  by  the  direct  light  of  a  lumi- 
nous object  that  we  see,  but  that  whatever  portion  of  its  light  which 


■!| 


TWILIGHT. 


41 


would  not  otherwise  reach  our  eyes  is  intercepted  in  its  course,  and  thrown 
back,  or  laterally,  upon  us,  becomes  to  us  a  neans  of  illumination.  Such 
reflective  obstacles  always  exist  floating  in  the  air.  The  whole  course  of  a 
sun-beam  penetrating  through  the  chink  of  a  window-shutter  into  a  dark 
room  is  visible  as  a  bright  lino  in  the  air;  and  even  if  it  be  stifled,  or  let 
out  through  an  opposite  crevice,  the  light  scattered  through  the  apartment 
from  this  source  is  sufficient  to  prevent  entire  darkness  in  the  room.  Tho 
luminous  lines  occasionally  seen  in  the  air,  in  a  sky  full  of  partially  bro- 
ken clouds,  which  the  vulgar  term  "  the  sun  drawing  water,"  are  simi- 
larly caused.  They  are  sunbeams,  through  apertures  in  the  clouds,  par- 
tially intercepted  and  reflected  on  the  dust  and  vapours  of  the  air  below. 
Thus  it  is  with  those  solar  rays  which,  after  the  sun  is  itself  concealed  by 
the  convexity  of  the  earth,  continue  to  traverse  the  higher  regions  of  the 
atmosphere  above  our  heads,  and  pass  through  and  out  of  it,  without  di- 
rectly striking  on  the  earth  at  all.  Some  portion  of  them  is  intercepted 
and  reflected  by  the  floating  particles  above  mentioned,  and  thrown  back, 
or  laterally,  so  as  to  reach  us,  and  afford  us  that  secondary  illumination, 

Fig.  5. 


which  is  twiliglt.  The  course  of  such  rays  will  be  immediately  understood 
from  the  aunexed  figure,  in  which  A  B  C  D  is  the  earth ;  A  a  point  on  its 
surface,  where  the  sun  S  is  in  the  act  of  setting ;  its  last  lower  ray  SAM 
just  grazing  the  surface  at  A,  while  its  superior  rays  S N,  SO,  traverse 
the  atmosphere  above  A  without  striking  the  earth,  leaving  it  finally  at 
the  points  P  Q  R,  after  being  more  or  less  bent  in  passing  through  it,  the 
lower  most,  the  higher  less,  and  that  which,  like  S  R  0,  merely  grazes 
the  exterior  limit  of  the  atmosphere,  not  at  all.  Let  us  consider  several 
points,  A,  B,  C,  D,  each  more  remote  than  the  last  from  A,  and  each  more 


c 

I 

i< 

0 

r 

0 

a 
r 

09 


42 


OUTLINES   OF  ASTRONOiMY. 


t  "If 


deeply  involved  in  the  earth's  shadow,  which  occupies  the  whole  space 
from  A  beneath  the  line  A  M.  Now,  A  just  receives  the  sun's  lust  direct 
ray,  and,  besides,  is  illuminated  by  the  whole  reflective  atmosphere  PQ 
R  r.  It  therefore  receives  twilight  from  the  whole  sky.  The  point  B, 
to  which  the  sun  has  set,  receives  no  direct  solar  light,  nor  any,  direct  or 
reflected,  from  all  that  part  of  its  visible  atmosphere  which  is  below  AP  M ; 
but  from  the  lenticular  portion  P  R  x,  which  is  traversed  by  the  sun's  rays, 
and  which  lies  above  the  visible  horizon  B  R  of  B,  it  receives  a  twilight, 
which  is  strongest  at  R,  the  point  immediately  below  whic'i  the  sun  is, 
and  fades  away  gradually  towards  P,  as  the  luminous  part  of  the  atmo- 
sphere  thins  off.  At  C,  only  the  last  or  thinnest  portion,  P  Q  z  of  the 
lenticular  segment,  thus  illuminated,  lies  above  the  horizon,  0  Q,  of  that 
place ;  here,  thcL,  the  twilight  is  feeble,  and  confined  to  a  small  space  in 
and  near  the  horizon,  which  the  sun  has  quitted,  while  at  D  the  twilight 
has  ceased  altogether. 

(45.)  When  the  sun  is  above  the  horizon,  it  illuminates  the  atmosphere 
and  clouds,  and  these  again  disperse  and  scatter  a  portion  of  its  light  in 
all  directions,  so  as  to  send  some  of  its  rays  to  every  exposed  point,  from 
every  point  of  the  sky.  The  generally  diffused  light,  therefore,  which  we 
enjoy  in  the  daytime,  is  a  phenomenon  originating  in  the  very  same  causes 
as  the  twilight.  Were  it  not  for  the  reflective  and  scattering  p.  ,ver  of  the 
atmosphere,  no  objects  would  be  visible  to  us  out  of  direct  sunshine ;  every 
shadow  of  a  passing  cloud  would  be  pitchy  darkness ;  the  stars  would  be 
visible  all  day,  and  every  apartment,  into  which  the  sun  had  not  direct 
admission,  would  be  involved  in  nocturnal  obscurity.  This  scattering  action 
of  the  atmosphere  on  the  solar  light,  it  should  bo  observed,  is  increased 
by  the  irregularity  of  temperature  caused  by  the  same  luminary  in  its 
different  parts,  which,  during  the  daytime,  throws  it  into  a  constant  state 
of  undulation,  and,  by  thus  bringing  together  masses  of  air  of  very  un- 
equal temperatures,  pro(1uces  partial  reflections  and  refractions  at  their 
common  boundaries,  by  which  some  portion  of  the  light  is  turned  aside 
from  the  direct  course,  and  diverted  to  the  purposes  of  general  illumina- 
tion. 

(46.)  From  the  explanation  we  aave  given,  in  arts.  39  and  40,  of  the 
nature  of  atmospheric  refraction,  and  the  mode  in  which  it  is  produced  in 
the  progress  of  a  ray  of  light  through  successive  strata,  or  layers  of  the 
atmosphere,  it  will  be  evident,  that  whenever  a  ray  passes  obliquely  from 
a  higher  level  to  a  lower  one,  or  vice  versd,  its  course  is  not  rectilinear, 
but  concave  downwards;  and  of  course  any  object  seen  by  means  of  such 
a  ray,  must  appear  deviated  from  its  true  place,  whether  that  object  be, 
]ike  the  celestial  bodies,  entirely  beyond  the  atmosphere,  or,  like  the  sum- 


TWILIGHT. 


46 


mits  of  mountains  seen  from  the  plains,  or  other  terrestrial  stations  at 
dififerent  levels  seen  from  eadh  other,  immersed  in  it.  Every  difference 
of  level,  accompanied,  as  it  must  x/e,  with  a  difference  of  density  in  the 
aerial  strata,  must  also  have,  corresponding  to  it,  a  certain  amount  of  re- 
fraction ;  less,  indeed,  than  what  would  bo  produced  by  the  whole  atmo- 
sphere, but  still  often  of  very  appreciable,  and  even  considerable,  amount. 
This  refraction  between  terrestrial  stations  is  termed  terrestrial  rr/rartion, 
to  distinguish  it  from  that  total  effect  which  is  only  produced  on  cclostiul 
objects,  or  such  as  are  beyond  the  atmosphere,  and  which  is  called  celes- 
tial or  astronomical  refraction.  -         '    *, 

(47.)  Another  effect  of  refraction  is  to  distort  the  visible  forms  and 
proportions  of  objects  seen  near  the  horizon.  The  sun,  for  instance,  which 
at  a  considerable  altitude  always  appears  round,  assumes,  as  it  approaches 
the  horizon,  a  flattened  or  oval  outline ;  its  horizontal  diameter  being  vis- 
ibly greater  than  that  in  a  vertical  direction.  When  very  near  the  horizon, 
this  flattening  is  evidently  more  considerable  on  the  lower  side  than  on  the 
upper;  so  that  the  apparent  form  is  neither  circular  nor  elliptic,  but  a  spe- 
cies of  oval,  which  deviates  more  from  a  circle  below  than  above.  This 
singular  effect,  which  any  one  may  notice  in  a  fine  sunset,  arises  from  the 
rapid  rate  at  which  the  refraction  increases  in  approaching  the  horizon. 
Were  every  visible  point  in  the  sun's  circumference  equally  raised  by  re- 
fraction, it  would  still  appear  circular,  though  displaced ;  but  the  lower 
portions  being  more  raised  than  the  upper,  the  vertical  diameter  is  thereby 
shortened,  while  the  two  extremities  of  its  horizontal  diameter  are  equally 
raised,  and  in  paraUol  directions,  ho  that  its  apparent  length  remains  the 
same.  The  dilated  size  (generally)  of  the  sun  or  moon,  when  seen  near 
the  horizon,  beyond  what  they  appear  to  have  when  high  up  in  the  sky, 
has  nothing  to  do  with  refraction.  It  is  an  illusion  of  the  judgment, 
arising  from  the  terrestrial  objects  interposed,  or  placed  in  close  coiupai*- 
ison  with  them.  In  that  situation  we  view  and  judge  of  them  as  we  do 
of  terrestrial  objects — in  detail,  and  with  an  acquired  habit  of  attention 
to  parts.  Aloft  wo  have  no  associations  to  guide  us,  and  their  insulation 
in  the  expanse  of  sky  leads  us  rather  to  undervalue  than  to  over-rate  their 
apparent  magnitudes.  Actual  measurement  with  a  proper  instrument  coi*- 
rects  our  error,  without,  however,  dispelling  our  illusion.  By  this  we 
learn,  that  the  sun,  when  just  on  the  horizon,  subtends  at  our  eyes  almost 
exactly  the  same,  and  the  moon  a  materially  less  angle,  than  when  seen 
at  a  great  altitude  in  the  sky,  owing  to  its  greater  distance  from  us  in  the 
former  situation  as  compared  with  the  latter,  as  will  be  explained  farther 
on. 

(48.)  After  what  has  been  said  of  the  small  extent  jf  the  atmosphere 


I 

V 


0 

law 

s 

Gi 
r 


i 


44 


OUTLINES   OF   ASTRONOMY. 


|i ', 


in  comparison  mth  the  moss  of  the  earth,  we  shall  have  little  hesitation 
in  admitting  those  luminaries  which  people  hnd  adorn  the  sky,  and  which, 
while  they  obviously  form  no  part  of  the  earth,  and  receive  no  support 
from  it,  are  yet  not  borne  along  at  random  like  clouds  upon  the  air,  nor 
drifted  by  the  winds,  to  be  external  to  our  atmosphere.  As  such  we  have 
considered  them  while  speaking  of  their  refractions  —  as  existing  in  the 
immensity  of  space  beyond,  and  situated,  perhaps,  for  any  thing  we  can 
perceive  to  the  contrary,  at  enormous  distances  from  us  and  from  each 
other. 

(40.)  Could  a  spectator  exist  unsustained  by  the  earth,  or  any  solid 
support,  he  would  see  around  him  at  one  view  the  whole  contents  of  space 
—  the  visible  constituents  of  the  universe :  and,  in  the  absence  of  any 
means  of  judging  of  their  distances  from  him,  would  refer  them,  in  the 
directions  in  which  they  were  seen  from  his  station,  to  the  concave  sur- 
face of  an  imaginary  sphere,  having  his  eye  for  a  centre,  and  its  surface 
at  some  vast  indeterminate  distance.  Perhaps  he  might  judge  those 
which  appear  to  him  large  and  bright,  to  be  nearer  to  him  than  the 
smalhr  and  less  brilliant;  but,  independent  of  other  moans  of  judging, 
he  would  have  no  warrant  for  this  opinion,  any  more  than  for  the  idea 
that  all  were  equidistant  from  him,  and  realty  arranged  on  such  a 
spherical  surface.  Nevertheless,  there  would  be  no  impropriety  in  his 
referrinf^  their  places,  geometrically  speaking,  to  those  points  of  such  a 
purely  imaginary  sphere,  which  their  respective  visual  rays  intersect ;  and 
there  would  be  much  advantage  in  so  doing,  as  by  that  means  their  ap- 
pearance and  relative  situation  could  be  accurately  measured,  recorded, 
and  mapped  down.  The  objects  in  a  landscape  are  at  every  variety  of 
distance  from  the  eye,  yet  we  lay  them  all  down  in  a  picture  on  one 
plane,  and  at  one  distance,  in  their  actual  apparent  proportions,  and  the 
likeness  is  not  taxed  with  incorrectness,  though  a  man  in  the  foreground 
should  be  represented  larger  than  a  mountain  in  the  distance.  So  it  is 
to  a  spectator  of  the  heavenly  bodies  pictured,  projected,  or  mapped  down 
on  that  imaginary  sphere  we  call  the  sky  or  heaven.  Thus,  we  may 
easily  conceive  that  the  moon,  which  appears  to  us  as  large  as  the  sun, 
though  less  bright,  may  owe  that  apparent  equality  to  its  greater  prox- 
imity, and  may  be  really  much  less ;  while  both  the  moon  and  sun  may 
only  appear  larger  and  brighter  than  the  stars,  on  account  of  the  remote- 
ness of  the  latter. 

(50.)  A  spectatr  ■  on  the  earth's  surface  is  prevented,  by  the  great 
mass  on  which  he  stands,  from  seeing  into  all  that  portion  of  space  which 
is  below  him,  or  to  see  which  he  must  look  in  any  degree  downwards. 
It  if  true  that,  if  his  place  of  observation  be  at  a  great  elevation,  the  dip 


of  the  horiz( 
hemisphere, 
to  luuk,  as  il 
his  visual  ri 
stances,  exce 
account  of  tl 
his  geograpl 
plane  passin 
the  earth) ;  i 
they  should 
some  rotatio 
which  he  oc( 
ferent  region 
the  objects  ( 
supposed,  mi 
stances. 

(51.)  A  t 
obtain  a  vio^ 
way  which  n 
standing  in  a 
by  its  trunk 


occupies  as  ai 
of  the  whole 
set  off  from  i 
fail  to  notice 
London  com( 
night  after  ni 


CHANQE  UF   HORIZON  IN   TRAVELLINQ. 


45 


of  the  horizon  will  bring  within  the  soopo  of  visit )Q  a  little  more  than  a 
hemisphere,  and  mf  tion,  wherever  he  may  be  }ituated,  will  enable  him 
to  louL,  as  it  were,  a  little  round  the  corner ;  but  the  zone  thus  added  to 
his  visual  range  can  hardly  ever,  unless  in  very  extraordinary  circum- 
stances, exceed  a  couple  of  degrees  in  breadth,  and  is  always  ill  seen  on 
account  of  the  vapours  near  the  horizon.  UnlesH,  then,  by  a  change  of 
his  geographical  situation,  he  should  shift  his  horizon  (which  is  always  a 
plane  passing  through  his  eye,  and  touching  the  Hpherical  convexity  of 
the  earth) ;  or  unless,  by  some  movements  proper  to  the  heavenly  bodies, 
they  should  of  themselves  come  above  his  horizon ;  or,  lastly,  unless,  by 
some  rotation  of  the  earth  itself  on  its  centre,  the  point  of  its  surface 
which  he  occupies  should  be  carried  round,  and  presented  towards  a  dif- 
ferent region  of  space ;  he  would  never  obtain  a  sight  of  almost  one  half 
the  objects  external  to  our  atmosphere.  But  if  any  of  these  cases  be 
supposed,  more,  or  all,  may  come  into  view  according  to  the  circum- 
stances. 

(51.)  A  traveller,  for  example,  shifting  his  locality  on  our  globe,  will 
obtain  a  view  of  celestial  objects  invisible  from  his  original  station,  in  a 
way  which  mo;'  be  not  inaptly  illustrated  by  comparing  him  to  a  person 
standing  in  a  ] -rk  close  to  a  large  tree.  The  massive  obstacle  presented 
by  its  trunk  cuts  off  his  view  of  all  those  parts  of  the  landscape  which  it 


Fig.  6. 


^i 


occupies  as  an  object  j  but  by  walking  round  it  a  complete  successive  view 
of  the  whole  panorama  may  be  obtained.  Just  in  the  same  way,  if  we 
set  off  from  any  station,  as  London,  and  travel  southwards,  we  shall  not 
fail  to  notice  that  many  celestial  objects  which  are  never  seen  from 
London  come  successively  into  view,  as  if  rising  up  above  the  horizon, 
night  after  night,  from  the  south,  although  it  is  in  reality  our  horizon, 


I 

5 


H 

0 
0 


I 


46 


OUTLINES   OP  ASTRONOMY. 


which,  travelling  with  us  southwards  round  the  sphere,  sinks  in  succes- 
sion beneath  them.  The  novelty  and  splendour  of  fresh  constellations 
thus  gradually  brought  into  view  in  the  clear  calm  nights  of  tropical 
climates,  in  long  voyages  to  the  south,  ia  dwelt  upon  by  all  who  have 
enjoyed  this  spectacle,  and  never  fails  to  impress  itself  on  the  rccollcttion 
among  the  most  delightful  and  interesting  of  the  associations  connected 
with  extensive  travel.  A  glance  at  the  accompanying  figure,  exhibiting 
three  successive  stations  of  u  traveller,  A,  B,  C,  with  the  horizon  corre- 
sponding to  each,  will  place  this  process  in  clearer  evidence  than  any 
description. 

(52.)  Again :  suppose  the  earth  itself  to  have  a  motion  of  rotation  on 
its  centre.  It  is  evident  that  a  spectator  at  rest  (as  it  appears  to  him) 
on  any  part  of  it  will,  unperceived  by  himself,  be  carried  round  with  it : 
unperceived,  we  say,  because  his  horizon  will  constantly  contain,  and  be 
limited  by,  the  same  terrestrial  objects.  He  will  have  the  same  land- 
scape constantly  before  his  eyes,  in  which  all  the  familiar  objects  in  it, 
which  serve  him  for  landmarks  and  directions,  retain,  with  respect  to 
himself  or  to  each  other,  the  same  invariable  situations.  The  perfect 
smoothness  and  equality  of  the  motion  of  so  vast  a  mass,  in  which  every 
object  he  sees  around  him  participates  alike,  will  (art.  15)  prevent  his 
entertaining  any  suspicion  of  his  actual  change  of  place.  Yet,  with 
respect  to  external  objects,  —  that  is  to  say,  all  celestial  ones  which  do 
not  participate  in  the  supposed  rotation  of  the  earth,  —  his  horizon  will 
have  been  all  the  while  shifting  in  its  relation  to  them,  precisely  as  in 
the  case  of  our  traveller  in  the  foregoing  article.  Recurring  to  the  figure 
of  that  article,  it  is  evidently  the  same  thing,  so  far  as  their  visibility  is 
concerned,  whether  ho  has  been  carried  by  the  earth's  rotation  succes- 
sively into  the  situations  A,  B,  C ;  or  whether,  the  earth  remaining  at 
rest,  ho  has  transferred  himself  personally  along  its  surface  to  those 
stations.  Our  spectator  in  the  park  will  obtain  precisely  the  same  view 
of  the  landscape,  whether  he  walk  round  the  tree,  or  whether  we  suppose 
it  sawed  off,  and  made  to  turn  on  an  upright  pivot,  while  he  stands  on  a 
projecting  step  attached  to  it,  and  allows  himself  to  be  carried  round  by 
its  motion.  The  only  difference  will  be  in  his  view  of  the  tree  itself,  of 
which,  in  the  f  >rmer  case,  he  will  see  every  part,  but,  in  the  latter,  only 
that  portion  of  it  which  remains  constantly  opposite  to  him,  and  imme- 
diately under  his  eye. 

(58.)  By  such  a  rotation  of  the  earth,  then,  as  we  have  supposed,  the 
horizon  of  a  stationary  spectator  will  be  constantly  depressing  itself  below 
those  objects  which  lie  in  that  region  of  space  towards  which  the  rotation 
is  carrying  him,  and  elevating  itself  above  those  in  the  opposite  quarter, 


admitting 
the  horizor 
all  such  clii 
selves  BO  s 
apprnacbinf 
horizon ;  ai 
them  as  \\i 
and  from  w 

(54.)  If 
the  same  di 
same  axis, 
position  fro 
—  it  is  mar 
tive  position 
the  same  pi 
except  sucl 
tion  still  CO 
setting,  and 
same  order, 
of  time,  ad 

(55.)  No 
the  most  im 
rising  and  £ 
of  the  heav( 
hours  of  th( 
the  regular  i 
of  that  grei 
astronomy ; 
of  the  same 

(56.)  A  1 
performed  ii 
the  motions 
our  ordinary 
It  muj>t  be  ii 
uniform  in  il 
or  diameter  < 
surface,  corn 
rotation  of  a 
ceivable,  in  ^ 


DIURNAL   ROTATION   OP  THE   EARTH. 


41 


admitting  into  view  the  former,  and  succesHivoiy  hiding  the  latter.  As 
the  liorizon  of  every  such  Hpcctator,  however,  appears  to  him  motionless, 
all  fluch  change/)  will  bo  referred  by  him  to  a  motion  in  fho  objects  them- 
selves so  successively  disclosed  and  concealed.  In  place  of  his  horizon 
approaching  the  stars,  therefore,  ho  will  judge  the  stars  to  approach  his 
horizon ;  and  when  it  passes  over  and  hides  any  of  them,  ho  will  consider 
them  as  having  sunk  below  it,  or  mt;  while  those  it  has  just  disclosed, 
and  from  which  it  is  receding,  will  seem  to  bo  rising  above  it. 

(54.)  If  wo  suppose  this  rotation  of  the  earth  to  continue  in  one  and 
the  same  direction,  —  that  is  to  say,  to  be  performed  round  one  and  the 
same  nxis^  till  it  has  completed  an  entire  revolution,  and  come  back  to  the 
position  from  which  it  set  out  when  the  spectator  began  his  observations, 
—  it  is  manifest  that  every  thing  will  then  bo  in  precisely  the  same  rela- 
tive position  as  at  the  outset :  all  the  heavenly  bodies  will  appear  to  occupy 
the  same  places  in  the  concave  of  the  sky  which  they  did  at  that  instant, 
except  such  as  may  have  actually  moved  in  the  interim ;  and  if  the  rota- 
tion still  continue,  the  same  phenomena  of  their  successive  rising  and 
setting,  and  return  to  the  same  places,  will  continue  to  be  repeated  in  the 
same  order,  and  (if  the  velocity  of  rotation  be  uniform)  in  equal  intervals 
of  time,  ad  infinitum, 

(55.)  Now,  in  this  we  have  a  lively  picture  of  that  grand  phenomenon, 
the  most  important  beyond  all  comparison  which  nature  presents,  the  daily 
rising  and  setting  of  the  sun  and  stars,  their  progress  through  the  vault 
of  the  heavens,  and  their  return  to  the  same  apparent  places  at  the  same 
hours  of  the  day  and  nighf  The  accomplishment  of  this  restoration  in 
the  regular  interval  of  twontj'-four  hours  is  the  first  instance  we  encounter 
of  that  great  law  of  periodicity,^  which,  as  we  shall  see,  pervades  all 
astronomy ;  by  which  expression  we  understand  the  continual  reproduction 
of  the  same  phenomena,  in  the  same  order,  at  equal  intervals  of  time. 

(56.)  A  free  rotation  of  the  earth  round  its  centre,  if  it  exist  and  be 
performed  in  consonance  with  the  same  mechanical  laws  which  obtain  in 
the  motions  of  masses  of  matter  under  our  immediate  control,  and  within 
our  ordinary  experience,  must  be  such  as  to  satisfy  two  ess 'utial  conditions. 
It  must  be  invariable  in  its  direction  with  respect  to  the  sphere  itself,  and 
uniform  in  its  velocity.  The  rotation  must  be  performc  i  round  an  axis 
or  diameter  of  the  sphere,  whose  poles  or  extremities,  where  it  meets  the 
surface,  correspond  always  to  the  same  points  on  the  sphere.  Modes  of 
rotation  of  a  solid  body  under  the  influence  of  external  agency  are  con- 
ceivable, in  which  the  poles  of  the  imaginary  line  or  axis  about  which  it. 


I 

\ 

3 

0 


0 

o 


'  TUfloUi,  a  gnng  round,  a  circulation  or  revolution. 


48 


OUTLINES  OF   ASTRONOMY. 


is  at  any  moment  revolving  shall  hold  no  fixed  places  on  the  surface,  but 
shift  upon  it  every  moment.  Such  changes,  however,  are  inconsistent 
Miith.  the  idea  of  a  rotation  of  a  body  of  regular  figure  about  its  axis  of 
symmetry,  performed  in  free  space,  and  without  resistance  or  obstruction 
from  any  surrounding  medium,  or  disturbing  influences.  The  complete 
absence  of  such  obstructions  draws  with  it,  of  necessity,  the  strict  fulfil- 
ment of  the  two  conditions  above  mentioned. 

(57.)  Now,  these  conditions  are  in  perfect  accordance  with  what  we 
observe,  and  what  recorded  observation  teaches  us,  in  respect  of  the  diur- 
nal motions  of  the  heavenly  bodies.  We  have  no  reason  to  believe,  from 
history,  that  any  sensible  change  has  taken  place  since  the  earliest  ages  in 
the  interval  of  time  elapsing  between  two  successive  returns  of  the  same 
star  to  the  same  point  of  the  sky ;  or,  rather,  it  is  demonstrable  from 
astronomical  records  that  no  such  change  has  taken  place.  And  with 
respect  to  the  other  condition,  —  the  permanence  of  the  axis  of  rotation, 
— the  appearances  which  any  alteration  in  that  respect  must  produce, 
would  be  marked,  as  we  shall  presently  show,  by  a  corresponding  change 
of  a  very  obvious  kind  in  the  apparent  motions  of  the  stars ;  which,  again, 
history  decidedly  declares  them  not  to  have  undergone. 

(58.)  But,  before  we  proceed  to  examine  more  in  detail  how  the  hypo- 
thesis of  the  rotation  of  the  earth  about  an  axis  accords  with  the  phe- 
nomena which  the  diurnal  motion  of  the  heavenly  bodies  oficrs  to  our 
notice,  it  will  be  proper  to  describe,  with  precision,  in  what  that  diurnal 
motion  consists,  and  how  far  it  is  participated  in  by  them  all ;  or  whether 
any  of  them  form  exceptions,  wholly  or  partially,  to  the  common  analogy 
of  the  rest.  We  will,  therefore,  suppose  the  reader  to  station  himself,  on 
a  clear  evening,  just  after  sunset,  when  the  first  stars  begin  to  appear,  in 
some  open  situation  whence  a  good  general  view  of  the  heavens  can  be 
obtained.  He  will  then  perceive,  above  and  around  him,  as  It  were,  a 
vast  concave  hemispherical  vault,  beset  with  stars  of  various  magnitudes, 
of  which  the  brightest  only  will  first  catch  bis  attention  in  the  twilight ; 
and  more  and  more  will  appear  as  the  darkness  increases,  till  the  whole 
sky  is  o^er-spangled  with  them.  When  he  has  awhile  admired  the  calm 
magnificence  of  this  glorious  spectacle,  the  theme  of  so  much  song,  and 
of  so  much  thought, — a  spectacle  which  no  one  can  view  without  emotion, 
and  without  a  longing  desire  to  know  something  of  its  nature  and  purport, 
—  let  him  fix  his  attention  more  particularly  on  a  few  of  the  most  bril- 
liant stars,  such  as  he  cannot  fail  to  recognize  again  without  mistake  after 
looking  away  from  them  for  some  time,  and  let  him  refer  their  apparent 
situations  to  some  surrounding  objects,  as  buildings,  trees,  &c.,  selecting 
purposely  such  as  are  in  difiercnt  quarters  of  his  horizon.     On  comparing 


them  again  ^ 
interval,  as  tl 
changed  theii 
ward  dircctio 
recede  from 
seen  to  appro; 
finally  sink  be 
will  be  seen 
procession,  w: 
quarter. 

(69.)  If  h< 
on  the  same  oi 
appears  to  des( 
the  sky;  that 
all  the  stars; 
respect  of  the 
lie  towards  th( 
only  remain  fo 
sight  only  the 
rise  between  th 
above  the  horij 
as  far  to  the  w 
as  rise  exactly 
semicircle,  anc 
between  the  c| 
regards  the  tii 
of  the  visible  I 
ferences.     Botl 
hours,  and  thel 
magnitudes  off 
northward;  thj 
rise  exactly  in 
will  notice,  at 
horizon  at  its 
never  reach  itl 
circles  round  o( 
centre  of  all  tl 
be  considered 
It  is  a  purely! 

*  We  suppose 
in  Europe,  for  ex 

4 


APPARENT  DIURNAL  MOTION. 


49 


them  again  with  their  respective  points  of  reference,  after  a  moderate 
interval,  as  the  night  advances,  he  will  not  fail  to  perceive  that  they  have 
changed  their  places,  and  advanced,  as  by  a  general  movement,  in  a  west- 
ward direction ;  those  towards  the  eastern  quarter  appearing  to  rise  or 
recede  from  the  horizon,  while  those  which  lie  towards  the  west  will  be 
seen  to  approach  it ;  and,  if  watched  long  enough,  will,  for  the  most  part, 
finally  sink  beneath  it,  and  disappear ;  while  others,  in  the  eastern  quarter, 
will  be  seen  to  rise  as  if  out  of  the  earth,  and,  joining  in  the  general 
procession,  will  take  their  course  with  the  rest  towards  the  opposite 
quarter. 

(59.)  If  he  persist  for  a  considerable  time  in  watching  their  motions, 
on  the  same  or  on  several  successive  nights,  be  will  perceive  that  each  star 
appears  to  describe,  as  far  as  its  course  lies  above  the  horizon,  a  circle  in 
the  sky ;  that  the  circles  so  described  are  not  of  the  same  magnitude  for 
all  the  stars;  and  that  those  described  by  different  stars  differ  greatly  in 
respect  of  the  parts  of  them  which  lie  above  the  horizon.     Some,  which 
lie  towards  the  quarter  of  the  horizon  which  is  denominated  the  South,* 
only  remain  for  a  short  time  above  it,  and  disappear,  after  describing  in 
sight  only  the  small  upper  segment  of  their  diurnal  circle ;  others,  which 
rise  between  the  south  and  east,  describe  larger  segments  of  their  circles 
above  the  horizon,  remain  proportionally  longer  in  sight,  and  set  precisely 
as  far  to  the  westward  of  south  as  they  rose  to  the  eastward ;  while  such 
as  rise  exactly  in  the  east  remain  just  twelve  hours  visible,  describe  a 
semicircle,  and  set  exactly  in  the  west.     With  those,  again,  which  rise 
between  the  east  and  north,  the  same  law  obtains;  at  least,  as  far  as 
regards  the  time  of  their  remaining  above  the  horizon,  and  the  proportion 
of  the  visible  segment  of  their  diurnal  circles  to  their  whole  circum- 
ferences.    Both  go  on  increasing;  they  remain  in  view  more  than  twelve 
hours,  and  their  visible  diurnal  arcs  are  more  than  semicircles.     But  the 
magnitudes  of  the  circles  themselves  diminish,  as  we  go  from  the  cast, 
northward ;  the  greatest  of  all  the  circles  being  described  by  those  which 
rise  exactly  in  the  east  point.     Carrying  his  eye  farther  northwards,  he 
^    will  notice,  at  length,  stars  which,  in  their  diurnal  motion,  just  graze  the 
horizon  at  its  north  point,  or  only  dip  below  it  for  a  moment ;  while  others 
never  reach  it  at  all,  but  continue  always  above  it,  revolving  in  entire 
circles  round  one  point  called  the  pole,  which  appears  to  be  the  common 
centre  of  all  their  motions,  and  which  alone,  in  the  whole  heavens,  may 
be  considered  immoveable.    Not  that  this  point  is  marked  by  any  star. 
It  is  a  purely  imaginary  centre ;  but  there  is  near  it  one  considerably 

'  We  suppose  our  observer  to  be  stationed  in  some  northern  latitude ;  some  where 
in  Europe,  for  example. 
4 


■  ^^ 

ffi 

V** 

g 
a 

C 
% 

2 


60 


OUTLINES   OF  ASTRONOMY. 


«    \ 


bright  star,  called  the  Pole  Star,  which  is  easily  recognized  by  the  very 
small  circle  it  describes;  so  small,  indeed,  that,  without  paying  particular 
attention,  and  referring  its  position  very  nicely  to  some  fixed  mark,  it  may 
easily  be  supposed  at  rest,  and  be,  itself,  mistaken  for  the  common  centre 
about  which  all  the  others  in  that  region  describe  their  circles ;  or  it  may 
be  known  by  its  configuration  with  a  very  splendid  and  remarkable  con- 
stellation or  group  of  stars,  called  by  astronomers  the  Great  Bear. 

(60.)  He  will  farther  observe,  that  the  apparent  relative  situations  of 
all  the  stars  among  one  another,  is  not  changed  by  their  diurnal  motion. 
In  whatever  parts  of  their  circles  they  are  observed,  or  at  whatever  hour 
of  the  night,  they  form  with  each  other  the  same  identical  groups  or  con- 
figurations, to  which  the  name  of  constellations  has  been  given.  It 
is  true,  that,  in  different  parts  of  their  course,  these  groups  stand  dif- 
ferently with  respect  to  the  horizon ;  and  those  towards  the  north,  when 
in  the  course  of  their  diurnal  movement  they  pass  alternately  above  and 
below  that  common  centre  of  motion  described  in  the  last  article,  become 
actually  inverted  with  respect  to  the  horizon,  while,  on  the  other  hand, 
they  always  turn  the  same  points  towards  the  pole.  In  short,  he  will 
perceive  that  the  whole  assemblage  of  stars  visible  at  once,  or  in  succes- 
sion, in  the  heavens,  may  be  regarded  as  one  great  constellation,  which 
seems  to  revolve  with  a  uniform  motion,  as  if  it  formed  one  coherent 
mass ;  or  as  if  it  were  attached  to  the  infernal  surface  of  a  vast  JboU^ 
sphere,  having  the  earlh,  or  rather  the  spectator,  in  its  centre,  anc^orni|lg 
round  an  axis  inclined  to  his  horizon,  so  as  to  pass  through  tliM  fi:^^ 
point  OT  pole  already  mentioned.  • 

(61.)  Lastly,  he  will  notice,  if  he  have  patience  to  outwatch  a  long 
winter's  night,  commencing  at  the  earliest  moment  when  the  stars  appear, 
and  continuing  till  morning  twilight,  that  those  stars  which  he  observed 
setting  in  the  west  have  again  risen  in  the  east,  while  those  which  were 
rising  when  he  first  began  to  notice  them  have  completed  their  course,  and  I 
are  now  set ;  and  that  thus  the  hemisphere,  or  a  great  part  of  it,  which  I 
was  then  above,  is  now  beneath  him,  and  its  place  supplied  by  that  which 
was  at  first  under  his  feet,  which  he  will  thus  discover  to  be  no  less! 
copiously  furnished  with  stars  than  the  other,  and  bespangled  with  groups  i 
no  less  permanent  and  distinctly  recognizable.     Thus  he  will  learn  that 
the  great  constellation  that  we  have  above  spoken  of  as  revolving  round  1 
the  pole  is  co-extensive  with  the  whole  surface  of  the  sphere,  being  in  j 
reality  nothing  less  than  a  universe  of  luminaries  surrounding  the  earth 
on  all  sides,  and  brought  in  succession  before  his  view,  and  referred  (each 
luminary  according  to  its  own  visual  ray  or  direction  from  his  eye)  to  the 
imaginary  spherical  surface,  of  which  he  himself  occupies  the  centre. 


zon,  and  shov 


APPARENT  DIURNAL   MOTION. 


61 


le  very 
rticular 
it  may 
1  centre 
it  may 
ble  con- 

tions  of 

motion. 

^-er  hour 

3  or  con- 
ven.  It 
land  dif- 
th,  when 
aove  and 
,  become 
er  hand, 
,  he  will 
n  succes- 
m,  which 

coherent 

3t  hollc^  j 

4  tamifg 

ih  a  long 
rs  appear, 

5  observed  1 
'hich  were  = 
ourse,  and  \ 
'  it,  which  \ 
;hat  which  I 
be  no  less- 
ith  groups 
learn  that 

^^ing  round 
!,  being  in , 
;  the  earth 
jrred  (each 
eye)  to  the 
)he  centre. 


(See  art.  49.)  There  is  always,  therefore  (he  woald  justly  argue),  a  star- 
bespangled  canopy  over  his  head,  by  day  as  well  as  by  night,  only  that 
the  glare  of  daylight  (which  he  perceives  gradually  to  eflFace  the  stars  as 
the  morning  twilight  comes  on)  prevents  them  from  being  seen.  And 
such  is  really  the  case.  The  stars  actually  continue  visible  through  teles- 
copes in  the  day-time ;  and,  in  proportion  to  the  power  of  the  instrument, 
not  only  the  largest  and  brightest  of  them,  but  even  those  of  inferior 
lustre,  such  as  scarcely  strike  the  eye  at  night  as  at  all  conspicuous,  are 
readily  found  and  followed  even  at  noonday, —  unless  in  that  part  of  the 
sky  which  is  very  near  the  sun, —  by  those  who  possess  the  means  of 
pointing  a  telescope  accurately  to  the  proper  places.  Indeed,  from  the 
bottoms  of  deep  narrow  pits,  such  as  a  well,  or  the  shaft  of  a  mine,  such 
bright  stars  as  pass  the  zenith  may  even  be  discerned  by  the  naked  eye ; 
and  we  have  ourselves  heard  it  stated  by  a  celebrated  optician,  that  the 
earliest  circumstance  which  drew  his  attention  to  astronomy  was  the 
regular  appearance,  at  a  certain  hour,  for  several  successive  days,  of  a 
considerah^  ■  star,  through  the  shaft  of  a  chimney.  Venus  in  our  climate, 
and  even  ,  ';  r  in  the  clearer  skies  of  tropical  countries,  are  often 
visible,  Wi  'r  .  L  any  artificial  aid,  to  the  naked  eye  of  one  who  knows 
nearly  where  to  look  for  them.  During  total  eclipses  of  the  sun,  the 
larger  stars  also  appear  in  their  proper  situations. 

(62.)  But  to  return  to  our  incipient  astronomer,  whom  we  left  contem- 
plating the  sphere  of  the  heavens,  as  completed  in  imagination  beneath 
his  feet,  and  as  rising  up  from  thence  in  its  diurnal  course.  There  is  one 
portion  or  segment  of  this  sphere  of  which  he  will  not  thus  obtain  a  view. 
As  there  is  a  segment  towards  the  north,  adjacent  to  the  pole  above  his 
horizon,  in  which  the  stars  never  set,  so  there  is  a  corresponding  segment, 
about  which  the  smaller  circles  of  the  more  southern  stars  are  described, 
in  which  they  never  rise.  The  stars  which  border  upon  the  extreme 
circumference  of  this  segment  just  graze  the  southern  point  of  his  hori- 
zon, and  show  themselves  for  a  few  moments  above  it,  precisely  as  those 
near  the  circumference  of  the  northern  segment  graze  his  northern  hori- 
zon, and  dip  for  a  moment  below  it,  to  re-appear  immediately.  Every 
point  in  a  spherical  surface  has,  of  course,  another  diametrically  opposite 
to  it ;  and  as  the  spectator's  horizon  divides  his  sphere  into  two  hemi- 
spheres—  a  superior  and  inferior  —  there  must  of  necessity  exist  a  de- 
pressed pole  to  the  south,  corresponding  to  the  elevated  one  to  the  north, 
and  a  portion  surro^mding  it,  perpetually  beneath,  as  there  is  anotber 
surrounding  the  north  pole,  perpetually  above  it. 

"  Hie  vertex  nobis  Bemper  subiimis ;  at  ilium 
Sub  pcdibus  nox  atra  videt,  manesque  profundi." — Virqil. 


I 


pi 

r 
0 
a 

S3 


52 


OUTLINES   OP  ASTRONOMY. 

One  pole  rides  high,  one,  phinged  beneath  the  main, 
Seeks  the  deep  nigiit,  and  Pluto's  dusky  reign. 


'■| 


(63.)  To  get  sight  of  this  segment,  he  must  travel  southwards.  In  so 
doing,  0  rew  set  of  phenomena  come  forward.  In  proportion  as  he 
advance  lO  the  south,  some  of  those  constellations  which,  at  his  original 
station,  barely  grazed  the  northern  horizon,  will  be  observed  to  sink  below 
it  and  set ;  at  first  remaining  hid  only  for  a  very  short  time,  but  gradually 
for  a  longer  part  of  the  twenty-four  hours.  They  will  continue,  however, 
to  circulate  about  the  same  point  —  that  is,  holding  the  same  iL.variable 
position  with  respect  to  the.  .  in  the  concave  of  the  heavens  among  the 
stars ;  but  this  point  itself  will  become  gradually  depressed  with  respect 
to  the  spectator's  horizon.  The  axis,  in  short,  about  which  the  diurnal 
motion  is  performed,  will  appear  to  have  become  continually  less  and  less 
inclined  to  the  horizon;  and  by  the  same  degrees  as  the  northern  poV.  is 
depressed  the  southern  will  rise,  and  constellations  surrounding  it  will 
come  into  view ;  at  first  momentarily,  but  by  degrees  for  longer  and  longer 
times  in  each  diurnal  revolution  —  realizing,  in  short,  what  we  have 
already  stated  in  art.  51. 

(64.)  If  he  travel  continually  southwards,  he  will  at  length  reach  a 
line  on  the  earth's  surface,  called  the  equator,  at  any  point  of  which, 
indifferently,  if  he  take  up  his  station  and  recommence  his  observations, 
he  will  find  that  he  has  both  the  centres  of  diurnal  motion  in  his  horizon, 
occupying  opposite  points,  the  northern  pole  having  been  depressed,  and 
the  southern  raised ;  so  that,  in  this  geographical  position,  the  diurnal 
rotation  of  the  heavens  will  appear  to  him  to  be  performed  about  a  hori- 
zontal axis,  every  star  describing  half  its  diurnal  circle  above  and  half 
beneath  his  horizon,  remaining  alternately  visible  for  twelve  hours,  and 
concealed  during  the  same  interval.  In  this  situation,  no  part  of  the 
heavens  is  concealed  from  his  successive  view.  In  a  night  of  twelve  hours 
(supposing  such  a  continuance  of  darkness  possible  at  the  equator)  the 
whole  sphere  will  have  passed  in  review  over  him — the  whole  hemisphere 
with  which  he  began  his  night's  observation  will  have  been  carried  down 
beneath  him,  and  the  entire  opposite  one  brought  up  from  below. 

(G5.)  If  he  pass  the  equator,  and  travel  still  farther  southwards,  the 
southern  poles  of  the  heavens  will  become  elevated  above  his  horizon,  and 
the  northern  will  sink  below  it ;  and  the  more,  the  farther  he  advances 
southward?;  and  when  arrived  at  a  station  as  far  to  the  south  of  the 
equator  as  that  from  which  he  started  was  to  the  north,  he  will  find  the 
whole  phenomena  of  the  heavens  reversed.  The  stars  which  at  his  origi- 
nal station  described  their  whole  diurnal  circles  above  his  horizon,  and 
never  set,  now  describe  them  entirely  below  it,  and  never  rise,  but  remain 


constantly  i 
station  he  n 
(66.)  FiE 
he  travel  no 
become  mor 
below  it.     I 
stars,  becaug 
remains  com 
each  star,  to( 
t  very  appear 
t«  >itb,  he  woi 
of  the  heave 
each  would  < 
endeavours  1 
pole  of  the  e 
mountable  d 
climate  :  but 
mena  of  thos 
what  must  su 
dence  with  it 
pole  of  the  ( 
has  been  less 
(67.)  The 
of  the  stars,  a 
on  any  specul 
voyagers.     It 
a  rotation  of 
ever,  it  will  I 
motion  in  gen 
remote  objectj 
scribed  statior 
(68.)  It  ha 
and  surroundi 
the  same  moti 
idea  to  object 
which  ho  leai 
advances   tow 
objects  at  rest 
we  are  in  moti 
other  —  they 
rapidly  along 


PARALLACTIC    MOTION. 


68 


ards,  the 
izon,  and 
advances 
I  of  the 
find  the 
his  origi- 
izon,  and 
it  remain 


constantly  invisible  to  him ;  and  vice  versd,  those  stars  which  at  his  former 
station  he  never  saw,  he  will  now  never  cease  to  see. 

(66.)  Finally,  if,  instead  of  advancing  southwards  from  his  first  station, 
he  travel  northwards,  he  will  observe  the  northern  pole  of  the  heavens  to 
become  more  elevated  above  his  horizon,  and  the  southern  more  depressed 
below  it.  In  conseauence,  his  hemisphere  will  present  a  less  variety  of 
stars,  because  a  greater  proportion  of  the  whole  surface  of  the  heavens 
raraains  constantly  visible  or  constantly  invisible :  the  circle  described  by 
each  star,  too,  becomes  more  nearly  parallel  to  the  horizon ;  and,  in  short, 
I  very  appearance  leads  to  suppose  that  could  he  travel  far  enough  to  the 
li  nth,  he  would  at  length  attain  a  point  vertically  under  the  northern  pole 
of  the  heavens,  at  which  none  of  the  stars  would  either  rise  or  set,  but 
each  would  circulate  round  the  horizon  in  circles  parallel  to  it.  Many 
endeavours  have  been  made  to  reach  this  point,  which  is  called  the  north 
pole  of  the  earth,  but  hitherto  without  success  j  a  barrier  of  almost  insur- 
mountable diflScuIty  being  presented  by  the  increasing  rigour  of  the 
climate  :  but  a  very  near  approach  to  it  has  been  made ;  and  the  pheno- 
mena of  those  regions,  though  not  precisely  such  as  we  have  described  as 
what  must  subsist  at  the  pole  itself,  have  proved  to  be  in  exact  correspon- 
dence with  its  near  proximity.  A  similar  remark  applies  to  the  south 
pole  of  the  earth,  which,  however,  is  more  unapproachable,  or,  at  least, 
has  been  less  nearly  approached,  than  the  north. 

(67.)  The  above  is  an  account  of  the  phenomena  of  the  diurnal  motion 
of  the  stars,  as  nodified  by  different  geographical  situations,  not  grounded 
on  any  speculation,  but  actually  observed  and  recorded  by  travellers  and 
voyagers.  It  is,  however,  in  complete  accordance  with  the  hypothesis  of 
a  rotation  of  the  earth  round  a  fixed  axis.  In  order  to  show  this,  how- 
ever, it  will  be  necessary  to  premise  a  few  observations  on  parallactic 
motion  in  general,  and  on  the  appearances  presenitv.  by  an  assemblage  of 
remote  objects,  when  viewed  from  different  parts  of  a  small  and  circum- 
scribed station. 

(68.)  It  has  been  shown  (art.  16)  that  a  spectator  in  smooth  motion, 
and  surrounded  by,  and  forming  part  of,  a  great  system  partaking  of 
the  same  motion,  is  unconscious  of  his  own  movement,  and  transfers  it  in 
idea  to  objects  external  and  unconnected,  in  a  contrary  direction )  those 
which  ho  leaves  behind  appearing  to  recede  from,  and  those  which  he 
advances  towards  to  approach,  him  Not  only,  however,  do  external 
objects  at  rest  appear  in  motion  gererally,  with  jrespect  to  ourselves  when 
we  are  in  motion  among  them,  but  they  appear  to  move  one  among  the 
other  —  they  shift  their  relative  apparent  places.  Let  any  one  travelling 
rapidly  along  a  high  road  fix  his  eye  steadily  on  any  object,  but  at  the 


I 

s 

< 


(3 

a 


^ 

2 


64 


OUTLINES   OF  ASTRONOMY. 


same  time  not  entirely  withdraw  his  attention  from  the  general  landscape, 
— he  will  see,  or  think  he  sees,  the  whole  landscape  thrown  into  rotation, 
and  moving  round  that  object  as  a  centre;  all  objects  between  it  and 
himself  appearing  to  move  hackwards,  or  the  contrary  way  to  his  own 
motion;  and  all  beyond  it,  forwards,  or  in  the  direction  in  which  he 
moves:  i  let  him  withdraw  hi8  eye  from  that  object,  and  fix  it  on 
another,  -  ,  n'^arer  one,  for  instance,  —  immediately  the  appearance  of 
rotation  sui.fts  also,  and  the  apparent  centre  about  which  this  illusive 
circulation  is  performed  is  transferred  to  the  new  object,  which,  for  the 
moment,  appears  to  rest.  This  apparent  change  of  situation  of  objects 
with  respect  to  one  another,  arising  from  a  motion  of  the  spectator,  is 
called  a  parallactic  motion.  To  see  the  reason  of  it  we  must  consider 
that  the  position  of  every  object  is  referred  by  us  to  the  surface  of  an 
imaginary  sphere  of  an  indefinite  radius,  having  our  eye  for  its  centre : 

Fig.  7. 


and,  as  we  advance  in  any  direction,  A  B,  carrying  this  imaginary  sphere 
along  with  us,  the  visual  rays  A  P,  A  Q,  by  which  objects  are  referred  to 
its  surface  (at  C,  for  instance),  shift  their  positions  with  respect  to  the 
line  in  which  we  move,  A  B,  which  serves  as  an  axis  or  line  of  reference, 
and  assume  new  positions,  B  P  p,  B  Q  g-,  revolving  round  their  respective 
objects  as  centres.  Their  intersections,  therefore,  p,  q,  with  our  visual 
sphere,  will  appear  to  recede  on  its  surface,  but  with  different  degrees  of 
angular  velocity  in  proportion  to  their  proximity ;  the  same  distance  of 
advance  A  B  subtending  a  greater  angle,  A  P  B  =  c  P  p,  at  the  near 
object  P  than  at  the  remote  one  Q. 

(69.)  A  consequence  of  the  familiar  appearance  we  have  adduced  in 
illustration  of  these  principles  is  worth  noticing,  as  we  shall  have  occa- 
sion to  refer  to  it  hereafter.  We  observe  that  every  object  nearer  to  us 
than  that  on  which  our  eye  is  fixed  appears  to  recede,  and  those  farther 
from  us  to  advance  in  relation  to  one  another.  If  then  we  did  not  know, 
or  could  not  judge  by  any  other  appearances,  wliich  of  two  objects  were 
nearer  to  us,  this  apparent  advance  or  recess  of  one  of  them,  when  the 
eye  is  kept  steadily  fixed  on  the  other,  would  furnish  a  criterion.     In  a 


PARALLACTIC    MOTION. 


65 


dark  night,  for  instance,  when  all  intermetliato  objects  arc  unseen,  the 
upparent  relative  movement  of  two  lights  which  we  are  assured  are  them- 
selves fixed,  will  decide  as  to  their  relative  proximities.  That  which  seems 
to  advance  with  us  and  gain  upon  the  other,  or  leave  it  behind  it,  is  the 
farthest  from  us. 

(70.)  The  apparent  angular  motion  of  an  object,  arising  from  a  change 
of  our  point  of  view,  is  called  in  general  jmmllax,  and  it  is  always  ex- 
pressed by  tJie  angle  APB  subtended  at  the  ohj'ect  P  (see  fig.  of  art.  68) 
by  a  line  joining  the  two  points  of  view  A  B  under  consideration.  For 
i<-  is  evident  that  the  difference  of  angular  position  of  P,  with  respect  to 
the  invariable  direction  ABB,  when  viewed  from  A  and  from  B,  is  the 
difference  of  the  two  angles  DBP  and  DAP ;  now,  DBP  being  the  exte- 
rior angle  of  the  triangle  ABP,  is  equal  to  the  sum  of  the  interior  and 
opposite,  DBP  =  DAP  +  APB,  whence  DBP  —  DAP  =  APB. 

(71.)  It  follows  from  what  has  been  said  that  the  amount  of  parallactic 
motion  arising  from  any  given  change  of  our  point  of  view  is,  ra:teris 
jmribus,  less,  as  the  distance  of  an  object  viewed  is  greater;  and  when 
that  distance  is  extremely  great  in  compar  with  the  change  in  our 
point  of  view,  the  parallax  becomes  insensible ;  or,  in  other  words,  objects 
do  not  appear  to  vary  in  situation  at  all.  It  is  on  this  principle,  that  in 
alpine  regions  visited  for  the  first  time  we  are  surprised  and  cjnfounded 
at  the  little  progress  we  appear  to  make  by  a  considerable  change  of 
place.  An  hour's  walk,  for  instance,  produces  but  a  small  parallactic 
change  in  the  relative  situations  of  the  vast  and  distant  masses  which 
surround  us.  Whether  we  walk  round  a  circle  of  a  hundred  yards  in 
diameter,  or  merely  turn  ourselves  round  in  its  centre,  the  distant  pano- 
rama presents  almost  exactly  the  same  aspect, — we  hardly  seem  to  have 
changed  our  point  of  view. 

(72.)  Whatever  notion,  in  other  respects,  we  may  form  of  the  stars,  it 
is  quite  clear  they  must  be  immensely  distant.  Were  it  not  so,  the  appa- 
rent angular  interval  between  any  two  of  them  seen  over-head  would  be 
much  greater  than  when  seen  near  the  horizon,  and  the  constellations, 
instead  of  preserving  the  same  appearances  and  dimensions  during  their 
whole  diurnal  course,  would  appear  to  enlarge  as  they  rise  higher  in  the 
sky,  as  we  see  a  small  cloud  in  the  horizon  swell  into  a  great  over- 
shadowing canopy  when  drifted  by  the  wind  across  our  zenith,  or  as  may 
be  seen  in  the  annexed  figure,  where  uh,  AB,  a 6,  are  three  different 
positions  of  the  same  stars,  as  they  would,  if  near  the  earth,  be  seen 
from  a  spectator  S,  under  the  visual  angles  «  S  b,  ASB.  No  such  change 
of  apparent  dimension,  however,  is  observed.  The  nicest  measurements 
.  of  the  apparent  angular  distance  of  any  two  stars  inter  se,  taken  in  any 


c 

■I 

I! 

3 
< 

0 


r 
a 
a 


C 


56 


')■    I 


OUTLINES   OF   ASTRONOMY. 
Fig.  8. 


parts  of  their  diurnal  course,  (after  allowing  for  the  unequal  effects  of 
refraction,  or  when  taken  at  such  times  that  this  cause  of  distortion  shall 
act  equally  on  both,)  manifest  not  the  slightest  perceptible  variation. 
Not  only  this,  but  at  whatever  point  of  the  earth's  surface  the  measure- 
ment is  performed,  the  results  are  ahsolntcli/  identical.  No  instruments 
ever  yet  invented  by  man  are  delicate  enough  to  indicate,  by  an  increase 
or  diminution  of  the  angle  subtended,  that  one  point  of  the  earth  is  nearer 
to  or  further  from  the  stars  than  another. 

(73.)  The  necessary  conclusion  from  this  is,  that  the  dimensions  of 
the  earth,  large  as  it  is,  are  comparatively  nothing,  absolutely  impercep- 
tible, when  compared  with  the  interval  which  separates  the  stars  from  the 
earth.  If  an  observer  walk  round  a  circle  not  more  than  a  few  yards  in 
diameter,  and  from  different  points  in  its  circumference  measure  with  a 
sextant  or  other  more  exact  instrument  adapted  for  the  purpose,  the 
angles  PAQ,  PBQ,  PCQ,  subtended  at  those  stations  by  two  well-defined 
points  in  his  visible  horizon,  PQ,  he  will  at  once  be  advertised,  by  the 
difference  of  the  re&ults,  of  his  change  of  distance  from  them  arising  from 
his  change  of  place,  although  that  difference  may  be  so  small  as  to  pro- 
duce no  change  in  their  general  aspect  to  his  unassisted  sight.  This  is 
one  of  the  innumerable  instances  where  accurate  measurement  obtained 
by  instrumental  means  places  us  in  a  totally  different  situation  in  respect 
to  matters  of  fact,  and  conclusions  thence  deducible,  from  what  we  should 
hold,  were  we  to  rely  in  all  cases  on  the  mere  judgment  of  the  eye.  To 
so  great  a  nicety  have  such  observations  been  carried  i)y  the  aid  of  an 
instrument  called  a  theodolite,  that  a  circle  of  the  diameter  above  men- 
tioned may  thus  be  rendered  sensible,  may  thus  be  detected  to  have  a 
size,  and  an  ascertainable  place,  by  reference  to  objects  distant  by  fully 
100,000  times  its  own  dimensions.  Observations,  differing,  it  is  true, 
somewhat  in  method,  but  identical  in  principle,  and  executed  with  quite 
as  much  exactness,  have  been  applied  to  the  stars,  and  with  a  result  such 
as  has  been  already  stated.     Hence  it  follows,  incon trover tibly,  that  the 


THE   DISTANCE  OF   THE   STARS  IMMENSE. 


w 


distance  of  the  stars  from  the  earth  cannot  be  so  small  as  100,000  of  the 
earth's  diameters.  It  is,  indeed,  incomparably  greater;  for  we  shall  here- 
after find  it  fully  demonstrated  that  the  distance  just  named,  immense  as 
it  may  appear,  is  yet  much  underrated. 

(74.)  From  such  a  distance,  to  a  spectator  with  our  faculties,  and 
furnished  with  our  instruments,  the  earth  would  be  imperceptible ;  and, 
reciprocally,  an  object  of  the  earth's  size,  placed  at  the  distance  of  the 
stars,  would  be  equally  undiscernible.  If,  therefore,  at  the  point  on  which 
a  spectator  stands,  we  draw  a  plane  touching  the  globe,  and  prolong  it  in 
imagination  till  it  attain  the  region  of  the  stars,  and  through  the  centre 
of  the  earth  conceive  another  plane  parallel  to  the  former,  and  co-exteroivo 
with  it,  to  pass;  these,  although  separated  throughout  their  whole  exteut 
by  the  same  interval,  viz.,  a  semi-diameter  of  the  earth,  will  yet,  on  ac- 
count of  the  vast  distance  at  which  that  interval  is  seen,  be  confounded 
together,  and  undistinguishable  from  each  other  in  the  region  of  the  stars, 
when  viewed  by  a  spectator  on  the  earth.  The  zone  they  there  include 
will  be  of  evanescent  breadth  to  his  eye,  and  will  only  mark  out  a  great 
circle  in  the  heavens,  one  and  the  same  for  both  the  stations.  This  great 
circle,  when  spoken  of  as  a  circle  of  the  sphere,  is  called  the  celestial  Jtori- 
zon  or  simply  the  horizon,  and  the  two  planes  just  described  are  also  spoken 
of  as  the  sensible  and  the  rational  horizon  of  the  observer's  station. 

(75.)  From  what  has  been  said  (art.  73)  of  the  distance  of  the  stars, 
it  follows,  that  if  we  suppose  a  spectator  at  the  centre  of  lie  earth  to  have 
his  view  bounded  by  the  rational  horizon,  in  exactly  the  same  manner  as 
that  of  a  corresponding  spectator  on  the  surface  is  by  his  sensible  horizon, 
the  two  observers  will  see  the  same  stars  in  the  same  relative  situations, 
each  beholding  that  entire  hemisphere  of  the  heavens  which  is  above  the 
celestial  horizon,  corresponding  to  their  common  zenith.     Now,  so  far  as 


c 

I 

s 

0 


o 
o 


r 


58 


OUTLINES   OF   ASTUONOMV. 


appearances  go,  it  is  clearly  the  same  thing  whithur  the  heavens,  that  is, 
all  space,  with  its  contents,  rcvt)lvo  round  a  npectator  at  rest  in  the  earth's 
centre,  or  whether  that  spectator  simply  turn  round  in  the  opposite  direc- 
tion in  his  place,  and  view  tbem  in  succession.  The  aspect  of  the  heavens, 
at  every  instant,  as  referred  to  his  horizon  (which  must  bo  supposed  to 
turn  with  him),  will  be  the  same  in  both  suppositions.  And  since,  as  has 
been  shown,  appearances  arc  also,  so  far  as  the  stars  are  concerned,  the 
same  to  a  spectator  on  the  surface  as  to  one  at  the  centre,  it  follows  that, 
whether  we  suppose  the  heavens  to  revolve  without  the  earth,  or  the  earth 
within  the  heavens,  in  the  oppo)iite  direction,  the  diurnal  phenomenon,  to 
all  its  inhabitants,  will  be  no  way  different. 

(70.)  The  Copernican  astronomy  adopts  the  latter  tts  the  true  explana- 
tion of  these  phenomena,  avoiding  thereby  the  necessity  of  otherwise  re- 
sorting to  the  cumbrous  mechanism  of  a  solid  but  invisible  sphere,  to 
which  the  stars  must  bo  supposed  attached,  in  order  that  they  may  be 
carried  round  the  earth  without  derangement  of  their  relative  situations 
inter  se.  Such  a  contrivance  would,  indeed,  suffice  to  explain  the  diurnal 
revolution  of  the  stars,  so  as  to  ''save  appearances;"  but  the  movements 
of  the  sun  and  moon,  us  well  as  t'  jse  of  the  planets,  are  incompatible  with 
such  a  supposition,  as  will  appear  when  we  come  to  treat  of  these  bodies. 
On  the  other  hand,  that  a  spherical  mass  of  moderate  dimensions  (or, 
rather,  when  conjpared  with  the  surrounding  and  visible  universe,  of  eva- 
nescent magnitude),  held  by  no  tie,  and  free  to  move  and  to  revolve,  should 
do  so,  in  conformity  with  those  general  laws  which,  so  far  as  we  know, 
regulate  the  motions  of  all  material  bodies,  is  so  far  from  being  a  postulate 
difficult  to  be  conceded,  that  the  wonder  would  rather  be  should  the  fact 
prove  otherwise.  As  a  postulate,  therefore,  we  shall  henceforth  regard  it ; 
and  as,  in  the  progress  of  our  work,  analogies  offer  themselves  in  its  sup- 
port from  what  we  observe  of  other  celestial  bodies,  we  shall  not  fail  to 
point  them  out  to  the  reader's  notice. 

(77.)  The  earth's  rotation  on  its  axis  so  admitted,  explaining,  as  it  evi- 
dently docs,  the  apparent  motion  "f  the  stars  in  a  completely  satisfactory 
manner,  prepares  us  for  the  frrtL'T  udnjission  of  its  motion,  bodily,  in 
space,  should  such  a  motion  enable  us  to  explain,  in  a  manner  equally  so, 
the  apparently  complex  and  eniginaticul  motions  of  the  sun,  moon,  and 
planets.  The  Copernican  astronomy  adopts  this  idea  in  its  full  extent, 
ascribing  to  the  earth,  in  addition  to  its  motion  of  rotation  about  an  axis, 
also  one  of  translation  or  transference  through  space,  in  such  a  course  or 
orhitf  and  so  regulated  in  direction  and  celerity,  as,  taken  in  conjunction 
with  the  motions  of  the  other  bodies  of  the  universe,  shall  render  a  ration- 


al account  o 
an  account  i 
intelligibly  I 
as  conclude 
it  is  rather  i 
simply  assu 
mechanical  ( 
Newtonian  i 
that  all  the 
no  others  ca 
law,  has  giv 
which  attacl 
(78.)  To 
reader  must 
solute  motioi 
rest  view  a  c 
themselves  ti 
what  they  w 
one  of  them, 
what  has  bet 
is  such  a  spc 
apparent  mo 
effect  of  his 
(or,  as  a  Gei 
only  to  him 
ing  a  positi 
rule  is  he  to 
self  in  moti 
no  means  fo 
caption  of  al 
I*  to  him  woul 
still  appean 
rence  to  th( 
(as,  indeed, 
real  movemc 
by  the  eye  a 
of  perspecti 
the  dimensi 
situated,  as, 
case  we  havi 


RELATIVE   MOTION. 


51 


as  it  cvi- 
itisfactory 
bodily,  in 
(]ually  so, 
noon,  and 
ill  extent, 
it  an  axis, 

course  or 
on  junction 


al  account  of  tho  appearances  thoy  successivoly  present, —  that  is  to  say, 
an  account  of  which  tho  several  parts,  postulates,  propositions,  deductions, 
intelligibly  cohere,  without  contradicting  each  other  or  tho  nature  of  things 
as  concluded  from  experience.  In  this  view  of  tho  Copernican  doctrine 
it  is  rather  a  geometrical  conception  than  a  physical  theory,  inasmuch  as  it 
simply  assumes  the  requisite  motions,  without  attempting  to  explain  their 
mechanical  origin,  or  assign  them  any  dependence  on  physical  causes.  Tho 
Newtonian  theory  of  gravitation  supplies  this  deficiency,  and,  by  showing 
that  all  the  motions  required  by  the  Copernican  conception  muxf,  and  that 
no  others  can,  result  from  a  single,  intelligible,  and  very  simple  dynamical 
law,  has  given  a  degree  of  certainty  to  this  conception,  as  a  matter  of  fact, 
which  attaches  to  no  other  creation  of  the  human  mind. 

(78.)  To  understand  this  conception  in  its  further  developments,  the 
reader  must  bear  steadily  in  mind  tho  distinction  between  relative  and  ah- 
solute  motion.  Nothing  is  easier  tu  perceive  than  that,  if  a  spectator  at 
rest  view  a  certain  number  of  moving  objects,  l.hoy  will  group  and  arrange 
themselves  to  his  vye,  at  each  successive  moment,  in  a  very  dift'eront  way  from 
what  they  would  do  were  ho  in  active  motion  among  them, —  if  he  formed 
one  of  them,  for  instance,  and  joined  in  their  dance.  This  is  evident  from 
what  has  been  said  before  of  parallactic  motion ;  but  it  will  bo  asked.  How 
is  such  a  spectator  to  disentangle  from  each  other  the  two  parts  of  tho 
apparent  motions  of  these  external  objects,  —  that  which  arises  from  the 
effect  of  his  own  change  of  place,  and  which  is  therefore  only  apparent 
(or,  as  a  German  metaphysician  would  say,  subjective  —  having  reference 
only  to  him  as  perceiving  it),  —  and  that  which  is  real  (or  object  ire  —  hav- 
ing a  positive  existence,  whether  perceived  by  him  or  not)  ?  By  what 
rule  is  he  to  ascertain,  from  the  appearances  presented  to  him  while  him- 
self in  motion,  what  would  he  the  appearances  were  ho  at  rest  ?  It  by 
no  means  follows,  indeed,  that  he  would  even  then  at  once  obtain  a  clear  con- 
ception of  all  the  motions  of  all  the  objects.  The  appearances  so  presented 
'  to  him  would  have  still  something  mhjective  about  them.  They  would  be 
still  appearances,  not  geometrical  realities.  They  would  still  have  a  refe- 
rence to  the  point  of  view,  which  might  be  very  unfavourably  situated 
(as,  indeed,  is  the  case  in  our  system)  for  affording  a  clear  notion  of  the 
real  movement  of  each  object.  No  geometrical  figure,  or  curve,  is  seen 
by  the  eye  as  it  is  conceived  by  the  mind  to  exist  in  reality.  The  laws 
of  perspective  interfere  and  alter  the  apparent  directions  and  foreshorten 
the  dimensions  of  its  several  parts.  If  the  spectator  be  unfavourably 
situated,  as,  for  instance,  nearly  in  the  plane  of  the  figure  (which  is  the 
case  we  have  to  deal  with),  they  may  do  so  to  such  an  extent,  as  to  make 


c 

I 

< 

0 


t 

o 
a 


Zi 


60 


OUTLINES   OP   ASTRONOMY. 


f 


a  considerablo  effort  of  imagination  necessary  to  pass  from  the  sensible  to 
the  real  form. 

(79.)  Still,  preparatory  to  this  ultimate  step,  it  is  first  necessary  that 
the  spectator  should  free  or  clear  the  appearances  from  the  disturbing 
influence  of  his  own  change  of  place.  And  this  he  can  always  do  by  the 
following  general  rule  or  proposition :  — 

The  relative  motion  of  two  bodien  in  the  same  as  if  cither  of  them 
were  at  rest,  and  all  its  motion  communicated  to  the  other  in  an  opposite 
direction} 

Hence,  if  two  bodies  move  alike,  they  will,  when  seen  from  each  other 
(without  reference  to  other  near  bodies,  but  only  to  the  starry  sphere), 
appear  at  rest.  Hence,  also,  if  the  absolute  motions  of  two  bodies  bo 
uniform  and  rectilinear,  their  relative  motion  is  so  also. 

(80.)  The  stars  are  so  distant,  that  as  we  have  seen  it  is  absolutely 
indifferent  from  what  point  of  the  earth's  surface  we  view  thcni.  Their 
configurations  inter  se  are  identically  the  same.  It  is  otherwise  with  the 
sun,  moon,  and  planets,  which  are  near  enough  (especially  the  moon)  to 
he  parallacticallj/  displaced  by  change  of  station  from  place  to  place  on 
one  globe.  In  order  that  astronomers  residing  on  different  points  uf  the 
earth's  surface  should  be  able  to  compare  their  observations  with  effect,  it 
is  necessary  that  they  should  clearly  understand  and  take  account  of  this 
effect  of  the  difference  of  their  stations  on  the  appearance  of  the  outward 
universe  as  seen  from  each.  As  an  exterior  object  seen  from  one  would 
appear  to  have  shifted  its  place  were  the  spectator  suddenly  transported  to 
the  other,  so  two  spectators,  viewing  it  from  the  two  stations  at  the  same 
instant,  do  not  see  it  in  the  same  direction.  Hence  arises  a  necessity  for 
the  adoption  of  a  conventional  centre  of  reference,  or  imaginary  station 
of  observation  common  to  all  the  world,  to  which  each  observer,  wherever 
situated,  may  refer  (or,  as  it  is  called,  reduce)  his  observations,  by  calcu- 
lating and  allowing  for  the  effect  of  his  local  position  with  respect  to  that 
common  centre  (supposing  him  to  possess  the  necessary  data).  If  there 
were  only  two  observers,  in  fixed  stations,  one  might  agree  to  refer  his 
observations  to  the  other  station ;  but,  as  every  locality  on  the  globe  may 
be  a  station  of  observation,  it  is  far  more  convenient  and  natural  to  fix 

'  This  proposition  is  equivalent  to  the  following,  which  precisely  meets  the  case  pro- 
posed, but  requires  somewhat  more  thought  for  its  clear  apprehension  than  can  perhaps 
be  expected  from  a  beginner :  — 

Prof. — If  two  bodies,  A  and  B,  be  in  motion  independently  of  each  other,  the  motion 
tahich  B  seen  from  A  would  appear  to  have  if  A  were  at  rest  is  the  same  with  that  which 
It  would  appear  to  have,  A  being  in  motion,  if,  in  addition  to  its  own  motion,  a  motion 
equal  to  A^s  and  in  the  same  direction  were  communicated  to  it. 


upon  a  point 
and  this  can 
luetic  change 
obacrvcr  sudd 
the  angle  C 
earth  which  j 


RELATIVE  MOTION. 


61 


upon  a  point  equally  related  to  all,  as  tho  common  point  of  reference  j 
and  this  can  bo  no  other  than  the  centre  of  tho  globe  itself.  The  paral- 
lactic change  of  apparent  place  which  would  arise  in  an  object,  could  any 
obaervcr  suddenly  transport  himself  to  the  centre  of  the  earth,  is  evidently 
tho  angle  C  S  P,  subtended  on  the  object  S  by  that  radius  C  P  of  tho 
earth  which  joins  the  centre  and  tho  place  P  of  observation. 


Fig.  10. 


I 

S 

0 

•Yl 


Irkw 


62 


OUTLINES   OF  ASTRONOMY. 


I    I 


1: 


m 


t 

4* 


1^- 


CHAPTER  II. 

TERMINOLOGY  AND  ELEMENTARY  GEOMETRICAL  CONCEPTIONS  AND 
RELATIONS.  —  TERMINOLOGY  RELATING  TO  THE  GLOBE  OF  THE 
EARTH  —  TO  THE  CELESTIAL  SPHERE.  —  CELESTIAL  PERSPECTIVE. 

(81.)  Several  of  the  terms  in  use  among  astronomers  have  been  ex- 
plained in  the  preceding  chapter,  and  others  used  anticipatively.  But  the 
technical  language  of  every  subject  requires  to  be  formally  stated,  both 
for  consistency  of  usage  and  definiteness  of  conception.  We  shall  there- 
fore proceed,  in  the  first  place,  to  define  a  number  of  terms  in  perpetual 
use,  having  relation  to  the  globe  of  the  earth  and  the  celestial  sphere. 

Definition  1.  The  axis  of  the  earth  is  that  diameter  about  which 
it  revolves,  with  a  uniform  motion,  from  west  to  east;  performing  one 
revolution  in  the  interval  which  elapses  between  any  star  leaving  a  cer- 
tain point  in  the  heavens,  and  returning  to  the  same  point  again. 

(8;{.)  Def.  2.  The  poles  of  the  earth  are  the  points  where  its  axis 
meets  its  surface.  The  North  Pole  is  that  nearest  to  Europe;  the  South 
Pole  that  most  remote  from  it. 

(84.)  Def.  3.  The  earth's  equator  is  a  great  circle  on  its  surface, 
equidistant  from  its  poles,  dividing  it  into  two  hemispheres  —  a  northern 
and  a  southern;  in  the  midst  of  which  are  situated  the  respective  poles 
of  the  earth  of  those  names.  The  plane  of  the  equator  is,  therefore,  a 
plane  perpendicular  to  the  earth's  axis,  and  pas.sing  through  its  centre. 

(85.)  Def.  4.  The  terrestrial  meridian  of  a  station  on  the  earth's 
surface,  is  a  great  circle  of  the  globe  passing  through  both  poles  and 
through  the  plane.  The  plane  of  the  meridian  is  the  plane  in  which 
that  circle  lies. 

(86.)  Def.  5.  The  sensible  and  the  rational  horizon  of  any  station 
have  been  already  defined  in  art.  74. 

(87.)  Def.  6.  A  meridian  line  is  the  line  of  intersection  of  the 
plane  of  the  meridian  of  any  station  with  the  plane  of  the  sensible 
horizon,  and  therefore  marks  the  north  and  south  points  of  the  horizon, 
or  the  directions  in  which  a  spectator  must  set  out  if  he  would  travel 
directly  towards  the  north  or  south  pole. 


(88.)  De 

angular  disi 

dian  :  it  is  i 

and  noriliwti 

in.     Thus,  t 

latitude.     T 

sidered  as  o 

structure  an 

niceties  of  a 

diiforent  mar 

(89.)  Dej 

surface  paral 

same  latitudi 

6P28'40". 

(90.)  Dei 

inclination  of 

point  to  recki 

servatory  at  ( 

tories  of  thcii 

island  of  Fen 

Greenwich. 

of  the  equate 

Greenwich;  ( 

pole  intluded 

(91.)  As  i 

said  to  be  ree 

tematic  rcguh 

computations, 

reckoned  inv: 

from  0  to  3tj 

either  2°  20' 

sense  in  whicl 

term,  the  latt( 

time  at  the  ra 

longitude  of  ] 

(92.)  Knoi 

down  on  an 

'  To  distinguii 
shall  invariably 
■•)    Great  confii 
for  both. 


TERMINOLOGY. 


63 


AND 
THE 
VE. 

en  cx- 
lut  tlio 
I,  both 

thcre- 
rpctual 
ere. 

,  which 
ng  one 
I  a  cer- 
ts axis 

South 

lurface, 
orthern 
e  poles 
cforc,  a 
itre. 
earth's 
es  and 
which 

station 

of  the 
sensible 
lorizon, 
1  travel 


(88.)  Dep.  7.  The  latitutlc  of  a  place  on  the  earth's  surface  is  its 
angular  distance  from  the  ofjuator,  measured  on  its  own  terrestrial  meri- 
dian :  it  is  reckoned  in  degrees,  minutes,  and  seconds,  from  0  up  to  90°, 
and  northwards  or  southwards  according  to  the  hemisphere  the  place  lies 
in.  Thus,  the  observatory  at  Greenwich  is  situated  in  51"  28'  40"  north 
latitude.  This  definition  of  latitude,  it  will  be  observed,  is  to  be  con- 
sidered as  only  temporary.  A  more  exact  knowledge  of  the  physical 
structure  and  figure  of  the  earth,  and  a  better  acquaintance  with  the 
niceties  of  astronomy,  will  render  some  modification  of  its  terras,  or  a 
diiFereiit  manner  of  considering  it,  necessary. 

(89.)  Def.  8.  Parallels  of  latitude  are  small  circles  on  the  earth's 
surface  parallel  to  the  equator.  Every  point  in  such  a  circle  has  the 
same  latitude.  Thus,  Greenwich  is  said  to  be  situated  in  the  parallel  of 
51°  28'  40". 

(90.)  Def.  9.  The  longitude  of  a  place  on  the  earth's  surface  is  the 
inclination  of  its  meridian  to  that  of  some  fixed  station  referred  to  as  a 
point  to  reckon  from.  English  astronomers  and  geographers  use  the  ob- 
servatory at  Greenwich  for  this  station ;  foreigners,  the  principal  observa- 
tories of  their  respective  nations.  Some  geographers  have  adopted  the 
island  of  Ferro.  Hereafter,  when  we  speak  of  longitude,  we  reckon  from 
Greenwich.  The  longitude  of  a  place  is,  therefore,  measured  by  the  arc 
of  the  equator  intercepted  between  the  meridian  of  the  place  and  that  of 
Greenwich ;  or,  which  is  the  same  thing,  by  the  spherical  angle  at  the 
pole  included  between  these  meridians. 

(91.)  As  latitude  is  reckoned  north  or  south,  so  longitude  h  \xmvX\y 
said  to  be  reckoned  west  or  east.  It  would  add  greatly,  however,  to  sys- 
tematic regularity,  and  tend  much  to  avoid  confusion  and  ambiguity  in 
computations,  were  this  mode  of  expression  abandoned,  and  longitudes 
reckoned  invariably  westward  from  their  origin  round  the  whole  circle 
from  0  to  360°.  Thus,  the  longitude  of  Paris  is,  in  common  parlance, 
either  2°  20'  22"  east,  or  357°  39'  38"  west  of  Greenwich.  But,  in  the 
sense  in  which  we  shall  henceforth  use  and  recommend  others  to  use  the 
term,  the  latter  is  its  proper  designation.  Longitude  is  also  reckoned  in 
time  at  the  rate  of  24  h.  for  360°,  oi  15°  per  hour.  In  this  system  the 
longitude  of  Paris  is  23  h.  50  m.  38^8.' 

(92.)  Knowing  the  longitude  and  latitude  of  a  place,  it  may  be  laid 
down  on  an  artificial  globe;  and  thus  a  map  of  the  earth  may  be  con- 

*  To  diatinguish  minutes  and  seconds  of  time  from  those  of  angular  measure  we 
shall  invariably  adhere  to  the  distinct  system  of  notation  here  adopted  (°  ' ",  and  h.  m. 
■.)  Great  confusion  sometimes  arises  from  the  practice  of  using  the  same  marka 
for  both. 


I 
I 


e^ 


OUTLINES  OF  ASTRONOMY. 


ti  \ 


Btructed.  Maps  of  particular  countries  are  deiached  portions  of  this 
general  map,  extended  into  planes;  or  rather,  they  are  representations 
on  planes  of  such  portions,  executed  according  to  certain  conventional 
systems  of  rules,  called  projections,  the  object  of  which  is  either  to 
distort  as  little  as  possible  the  outlines  of  countries  from  what  they  are 
on  the  globe — or  to  establish  easy  means  of  ascertaining,  by  inspection  or 
graphical  measurement,  the  latitudes  and  longitudes  of  places  which 
occur  in  them,  without  referring  to  the  globe  or  to  books — or  for  other 
peculiar  uses.     See  Chap.  IV. 

(93.)  Def.  10.  The  Tropics  are  two  parallels  of  latitude,  one  on  the 
north  and  the  other  on  the  south  side  of  the  equator,  over  every  point 
of  which  respectively,  the  sun  in  its  diurnal  course  passes  vertically  on 
the  21st  of  March  and  the  21st  of  September  in  every  year.  Their 
latitudes  are  about  23°  28'  respectively,  north  and  south. 

(94.)  Def.  11.  The  Arctic  and  Antarctic  circles  are  two  small  circles 
or  parallels  of  latitude  as  distant  from  the  north  and  south  poles  as  the 
tropics  are  from  the  equator,  that  is  to  say,  about  23°  28' ;  their  latitudes, 
therefore,  are  about  66°  32'.  "We  say  about,  for  the  places  of  these 
circles  and  of  the  tropics  are  continually  shifting  on  the  earth's  surface,  • 
though  with  extreme  slowness,  as  will  be  explained  in  its  proper  place. 

(95.)  Def.  12.  The  sphere  of  the  heavens  or  of  the  stars  is  an  ima- 
ginary spherical  surface  of  infinite  radius,  having  the  eye  of  any  specta- 
tor for  its  centre,  and  which  may  be  conceived  as  a  ground  on  which  the 
stars,  planets,  &c.,  the  visible  contents  of  the  universe,  are  seen  projected 
as  in  a  vast  picture.' 

(96.)  Def.  13.  The  poles  of  the  celestial  sphere  are  the  points  of  that 
imaginary  sphere  towards  which  the  earth's  axis  is  directed. 

(97.)  Def.  14.  The  celestial  equator,  or,  as  it  is  often  called  by  as- 


1  The  ideal  sphere  >  ithout  us,  to  which  we  refer  the  places  of  objects,  and  which 
we  carry  along  with  us  wherever  we  go,  is  no  doubt  intimately  connected  by  associa- 
tion, if  not  entirely  dependent  on  that  obscure  perception  of  sensation  in  the  retinte  of 
our  eyes,  of  which,  even  when  closed  and  unexcited,  we  cannot  entirely  divest  them. 
We  have  a  real  spherical  surface  within  our  eyes,  the  seat  of  sensation  and  vision, 
corresponding;  point  fo>  point,  to  the  external  sphere.  On  this  the  stars,  &.c.  are  really 
mapped  down,  as  we  have  supposed  them  in  the  text  to  be,  on  the  imaginary  concave 
of  the  heavens.  When  the  whole  surface  of  the  retina  is  excited  by  light,  habit  leads 
us  to  associate  it  with  the  idea  of  a  real  surface  existing  without  us.  Thus  we  become 
impressed  with  the  notion  of  a  thy  and  a  heaven,  but  the  concave  surface  of  the  retina 
itself  is  the  true  seat  of  all  visible  angular  dimension  and  angular  motion.  The  sub- 
stitution of  the  retina  for  the  heavens  would  be  awkward  and  inconvenient  in  lan^ruage, 
but  it  may  always  be  mentally  made.  (See  Schiller's  pretty  enigma  on  the  eye,  in  his 
Turandot.) 


TERMINOLOaT. 


65 


trcnomers,  the  equinoctial,  is  a  great  circle  of  the  celestial  sphere,  marked 
out  by  the  indefinite  extension  of  the  plane  of  the  terrestrial  equator. 

(98.)  Def.  15.  The  celestial  horizon  of  any  place  is  a  great  circle  of 
the  sphe!(»  marked  out  by  the  indefinite  extension  of  the  plane  of  any 
spectator'::;  sensible  or  (which  comes  to  the  same  thing  as  will  presently 
be  shown,)  his  rational  horizon,  as  in  the  case  of  the  equator. 

(99.)  Def.  16.  The  zenith  and  nadir^  of  a  spectator  are  the  two 
pointib  of  the  sphere  of  the  heavens,  vertically  over  his  head,  and  verti- 
cally under  his  feet,  or  the  poles  of  the  celestial  horizon  j  that  is  to  say, 
points  90°  distant  from  every  point  in  it. ' 

(100.)  Def.  17.  Vertical  circles  of  the  sphere  are  great  circles  passing 
through  the  zenith  and  nadir,  or  great  circles  perpendicular  to  the  horizon. 
On  these  are  measured  the  altitiules  of  objects  above  the  horizon  —  the 
complements  to  which  are  their  zenith  distances. 

(101.)  Def.  18.  The  celestial  meridian  of  a  spectator  is  the  great  circle 
marked  out  on  the  sphere  by  the  prolongation  of  the  plane  of  his  terres* 
trial  meridian.  If  the  earth  be  supposed  at  rest,  this  is  a  fixed  circle,  and 
all  the  stars  are  carried  across  it  in  their  diurnal  courses  from  east  to  west. 
If  the  stars  rest  ani  the  earth  rotate,  the  spectator's  meridian,  like  his 
horizon  (art.  52),  sweeps  daily  across  the  stars  from  west  to  east.  When- 
ever in  future  we  speak  of  the  meridian  of  a  spectator  or  observer,  we 
intend  the  celestial  meridian,  which  being  a  circle  passing  through  the 
poles  of  the  heavens  and  the  zenith  of  the  observer,  is  necessarily  a  verti- 
cal circle,  and  passes  through  the  north  and  south  points  of  the  horizon. 

(102.)  Def.  19.  The  prime  vertical  is  a  vertical  circle  perpendicular  to 
the  meridian,  and  which  therefore  passes  through  the  east  and  west  points 
of  the  horizon. 

(108.)  Def.  20.  Azimuth  is  the  angular  distance  of  a  celestial  object 
from  the  north  or  south  point  of  the  horizon  (according  as  it  is  the  north 
or  south  pole  which  is  elevated),  when  the  object  is  referred  to  the  horizon 
by  a  vertical  circle ;  or  it  is  the  angle  comprised  between  two  vertical 
planes  —  one  passing  through  the  elevated  pole,  the  other  through  the 
object.  Azimuth  may  be  reckoned  eastwards  or  westwards,  from  the 
north  or  south  point,  and  is  usually  so  reckoned  only  to  180°  either  way. 
But  to  avoid  confusion,  and  to  preserve  continuity  of  interpretation  when 
algebraic  symbols  are  used  (a  point  of  essential  importance,  hitherto  too 
little  insisted  on),  we  shall  always  reckon  azimuth  from  the  points  of  the 
horizon  most  remote  from  the  elevated  pole,  westward  (so  as  to  agree  in 
general  directions  with  the  apparent  diurnal  motion  of  the  stars),  and 


tow 

?! 
E2 

I 

o 
a 

C 
0. 


2 


'  From  Arabic  words, 
whence  our  nether. 

5 


Nadir  corresponds  evidently  to  the  German  nieder,  (down.) 


66 


OUTLINES  OF  ASTRONOMY. 


carry  its  reckoning  from  0°  to  300°  if  always  reckoned  positive,  consider- 
ing the  eastward  reckoning  as  negative. 

(104.)  Def.  21.  The  altitude  of  a  heavenly  body  is  its  apparent  angular 
elevation  above  the  horizon.  It  is  the  complement  to  90°,  therefore,  of 
its  zenith  distance.  The  altitude  and  azimuth  of  an  object  being  known, 
its  place  in  the  visible  ueavens  is  determined. 

(105.)  Def.  22.  The  declination  of  a  heavenly  body  is  its  angular 
distance  from  the  eqv.inoctial  or  celestial  equator,  or  *he  complement  to 
90°  of  its  angular  distance  from  the  nearest  pole,  which  latter  distance  is 
called  its  Polar  distance.  Declinations  ar«>  reckoned  plus  or  minus, 
according  as  the  object  is  situated  in  the  northern  or  southern  celestial 
hemisphere.  Polar  distances  are  always  reckoned  from  the  North  Pole, 
from  0°  up  to  180°,  by  which  all  doubt  or  ambiguity  of  expression  with 
respect  to  sign  is  avoided. 

(106.)  Def.  23.  Hour  circles  of  the  sphere,  or  circles  of  declination, 
are  great  circles  passing  through  the  poles,  and  of  course  perpendicular  to 
the  equinoctial.  The  hour  circle,  passing  through  any  particular  heavenly 
body,  serves  to  refer  it  to  a  point  in  the  equinoctial,  as  a  ve  ical  circle 
does  to  a  point  in  the  horizon. 

(107.)  Def.  24.  The  hour  angle  of  a  heavenly  body  is  the  angle  at 
the  pole  included  between  the  hour  circle  passing  through  the  body,  and 
the  celestial  meridian  of  the  place  of  observation.  We  shall  always 
reckon  it  positively/  from  the  U2)j)er  culmination  (art.  125)  westwards,  or 
in  conformity  with  the  apparent  diurnal  motion,  completely  round  the 
circle  from  0°  to  360°.  Hour  angles,  generally,  are  angles  included  at 
the  pole  between  different  tour  circles. 

(108.)  Def.  25.  The  right  wrension  of  a  heavenly  body  is  the  arc  of 
the  equinoctial  included  between  a  certain  point  in  that  circle  called  the 
Vernal  Equinox^  and  the  point  in  the  same  circle  to  which  it  is  referred 
by  the  circle  of  declination  passing  through  it.  Or  it  is  the  angle  included 
between  two  hour  circles,  one  of  which  passes  through  the  vernal  equinox 
(and  is  called  the  equinoctial  colure),  the  other  through  the  body.  How 
the  place  of  this  initial  point  on  the  equinoctial  is  determined,  will  be 
explained  further  on. 

(109.)  The  right  ascensions  of  celestial  objects  arc  always  reckoned 
rasttoards  from  the  equinox,  and  are  estimated  either  in  degrees,  minutes, 
and  seconds,  as  in  the  case  of  terrestrial  longitudes,  from  0°  to  360°, 
which  completes  the  circle;  or,  in  time,  in  hours,  minutes,  and  seconds, 
from  Oh.  to  24h.  The  apparent  diurnal  motion  of  the  heavens  being 
contrary  to  the  real  motion  of  the  earth,  this  is  in  conformity  with  the 
westward  reckoning  of  longitudes.  (Art.  91.)  .•  ,„v »,  ^. 


% 


Jf 


TERMINOLOGY. 


6T 


ingular 
■ore,  of 
known, 

angular 
nent  to 
stance  is 
minus, 
celestial 
th  Pole, 
ion  with 

jlination,  || 
licular  to  | 
heavenly 
cal  circle 

I  angle  at 
)ody,  and 

II  always 
wards,  or 
ound  the  i^ 
eluded  at 

he  arc  of 
ailed  the 
s  referred 
included  j 
il  equinox 
y.  How 
d,  will  be 


(110.)  Sidereal  time  is  reckoned  by  the  diurnal  motion  of  the  stars, 
or  rather  of  that  point  in  the  equinoctial  from  which  right  ascensions  are 
reckoned.  This  point  may  be  considered  as  a  star,  though  no  star  is,  in 
fact,  there;  and,  moreover,  the  point  itself  is  liable  to  a  certain  slow 
variation,  —  so  slow,  however,  as  not  to  affect,  perceptibly,  the  interval, 
of  any  two  of  its  successive  returns  to  the  meridian.  This  interval  is 
called  a  sidereal  day,  and  is  divided  into  24  sidereal  hours,  and  these  again 
into  minutes  and  seconds.  A  clock  which  marks  sidereal  time,  i.  e.  which 
goes  at  such  a  rate  as  always  to  show  Oh.  Om.  Os.  when  the  equinox  comes  on 
the  meridian,  is  called  a  sidereal  clock,  and  is  an  indispensable  piece  of  furni- 
ti  -e  in  every  observatory.  Hence  the  hour  angle  of  an  object  reduced  to 
time  at  the  rate  of  15°  per  hour,  expresses  the  interval  of  sidereal  time 
by  which  (if  its  reckoning  be  positive)  it  has  past  the  meridian ;  or,  if 
negative,  the  time  it  wants  of  arriving  at  tho  meridian  of  the  place  of 
observation.  So  also  the  right  ascension  of  an  object,  if  converted  into 
time  at  the  same  rate  (since  360"  being  described  uniformly  in  24  hours, 
15°  must  be  so  described  in  1  hour),  will  express  the  interval  of  sidereal 
time  which  elapses  from  the  passage  of  the  vernal  equinox  across  the 
meridian  to  that  of  the  object  next  subsequent. 

(111.)  As  a  globe  or  maps  may  be  made  of  the  whole  or  particular 
regions  of  the  surface  of  the  earth,  so  also  a  globe,  or  general  map  ol  'je 
heavens,  as  well  as  charts  of  particular  parts,  may  be  constructed,  and  the 
stars  laid  down  in  their  proper  situations  relative  to  each  other,  and  to 
the  poles  of  the  heavens  and  the  celestial  equator.  Such  a  representa- 
tion, once  made,  will  exhibit  a  true  appearance  of  the  stars  as  they 
present  themselves  in  succession  to  every  spectator  on  the  surface,  or  as 
they  m?.y  be  conceived  to  be  seen  at  once  by  one  at  the  centre  of  the 
globe.  It  is,  therefore,  independent  of  all  geographical  localities.  There 
will  occur  in  such  a  representation  neither  zenith,  nadir,  nor  horizon  — 
neither  east  nor  west  points ;  and  although  great  circles  may  be  drawn  on 
it  from  pole  to  pole,  corresponding  to  terrestrial  meridians,  they  can  no 
longer,  in  this  point  of  view,  be  regarded  as  the  celestial  meridians  of 
fixed  points  on  the  earth's  surface,  since,  in  the  course  of  one  diurnal 
revolution,  every  point  in  it  passes  beneath  each  of  them.  It  is  on 
account  of  this  change  of  conception,  and  with  a  view  to  establish  a  com- 
plete distinction  between  the  two  branches  of  Geography  and  Uranogra- 
phy,^  that  astronomers  have  adopted  diiFerent  terms,  (viz.  declination  and 
right  ascension)  to  represent  those  arcs  in  the  heavens  which  correspond 
to  latitudes  and  longitudes  on  the  earth.     It  is  for  this  reason  that  they 


c 

I 

m 
m 

•< 

o 

I 

o 
o 


2 


T17,  the  earih ;  y^a^tw,  to  describe  or  represent ;  ovpavos,  the  heaven. 


68 


0U11.INES   OF  ASTRONOMY. 


term  tbe  equator  of  the  hoavens  the  equinoctial;  that  what  are  meridians 
on  the  earth  are  called  hour  civles  in  the  heavens,  and  the  angles  they 
include  betwcea  them  at  the  poles  are  called  hour  anglea.  ^VU  tliis  is 
convenient  and  intelligible;  and  had  they  been  content  vtfitli  this  noxiea- 
olature,  no  confusion  could  ever  have  arisen.  Uniuckil  ',  the  early 
astronomers  have  eiuployed  also  the  words  latitude  and  iougitmie  in  their 
uranography,  in  speaking  of  arcs  of  circles  not,  corresponding  to  tiiose 
meant  by  the  same  words  on  the  earth,  but  havin|^f;  referent  o  to  the  motion 
of  the  sun  and  planets  among  the  stars.  Tt  is  now  too  late  to  remedy 
this  confusion,  which  is  ingiuflcd  into  every  existing  work  on  astronomy : 
we  can  only  regret,  and  warn  the  reader  of  itj  that  Iia  may  be  ou  h^ 
guard  when,  at  a  more  advanced  period  of  our  work,  we  ahall  have  occsi- 
sion  to  define  and  uso  the  terms  in  their  celestiol  senfe,  at  the  sai;  t,  time 
urgently  ;  ^vsomin ending  to  future  writers  the  adoption  of  otl>ors  in  their 
places. 

(112.)  Ic  r'VTiains  to  illustrate  these  descriptions  by  reference  to  a 
figure.     Let  C  be  the  centre  of  the  earth,  N  C  S  its  axis ;  then  are  N 


^<iiVt:  - 


and  S  its  poles;  E  Q  its  equator;  A  B  the  parallel  of  latitude  of  the 
station  A  on  its  surface ;  A  P  parallel  to  S  C  N,  the  direction  in  which 
an  observer  at  A  will  see  the  elevated  pole  of  the  heavens ;  and  A  Z,  the 
prolongation  of  thq  terrestrial  radius  C  A,  that  of  his  zenith.  N  A  E  S 
will  be  his  meridian ;  N  G  S  that  of  some  fixed  station,  as  Greenwich ; 
and  G  E,  or  the  spherical  angle  G  N  E,  his  longitude,  and  E  A  his  lati- 
tude.    Moreover,  if  n  s  be  a  plane  touching  the  surface  in  A,  this  will 


be  his  sens 
with  his  mi 
south  pointc 
(113.)  A 
stationed  at 
let  the  anne 
tor;  Z  his  z 
the  sphere, 
elevated  and 
pole,  and  H 
to  P^,  will 
be  the  right 
of  any  star  o 
S  Tp;  and 


about  the  pole 
Z  S  M,  0  M 
distance.   H  a 
of  hit,  horizoi 
circles,  w  pat 
south  points, 
which  and  th( 
occukation,  be 
all  the  zone  of 
one  of  them, 
circle  represen 
sented  by  A 


TERMINOLOGY. 


69 


be  his  sensible  horizon :  n  A  s  marked  on  that  plane  by  its  intersection 
with  his  meridian  will  bo  his  meridian  line,  and  n  and  s  the  north  and 
south  points  of  his  horizon. 

(113.)  Again,  neglecting  the  size  of  the  earth,  or  conceiving  him 
stationed  at  its  centre,  and  referring  every  thing  to  his  rational  horizon ; 
let  the  annexed  figure  represent  the  sphere  of  the  heavens;  C  the  specta- 
tor; Z  his  zenith;  and  N  his  nadir:  then  will  H  A  0,  a  great  circle  of 
the  sphere,  whose  poles  are  Z  N,  be  his  celestial  horizon;  P  p  the 
elevated  and  dressed  poles  of  the  heavens ;  H  P  the  altitude  of  the 
pole,  and  H  P  Z  £  0  his  meridian ;  E  T  Q,  a  great  circle  perpendicular 
to  P^,  will  be  the  equinoctial;  and  if  T  represent  the  equinox,  r  T  will 
be  the  right  ascension,  T  S  the  declination,  and  P  S  the  polar  distance 
of  any  star  or  object  S,  referred  to  the  equinoctial  by  the  hour  circle  P 
Sip;  and  BSD  will  be  the  diurnal  circle  it  will  appear  to  describe 


.%    ::     ^    >:'«i 


Fig. 

12 

1 1 .', . 

^- 

jk^ 

S___ 

""SE 

! 

yy 

7 

/ 

/rk 

^ 

nK--'' 

L 

7^ 

A\ 

rv7 

1 

-^1 

/^ 

^^ 

// 

DV 

<r= 

^ 

/ 

jp 

jsr 


about  the  pole.  Again,  if  we  refer  it  to  the  horizon  by  the  vertical  circle 
Z  S  M,  0  M  will  be  its  azimuth,  M  S  its  altitude,  and  Z  S  its  zenith 
distance.  H  and  O  are  the  north  and  south,  e  w  the  east  and  west  ppints 
of  hib  horizon,  or  of  the  heavens.  Moreover,  if  H  A,  0  o,  be  small 
circles,  ir  parallels  of  declination,  touching  the  horizon  in  its  north  and 
south  points,  H  h  will  be  the  circle  of  perpetual  apparition,  between 
which  and  the  elevated  pole  the  stars  never  set;  0  o  that  of  perpetual 
occuUation,  between  which  and  the  depressed  pole  they  never  rise.  In 
all  the  zone  of  the  heavens  between  H  h  and  0  o,  they  rise  and  set ;  any 
one  of  them,  as  S,  remaining  above  the  horizon  in  that  part  of  its  diurnal 
circle  represented  by  a  B  A,  and  below  it  throughout  all  the  part  repre- 
sented by  A  D  a.     It  will  exercise  the  reader  to  construct  this  figure  for 


< 

o 

^  I 
E 

o 
p 


9 


70 


OUTLINES   OF  ASTRONOMY. 


;;  • 


several  different  elevations  of  the  pole,  and  for  a  variety  of  positions  of 
the  star  S  in  each. 

(114.)  Celestial  perspective  is  that  branch  of  the  general  science  of 
perspective  which  teaches  us  to  conclude,  from  a  knowledge  of  the  real 
situation  and  forms  of  objects,  lines,  angles,  motions,  &o.  with  respect  to 
the  spectator,  their  apparent  aspects,  as  seen  by  him  projected  on  the 
imaginary  concave  of  the  heavens;  and,  vice  versd,  from  the  apparent 
configurations  and  movements  of  objects  so  seen  projected,  to  conclude, 
so  far  as  they  can  be  thence  concluded,  their  real  geometrical  relations  to 
each  other  and  to  the  spectator.   It  agrees  with  ordinary  perspective  when 
only  a  small  visual  area  is  contemplated,  because  the  concave  ground  of 
the  celestial  sphere,  for  a  small  extent,  may  be  regarded  as  a  plane  sur- 
face,  on  which  objects  are  seen  projected  or  depicted  as  in  common  per- 
spective.    But  when  large  amplitudes  of  the  visual  area  are  considered, 
or  when  the  whole  contents  of  space  are  regarded  as  projected  on  the 
whole  interior  surface  of  the  sphere,  it  becv.'Mes  necessary  to  use  a  different 
phraseology,  and  to  resort  to  a  different  form  of  conception.     In  common 
perspective  there  is  a  single  "  point  of  sight,"  or  "  centre  of  the  picture," 
the  visual  line  from  the  eye  to  which  is  perpendicular  to  the  "  plane  of 
the  picture,"  and  all  straight  lines  are  represented  by  straight  lines.     In 
celestial  perspective,  every  point  to  which  the  view  is  for  the  moment 
directed,  is  equally  entitled  to  be  condidered  as  the  "  centre  of  the  pic- 
ture," every  portion  of  the  surface  of  the  sphere  being  similarly  related 
to  the  eye.     Moreover,  every  straight  line  (supposed  to  be  indefinitely 
prolonged)  is  projected  into  a  semicircle  of  the  sphere,  that,  namely,  in 
which  a  plane  passing  through  the  line  and  the  eye  cuts  its  surface.   And 
every  system  of  parallel  straight  lines,  in  whatever  direction,  is  projected 
into  a  system  of  semicircles  of  the  sphere,  meeting  in  two  common  apexes, 
or  vanishing  points,  diametrically  opposite  to  each  other,  one  of  which 
corresponds  to  the  vanishing  poiut  of  parallels  in  ordinary  perspective ; 
the  other,  in  such  perspective  has  no  existence.     In  other  words,  every 
point  in  the  sphere  to  which  the  eye  is  directed  may  be  regarded  as  one 
of  the  vanishing  points,  or  one  apex  of  a  system  of  straight  lines,  parallel 
to  that  radius  of  the  sphere  which  passes  through  it,  or  to  the  direction 
of  the  line  of  sight,  seen  in  perspective  from  the  earth,  and  the  points 
diametrically  opposite,  or  that  from  which  he  is  looking,  as  the  other. 
And  any  great  circle  of  the  sphere  may  similarly  be  regarded  as  the 
vanishing  circle  of  a  system  of  planes,  parallel  to  its  own. 

(115.)  A  familiar  illustration  of  this  is  often  to  be  had  by  attending  to 
the  lines  of  light  seen  in  the  air,  whei  ♦he  sun's  rays  are  darted  through 
apertures  in  clouds,  the  sun  itself  being  at  the  time  obscured  behind  them. 


r.' 


These  lines 

almost  infin 

thrown  int( 

common  in 

obscured)  m 

only  is  most 

sun.     But 

verging  tovi 

depressed  b( 

quently  noti 

Occasionally 

of  sunbeami 

to  horizon  ( 

streamers  oi 

parallel,  or  i 

appear  to  d 

pended,  wou 

west  of  norl 

course  of  gr( 

the  point  dia 

eastward  of 

for  its  centre 

direction  wh 

periodical  re( 

meet  nearly 

near  approac 

those  occasio 

(116.)  In 

the  north  an( 

system  of  lin 

of  those  of 

observation, 

every  place 

'  It  is  in  sue 
of  plane  perspe 
on  one  occasior 
than  usual  gran 
P.  H.,  the  sun 
whose  aperture 
hemisphere  aln 
of  Mont  Blanc 
pression  produc 
mountain,  and  < 


il 


1 


CELESTIAL   PERSPECTIVE. 


m 


nee  of 
le  real 
pect  to 
on  tbe 
)parent 
Qclude, 
bions  to 
e  when 
and  of 
me  sur- 
lon  per- 
sidered, 
on  the 
iifferent 
common 
)icture," 
►lane  of 
les.     In 
moment 
the  pic- 
r  related 
efinitely 
mely,  in 
;e.    And 
)rojectcd 
,  apexes, 
)f  which 
jpective ; 
Is,  every 
i  as  one 
,  parallel  U 
direction  •  * 
ko  points 
16  other, 
d  as  the 


These  lines  which,  marking  the  course  of  rays  emanating  from  a  point 
almost  infinitely  distant,  are  to  bo  considered  us  parallel  straight  lines,  are 
thrown  into  great  circles  of  tho  sphere,  having  two  apexes  or  points  of 
common  intersection  —  one  in  the  place  where  the  sun  itself  (if  not 
obscured)  would  be  seen.  The  other  diametrically  opposite.  The  first 
only  is  most  commonly  suggested  when  tho  spectator's  view  is  towards  tho 
sun.  But  in  mountainous  countries,  the  phcuumenon  of  sunbeams  con- 
verging towards  a  point  diametrically  opposite  to  the  sun,  and  as  much 
depressed  below  the  horizon  as  the  sun  is  elevated  above  it,  is  not  unfre- 
quently  noticed,  the  back  of  the  spectator  being  turned  to  the  sun's  place. 
Occasionally,  but  much  more  rarely,  tho  whole  course  of  such  a  system 
of  sunbeams,  stretching  in  semicircles  across  the  hemisphere  from  horizon 
to  horizon  (the  sun  being  near  setting),  may  be  seen.'  Thus  again,  tho 
streamers  of  the  Aurora  Borealis,  which  are  doubtless  electrical  rays, 
parallel,  or  nearly  parallel  to  each  other,  and  to  the  dipping  needle,  usually 
appear  to  diverge  from  the  point  towards  which  tlio  needle,  freely  sus- 
pended, would  dip  northwards  (i.  e.  about  70°  below  the  horizon  and  23° 
west  of  north  from  London),  and  in  their  upward  progress  pursue  the 
course  of  great  '  ircles  till  they  again  converge  (in  appearance)  towards 
the  point  diametrically  opposite  (/.  e.  70°  above  the  horizon,  and  23°  to  the 
eastward  of  south),  forming  a  sort  of  canopy  over-head,"  having  that  point 
for  its  centre.  So  also  in  the  phenomenon  of  shooting  stars,  the  lines  of 
direction  which  they  appear  to  take  on  certain  remnrkable  occasions  of 
periodical  recurrence,  are  observed,  if  prolonged  backwards,  apparently  to 
meet  nearly  in  one  point  of  the  sphere ;  a  certain  indication  of  a  general 
near  approach  to  parallelism  in  the  real  directions  of  their  motions  on 
those  occasions.     On  which  subject  more  hereafter. 

(116.)  In  relation  to  this  idea  of  celestial  perspective,  we  may  conceive 
the  north  and  south  poles  of  the  sphere  as  the  two  vanishing  points  of  a 
system  of  lines  parallel  to  the  axis  of  the  earth ;  and  the  zenith  and  nadir 
of  those  of  a  system  of  perpendiculars  to  its  surface  at  the  place  of 
observation,  &c.  It  will  be  shown  that  the  direction  of  a  plumh-Une,  at 
every  place  is  perpendicular  to  the  surface  of  still  water  at  that  place 

'  It  is  in  such  cases  only  that  we  conceive  them  as  circles,  the  ordinary  conventions 
of  plane  perspective  becominf;  untenable.  Tho  author  had  the  good  fortune  to  witness 
on  one  occasion  th.;.  phenomenon  described  in  the  text  under  circumstances  of  more 
than  usual  grandeur.  Approaching  Lyons  from  the  south  on  Sept.  30, 1826,  about  5^  h. 
p.  M.,  the  sun  was  seen  nearly  setting  behind  broken  masses  of  stormy  cloud,  from 
whose  apertures  streamed  forth  beams  of  rose*coloured  light,  traceable  all  across  the 
hemisphere  almost  to  their  opposite  point  of  convergence  behind  the  snowy  precipices 
of  Mont  Blanc,  conspicuously  visible  at  nearly  100  miles  to  the  eastward.  The  im- 
pression produced  was  that  of  another  but  feebler  sun  about  to  rise  from  behind  the 
mountain,  and  darting  forth  precursory  beams  to  meet  those  of  the  real  one  opposite. 


c 

I 

S 

< 

o 


¥^ 

r 
o 

o 


63 


% 


72 


OUTLINES   OP  ASTRONOMY. 


which  is  tho  truo  horizon,  and  though  mathematioally  speaking  no  two 
plunib-Iincs  are  exactly  parallel  (since  they  converge  to  tho  earth's  centre), 
yet  over  very  small  tracts,  such  as  tho  area  of  a  building  —  in  one  and 
tho  name  town,  &c.,  the  difference  from  exact  parallelism  is  so  small  that 
it  may  be  practically  disregarded.'  To  a  spectator  looking  upwards  such 
a  system  of  plumb-lines  will  appear  to  converge  to  his  zenith ;  downwards, 
to  his  nadir. 

(117.)  So  also  the  celestial  equator,  or  the  equinoctial,  must  be  con- 
ceived as  the  vaniHhing  circle  of  a  system  of  planes  parallel  to  the  earth's 
equator,  or  perpendicular  to  its  axis.  The  celestial  horizon  of  any  spec- 
tator is  in  like  manner  the  vanishing  circle  of  all  planes  parallel  to  his 
truo  horizon,  of  which  planes  his  rational  horizon  (passing  through  the 
earth's  centre)  is  one,  and  bis  aemible  horizon  (the  tangent  plane  of  his 
station)  another. 

(118.)  Owing,  however,  to  tho  absence  of  all  the  oirdinary  indications 
of  distance  which  influence  our  judgment  in  respect  of  terrestrial  objects, 
owing  to  the  wart  of  determinate  figure  and  magnitude  in  the  stars  and 
planets  as  commonly  seen  —  the  projection  of  the  celestial  bodies  on  the 
ground  of  the  heavenly  concave  is  not  usually  regarded  in  this  its  truo 
light,  of  a  po'Hpectioe  representation  or  picture^  and  it  even  requires  an 
effort  of  imogination  to  conceive  them  in  their  true  relations,  as  at  vastly 
different  distances,  one  behind  the  other,  and  forming  with  one  another 
lines  of  junction  violently  foreshortened,  and  including  angles  altogether 
differing  from  those  which  their  projected  representations  appear  to  make. 
To  do  so  at  all  with  effect  presupposes  a  knowledge  of  their  actual  situa- 
tions in  space,  which  it  is  the  business  of  astronomy  to  arrive  at  by  appro- 
priate considerations.  But  the  connections  which  subsist  among  the 
several  parts  of  the  picture,  the  purely  geometrical  relations  among  the 
angles  and  sides  of  the  spherical  triangles  of  which  it  consists,  constitute, 
under  the  name  of  Uranometry,'  a  preliminary  and  subordinate  branch  of 
the  general  science,  with  which  it  is  necessary  to  bo  familiar  before  any 
further  progress  can  be  made.  Some  of  the  most  elementary  and  fre- 
quently occurring  of  these  relations  we  proceed  to  explain.  And  first,  as 
immediate  consequences  of  the  above  definitions,  the  following  propositions 
will  be  borne  in  mind. 

(119.)  The  altitude  of  the  <  levatedpole  is  equal  to  the  latitude  of  the 
spectator's  geographical  station. 

For  it  appears,  see  fg.  art.  112,  that  the  angle  PAZ  between  the 

'  An  interval  of  a  mile  corresponds  to  a  convergence  of  plumb-lines  amounting  to 
nomewhat  less  space  than  a  minute. 
. .  s  Ovpavo{,  the  heavens ;  /itrptiv,  to  measure :  the  measurement  of  the  heavens. 


*'■ 


pole  and  tl 
being  righ 
is  the  clovi 
earth's  ceni 
(120.)  1 
pole  of  tho 
less  and  loi 
his  horizon 
below,  whil 
the  south  p( 
in  the  zeniti 
(121.)  Tl 
successively, 
And,  since  t 
which  elapse 
different  plai 
(122.)    Vi 
coming  on  t 
time,  is  the  n 
(123.)  Th 
points,  and  tl 
tude  of  the  p 
40",  tho  altit 
SS^'  31'  20". 
the  equinocti 
are  the  poles 
horizon  are  t 
the  poles  of  h 
(124.)  All 
altitudes)  on 
serve  them,  b< 
atmosphere,  a< 
(125.)  All 
come  twice  or 
tion ;  once  abi 
and  lower  culn 
(126.)  The 
in  tho  solution 
angled,  accordi 
etry,  which  we 
appropriate  tre 


ELEMENTARY    KELATIONS. 


n 


catioDS 
)bject8, 
Lrs  and 
on  the 
its  true 
lires  an 
t  vastly 
another 
ogether 
3  make. 
1  situa- 
f  appro- 
»ng  the 
ong  the 
astitute, 
■aneh  of 
)re  any 
md  fro- 
first,  as 
)Ositions 


pole  and  the  wnith  is  equal  to  N  0  A,  and  the  angles  Z  A  n  and  N  C  E 
being  right  angles,  we  have  P  A  n=A  C  E.  Now  the  former  of  these 
is  the  elevation  of  the  pole  as  seen  from  E,  the  latter  is  the  angle  at  the 
earth's  eentre  subtended  by  the  are  E  A,  or  the  latitude  of  the  place. 

(120.)  Hence  to  a  spectator  at  the  north  polo  of  the  earth,  the  north 
pole  of  the  heavens  is  in  his  zenith.  As  he  travels  southward  it  becomes 
less  and  less  elevated  till  he  reaches  the  equator,  when  both  poles  are  in 
bis  horizon  —  south  of  the  equator  the  north  polo  becomes  depressed 
below,  while  the  south  rises  above  his  horizon,  and  continues  to  do  so  till 
the  south  pole  of  the  globe  is  reached,  when  that  of  the  heavens  will  bo 
in  the  zenith.  m 

(121.)  The  same  stare,  in  their  diurnal  revolution,  come  to  tne  meridian, 
succemvelj/,  of  every  place  on  the  globe  once  in  twenty-four  sidereal  hours. 
And,  since  the  diurnal  rotation  is  uniform,  the  interval,  in  sidereal  time, 
which  elapses  between  the  same  star  coming  upon  the  meridians  of  two 
different  places  is  measured  by  the  ditTerence  of  longitudes  of  the  places. 

(122.)  Vice  versd  —  the  interval  elapsing  between  two  (Jiffermt  stars 
coming  on  the  meridian  of  one  ntid  the  same  place,  expressed  in  sidereal 
time,  is  the  measure  of  the  difference  of  right  ascensions  of  the  stars. 

(123.)  The  equinoctial  intersects  the  horizon  in  the  east  and  west 
points,  and  the  meridian  is  a  point  whose  altitude  is  equal  to  the  co-lati- 
tude of  the  place.  Thus,  at  Greenwich,  of  which  the  latitude  is  51"  28' 
40",  the  altitude  of  the  intersection  of  the  equiioctial  and  meridian  is 
38°  31'  20".  The  north  and  south  poles  of  the  heavens  are  the  poles  of 
the  equinoctial.  The  oast  and  west  points  of  the  horizon  of  a  spectator 
are  the  poles  of  his  celestial  meridian.  The  north  and  south  points  of  his 
horizon  are  the  poles  of  his  prime  vertical,  and  his  zenith  and  nadir  are 
the  poles  of  his  horizon. 

(124.)  All  the  heavenly  bodies  culminate  {i.  e.  come  to  their  greatest 
altitudes)  on  the  meridian ;  which  is,  therefore,  the  best  8ituat;ou  to  ob- 
serve them,  being  least  confused  by  the  inequalities  and  vapour;^  oi  the 
atmosphere,  as  well  as  least  displaced  by  refraction. 

(125.)  All  celestial  objects  within  the  circle  of  perpetual  apparition 
come  twice  on  the  meridian,  above  the  horizon,  in  every  diurnal  revolu- 
tion ;  once  above  and  once  below  the  pole.  These  are  called  their  vjjj)er 
and  lower  culminations. 

(126.)  The  problems  of  uranometry,  as  we  have  described  it,  consist 
in  the  solution  of  a  variety  of  spherical  triangles,  both  right  and  oblique 
angled,  according  to  the  rules,,  and  by  the  formulae  of  spherical  trigonom- 
etry, which  we  suppose  known  to  the  reader,  or  for  which  he  will  consult 
appropriate  treatises.    We  shall  only  here  observe  generally,  that  in  all 


c 

I 

m 
</) 

-< 

0 

b 
o 

C9 


9 


74 


OUTLINES   OF  ASTRONOMY. 


^ 


5  ' 


problems  in  which  sphcrioal  geomotry  is  ooncorncd,  the  student  will  find 
it  11  ii.soful  practical  nmxitn  ruthor  to  consider  the  polos  of  the  great  circles 
which  the  question  before  him  refers  to  than  the  circles  themselves.  To 
use,  for  example,  in  the  relations  he  has  to  consider,  polar  distances  rather 
thiiu  declinations,  zenith  distances  rather  than  altitudes,  &o.  Bearing 
this  in  mind,  there  are  few  problems  in  uranometry  which  will  offer  any 
ditficulty.  The  following  uro  the  combinations  which  most  commonly 
occur  for  solution  when  the  place  of  one  celestial  object  only  OQ  the  sphere 
is  concerned. 

(127.)  In  the  triangle  ZPS,  Z  is  tlio  zenith,  P  the  devoted  pole,  and 
S  the  star,  sun,  or  other  celestial  object.  In  this  triangle  occur,  1st,  PZ, 
which  being*he  complement  of  PH  (the  ultitude  of  the  polo),  is  ob- 
viously the  complement  of  the  latitude  (or  the  co-latitude,  as  it  is  called) 
of  the  place;  2d,  P  S,  tho^>o/«r  dintance,  or  the  complement  of  the  decli- 
nation (co-dccUnation)  of  the  star;  3d,  Z  S,  the  zenith  distance  or  co-alti- 
titde  of  the  star.  If  P  S  be  greater  than  90°,  the  object  is  situated  on 
tho  side  of  the  equinoctial  opposite  to  that  of  the  elevated  pole.  If  Z  S 
be  so,  the  object  is  below  the  horizon. 


if  V 


In  the  same  triangle  the  angles  are,  1st,  Z  P  S  the  lower  angle ;  2d,  P  Z  S 
(the  supplement  of  S  Z  0,  which  latter  is  the  azimuth  of  the  star  or  other 
heavenly  body),  3d,  P  S  Z,  an  angle  which,  from  the  infrequency  of  any 
practical  reference  to  it,  has  not  acquired  a  name.' 


'  In  the  practical  discussion  oTthe  measures  of  double  stars  and  other  objects  by  the 
aid  of  the  position  micrometer  his  angle  is  sometimes  required  to  be  iinown ;  and 
when  BO  required,  it  will  be  not  inconveniently  retierred  to  as  "  the  angle  of  position 
of  the  zenith." 


ELEMENTARY  RELATIONS. 


The  following  iivo  astronomical  magnitudes,  then,  occur  among  the  sides 
of  this  moflt  useful  trianglo :  viz.,  Ist,  The  co-lutitude  of  the  place  of 
observation;  2d,  the  polar  distance;  8d,  the  zenith  distance;  4th,  the 
hour  angle;  and  5th,  the  sub-uziniuth  (supplement  of  azimuth)  of  a  givou 
celestial  object;  and  by  its  solution  therefore  may  all  problems  be  resolved, 
in  which  three  of  these  magnitudes  are  directly  or  indirectly  given,  und 
the  other  two  required  to  be  found. 

(128.)  For  example,  suppose  the  time  of  rising  or  setting  of  tho  sun 
or  of  a  star  were  required,  having  given  its  right  ascension  and  polar  dis- 
tance. The  star  rises  when  apparently  on  the  horizon,  or  reallif  about 
84'  below  it  (owing  to  refraction),  so  that,  at  the  moment  of  its  apparent 
risii'S'  its  zenith  distance  is  90°  34'=Z  S.  Its  polar  distance  PS  being  also 
given,  and  tho  co-ktitudo  Z  P  of  the  place,  we  have  given  the  thruc  sidus 
of  the  triangle,  to  find  tho  hour  angle  ZPS,  which,  being  known,  is  to 
bo  added  to  or  subtracted  from  tho  star's  right  ascension,  to  give  the  side- 
real time  of  setting  or  rising,  which,  if  wo  please,  may  bo  converted  into 
solar  time  by  the  proper  rules  and  tables. 

(120.)  As  another  cxainplo  of  tho  use  of  the  same  triangle,  we  may 
propose  to  find  the  local  sidereal  time,  and  the  latitude  of  the  place  of 
observation,  by  observing  equal  altitudes  of  tho  same  star  east  and  west 
of  tho  meridian,  and  noting  the  interval  of  the  observations  in  sidereal 
time. 

The  hour  angles  corresponding  to  equal  altitudes  of  a  fixed  star  being 
equal,  the  hour  angle  east  or  west  will  be  measured  by  half  tho  observed 
interval  of  tho  observations.  In  our  triangle,  then,  we  have  given  thid 
hour  angle  ZPS,  the  polar  distance  P  S  of  the  star,  and  Z  S,  its  co- 
altitude  at  the  moment  of  observation.  Hence  we  may  find  P  Z,  tho 
co-lutitude  of  the  place.  Moreover,  tho  hour  ongle  of  the  star  being 
known,  and  also  its  right  ascension,  the  point  of  the  equinoctial  is  known, 
which  is  on  the  meridian  at  the  moment  of  observation ;  and,  therefore, 
the  local  sidereal  time  at  that  moment.  This  is  a  very  useful  observation 
for  determining  the  latitude  and  time  at  an  unknown  station. 


4 


C 

I 


> 

o 
a 

C 

09 


76 


OUTLINES  OP  ASTRONOMY. 


i 


CHAPTER  III.' 

OP  THE  NATURE  OP  ASTRONOMICAL  INSTRUMFNT8  AND  OBSERVATIONS 
IN  GENERAL. — OF  SIDEREAL  AND  SOLAR  TIME. — OP  THE  MEASURE- 
MENTS OP  TIME.  —  CLOCKS,  CHRONOMETERS. — OP  ASTRONOMICAL 
MEASUREMENTS. — PRINCIPLE  OP  TELESCOPIC  SIGHTS  TO  INCREASE 
THE  ACCURACY  OP  POINTING.  —  SIMPLEST  APPLICATION  OP  THIS 
PRINCIPLE. —  THE  TRANSIT  INSTRUMENT. —  OP  THE  MEASUREMENT 
OP  ANGULAR  INTERVALS.  —  METHODS  OP  INCREASING  THE  ACCU- 
RACY OP  READING. — THE  VERNIER. —  THE  MICROSCOPE. —  OP  THE 
MURAL  CIRCLE.  —  THE  MERIDIAN  CIRCLE. — FIXATION  OP  POLAR 
AND  HORIZONTAL  POINTS. — THE  LEVEL,  PLUMB-LINE,  ARTIFICIAL 
HORIZON. — PRINCIPLE  OP  COLLIMATION. — COLLIMATORS  OF  RITTEN- 
HOUSE,  KATER,  AND  BENZENBERO. — OP  COMPOUND  INSTRUMENTS 
WITH  CO-ORDINATE  CIRCLES. — THE  EQUATORIAL,  ALTITUDE,  AND 
AZIMUTH  INSTRUMENTS. — THEODOLITE. — OP  THE  SEXTANT  AND 
REFLECTING  CIRCLE. — PRINCIPLE  OP  REPETITION.  —  OP  MICROME- 
TERS.—  PARALLEL  WIRE  MICROMETER. — PRINCIPLE  OP  THE  DU- 
PLICATION OP  IMAGES. —  THE  HELIOMETER. —  DOUBLE  REFRACTING 
EYE-Pr  OE. — VARIABLE  PRISM  MICROMETER. — OP  THE  POSITION 
MICROMETER. 

(130.)  Our  Srst  chapters  have  heen  devoted  to  the  acquisition  chiefly 
of  preliminary  notions  respecting  the  globe  we  inhabit,  its  relation  to  the 
celestial  objects  which  surround  it,  and  the  physical  circumstances  under 
which  all  astronomical  observations  must  be  made,  as  well  as  to  provide 
ourselves  with  a  stock  of  technical  words  and  elementary  ideas  of  most 
frequent  and  familiar  use  in  the  sequel.  We  might  now  proceed  to  a 
more  exact  and  detailed  statement  of  the  facts  and  theories  of  astronomy ; 
b'rt,  in  order  to  do  this  with  full  effect,  it  will  be  desirable  that  the 
rv;ader  be  made  acquainted  with  the  principal  means  which  astronomers 

'  The  Btiident  who  is  anxious  to  become  acquainted  with  the  c))ief  subject  matter 
of  this  work,  may  defer  the  reading  of  that  part  of  this  chapter  which  is  devoted  to 
the  description  of  particular  instruments,  or  content  himself  with  a  cursory  perusal 
of  it,  until  farther  advanced,  when  it  will  be  necessary  to  return  to  it. 


possess,  of 
the  data  oi 
oertaining 
they  are  c 
that  he  can 
or  the  degr 
cedent  to  I 
certainly  be 
whether  an 
results,  to  s 
representati 
(131.)  A 
most  refinec 
proach  to  g 
n>ay  be  thou 
quired,  to  ti 
equal  parts, 
J^tely  on  its 
it  is  found  t( 
ordinary,  wh( 
to  the  purpo 
of  division  b 
mentj  and  tlj 
unsteadiness 
which  originJ 
expansion  anJ 
and  their  unl 
perceptible  a{ 
circumference 
of  an  inch, 
use  of  magnJ 
astronomical 
ployed  in  obsj 
rendered  a  di( 
a  circle,  subt 
radius,  so  tha| 
linear  extent 
ful  microsoop. 
therefore,  ihel 
circle  of  suchf 
mounted),  3e 


NATURE  OF  ASTRONOMICAL  INSTRUMENTS. 


77 


possess,  of  determining,  with  the  degree  of  nicety  their  theories  require, 
the  data  on  which  they  ground  their  conclusions ;  in  other  words,  of  as- 
certaining by  measurement  the  apparent  and  real  magnitudes  with  which 
they  are  conversant.  It  is  only  when  in  possession  of  this  knowledge 
that  he  can  fully  appreciate  either  the  truth  of  the  theories  themselves, 
or  the  degree  of  reliance  to  be  placed  on  any  of  their  conclusions  ante- 
cedent to  trial :  since  it  is  only  by  knowing  what  amount  of  error  can 
certainly  be  perceived  and  distinctly  measured,  that  he  can  satisfy  himself 
whether  any  theory  offers  so  close  an  approximation,  in  its  numerical 
results,  to  actual  phenomena,  as  will  justify  him  in  receiving  it  as  a  true 
representation  of  nature. 

(131.)  Astronomical  instrument-making  may  be  justly  regarded  as  the 
most  refined  of  the  mechanical  arts,  and  that  in  which  the  nearest  ap- 
proach to  geometrical  precision  is  required,  and  has  been  attained.     It 
may  be  thought  an  easy  thing,  by  one  unacquainted  with  the  niceties  re- 
quired, to  turn  a  circle  in  metal,  to  divide  its  circumference  into  860 
equal  parts,  and  these  again  into  smaller  subdivisions, — to  place  it  accu- 
rately on  its  centre,  and  to  adjust  it  in  a  given  position ;  but  practically 
it  is  found  to  be  one  of  the  most  difficult.     Nor  will  this  appear  extra- 
ordinary, when  it  is  considered  that,  owing  to  the  application  of  telescopes 
to  the  purposes  of  angular  measurement,  every  imperfection  of  structure 
of  division  becomes  magnified  by  the  whole  optical  power  of  that  instru- 
ment ;  and  that  thus,  not  only  direct  errors  of  workmanship,  arising  from 
unsteadiness  of  hand  or  imperfection  of  tools,  but  those  inaccuracies 
which  originate  in  far  more  uncontrollable  causes,  such  as  the  unequal 
expansion  and  contraction  of  metallic  masses,  by  a  change  of  temperature, 
and  their  unavoidable  flexure  or  bending  by  their  own  weight,  become 
perceptible  and  measurable.    An  angle  of  one  minute  occupies,  on  the 
circumference  of  a  circle  of  10  inches  in  radius,  oaly  about  ^^^th  part 
of  an  inch,  a  quantity  too  small  to  be  certainly  dealt  with  without  the 
use  of  magnifying  glasses;   yet  one  minute  is  a  gross  quantity  in  the 
astronomical  measurement  of  an  angle.     With  the  instruments  now  em- 
ployed in  observatories,  a  single  second,  or  the  60th  part  of  a  minute,  is 
rendered  a  distinctly  visible  and  appreciable  quantity.    Now,  the  arc  of 
a  circle,  subtended  by  one  second,  is  less  than  the  200,000th  part  of  the 
radius,  so  that  on  a  circle  of  6  feet  in  diameter  it  would  occupy  no  greater 
linear  extent  than  ^Vni;^^  P^'^  ^^  ^^  i°^^  >  ^  quantity  requiring  a  power- 
ful microscope  to  be  discerned  at  all.     Let  any  one  figure  to  himself, 
therefore,  the  4Jfficulty  of  placing  on  the  circumference  of  a  metallic 
circle  of  such  dimensions  (supposing  the  difficulty  of  its  construction  sur- 
mounted), 360  mar!ks,  dots,  or  cognizable  divisions,  which  shall  all  bo 


c 

(A 
< 

o 


pi 

r 

o 

p 


C 

0€ 


78 


OUTLINES   OF  ASTRONOMY. 


■fi    • 


true  to  their  places  within  such  narrow  limits ;  to  say  nothing  of  the  suh- 
division  of  the  degrees  so  marked  oflF  into  minutes,  and  of  these  again 
into  seconds.  Such  a  work  has  probably  baffled,  and  will  probably  for 
ever  continue  to  baflBe,  the  utmost  stretch  of  human  skill  and  industry ; 
nor,  if  executed,  could  it  endure.  The  ever-varying  fluctuations  of  heat 
and  cold  have  a  tendency  to  produce  not  merely  temporary  and  transient, 
but  permanent,  uncompensated  changes  of  form  in  all  considerable  masses 
of  those  metals  which  alone  are  applicable  to  such  uses ;  and  their  own 
weight,  however  symmetrically  formed,  must  always  be  unequally  sus- 
tained, since  it  is  impossible  to  apply  the  sustaining  power  to  evert/  part 
separately  :  even  could  this  be  done,  at  all  events  force  must  be  used  to 
move  and  to  fix  them ;  which  can  never  be  done  without  producing  tem- 
porary and  risking  permanent  change  of  form.  It  is  true,  by  dividing 
them  on  their  centres,  and  in  the  identical  places  they  are  destined  to 
occupy,  and  by  a  thousand  ingenious  and  delicate  contrivances,  wonders 
have  been  accomplished  in  this  department  of  art,  and  a  degree  of  perfec- 
tion has  been  given,  not  merely  to  cJtp/s  d'ccuvre,  but  to  instruments  of 
moderate  prices  and  dimensions,  and  in  ordinary  use,  which,  on  due  con- 
sideration, must  appear  very  surprising.  But  though  we  are  entitled  to 
lo(.)k  for  wonders  at  the  hands  of  scientific  artists,  we  are  not  to  expect 
miracles.  The  demands  of  the  astronomer  will  always  surpass  the  power 
of  the  artist ;  and  it  must,  therefore,  be  constantly  the  aim  of  the  former 
to  make  himself,  as  far  as  possible,  independent  of  the  imperfections  inci- 
dent to  every  work  the  latter  can  place  in  his  hands.  He  must,  therefore, 
endeavour  so  to  combine  his  observations,  so  to  choose  his  opportunities, 
and  so  to  familiarize  himself  with  all  the  causes  which  may  produce  in- 
strumental deraugcriient,  and  with  all  the  peculiarities  of  structure  and 
material  of  each  iiiHtiuinent  he  possesses,  as  not  to  allow  himself  to  be 
misled  by  their  errors,  but  to  extract  from  their  indications,  as  far  as  pos- 
sible, all  that  is  true,  and  reject  all  that  is  erroneous.  It  is  in  this  that 
the  art  of  the  practical  astronomer  consists,  —  an  art  of  itself  (jf  a  curious 
and  intricate  nature,  and  of  which  we  can  here  only  notice  som*  of  the 
leading  and  general  features. 

(132.)  The  great  aim  of  the  practical  astronomer  being  dwiiM^nJ 
correctness  in  the  results  of  instrumental  measurement,  his  constant  care 
and  vigilance  must  be  directed  to  the  detection  and  compeiisation  of  '^W0*, 
either  by  annihilatinjr,  or  by  taking  account  of,  and  allowing  for  tb^m. 
^ow,  if  we  examine  the  sources  from  which  errors  may  arise  in  any 
instrumental  determination,  we  shall  find  them  chiefly  radueiblt;  to  three 
principal  heads :  — 

(138.)  1st,  Kxternal   or  incidental  causes  of  error;   compr«lteD4iog 


such  as  de 

tuations  of 

lated  value 

the  extent  ^ 

perature  of 

used,  by  alt 

and  others  ( 

(134.)  2 

inexpertnesf 

occurrence  i 

from  atmosf 

ment,  and  th 

from  momec 

of  screws,  <& 

(135.)  3d 
to  which  ast 
may  be  deei 
principal  clas 
ment  not  hci 
Thus,  if  a  pi 
be  slightly  flj 
it  should)  coi 
be  in  reality 
intended'  to  b 
intervals, — r' 
mere  speculat 
observer  has  i 
riSO,)  Th, 
as  arise  Ufma 
have;  an*!  U 
no+  b4«-j»»g  pr, 
*omo  are  una 
soil  or  bwildir, 
minute  to  bo 
astrr>noinic!<l 
*'>r]<ijian»bip 
^<-,  but  >• '  f/f 
v>f  'rror- 
<boiw>  irfffjfded 
meD*  \am  or 


INSTRUMENTAL   AND   OTHER    SOURCES    OF    ERROR. 


79 


such  as  depend  on  external,  uncontrollable  circumstances :  such  as,  fluc- 
tuations of  weather,  which  disturb  the  amount  of  refraction  from  its  tabu- 
lated value,  and,  being  reducible  to  no  fixed  law,  induce  uncertainty  to 
the  extent  of  their  own  possible  magnitude ;  such  as,  by  varying  the  tem- 
perature of  the  air,  vai-y  also  the  form  and  position  of  the  instruments 
used,  by  altering  the  relative  magnitudes  and  the  tension  of  their  parts; 
and  others  of  the  like  nature. 

(134.)  2dly,  Errors  of  ohservation:  such  as  arise,  for  example,  from 
inexpertness,  defective  vision,  slowness  in  seizing  the  exact  instant  of 
occurrence  of  a  phenomenon,  or  precipitancy  in  anticipating  it,  &c. ; 
from  atmospheric  indistinctness ;  insufficient  optical  power  in  the  instru- 
ment, and  the  like.  Under  this  head  may  also  be  classed  all  errors  arising 
from  momentary  instrumental  derangement, — slips  in  clamping,  looseness 
of  screws,  &c. 

(135.)  3dly,  The  third,  and  by  far  the  most  numerous  class  of  errors 
to  which  astronomical  measurements  are  liable,  arise  from  causes  which 
may  be  deemed  instrumental,  and  which  may  be  subdivided  into  two 
principal  classes.  The  first  comprehends  those  which  arise  from  an  instru- 
ment not  heinff  what  it  professes  to  be,  which  is  error  of  workmanship. 
Thus,  if  a  pivot  or  axis,  instead  of  being,  as  it  ought,  exactly  cylindrical, 
be  slightly  flattened,  or  elliptical, — if  it  be  not  exactly  (as  it  is  intended 
it  should)  concentric  with  the  circle  it  carries;  — if  this  circle  (so  called) 
be  in  reality  not  exactly  circular,  or  not  in  one  plane ;  —  if  its  divisions, 
intcndfco  to  be  precisely  equidistant,  should  be  placed  in  reality  at  unequal 
intervals, — r-^d  a  hundred  other  things  of  the  same  sort.  T'lese  are  not 
mere  speculative  sources  of  error,  but  practical  annoyances,  which  every 
observer  has  to  contend  with. 

(136.)  The  otlyr  subdivision  of  instrumental  errors  comprehends  such 
as  arise  fp<mi  an  inetrumcnt  not  being  placed  in  tho  jjosition  it  ought  to 
havo ;  anol  from  those  of  its  parts,  which  are  made  purposely  moveable, 
no+  i '  ■  properly  deposed  inter  se.  These  are  errors  of  adjustmnit. 
Souii  ...  unavoidable,  as  they  arise  from  a  general  unsteadiness  of  the 
soil  or  i-itjildinj?  in  whicli  the  instruments  are  placed  ;  which,  though  too 
minutfl  f;0  be  noticed  in  any  other  way,  become  a'^nreciable  in  delicate 
astrrmomical  r)bservatio»s  ;  others,  again,  are  consequence,  of  imporfoct 
w'»rkiii!inf«l)ip  *«  where  an  jfl#trument  once  well  adjusted  will  not  remain 
f-d,  but  /->'p  f\  v>3(tHig  m/i  luting.  But  the  most  important  of  this  class 
v>f  ( rror«  ?.r. ■*<(■.  ffftf  ^^f^  T^on-rxistence  of  natural  indications,  other  than 
'hosf  -diffmie^  by  a^i:  -u.cal  okservations  themselves,  whether  an  instru 
meot  A«t  or  has  not  the  exact  position,  with  respect  to  the  horizon  and  its 


< 
o 


K 

tat* 

r 

o 

a 


C 


80 


OUTLINES  OF  ASTRONOMY. 


i 


cardinal  points,  the  axis  of  the  earth,  or  to  other  principal  astronomical 
lines  and  circles,  which  it  ought  to  have  to  fulfil  properly  its  objects. 

(1;J7.)  Now,  with  respect  to  the  first  two  classes  of  error,  it  must  be 
observed,  that,  in  so  far  as  they  cannot  be  reduced  to  known  laws,  and 
thereby  become  subjects  of  calculation  and  due  allowance,  they  actually 
vitiate,  to  their  full  extent,  the  results  of  any  observations  in  which  they 
subsist.  Being,  however,  in  their  nature  casual  and  accidental,  their 
eftects  necessarily  lie  sometimes  one  way,  sometimes  the  other ;  Bometimes 
diminishing,  sometimes  tending  to  increase  the  results.  Hence,  by  greatly 
multiplying  observations,  under  varied  circumstances,  by  avoiding  uufa- 
T3urable,  and  taking  advantage  of  favourable  circumstances  of  weather, 
or  otherwise  using  opportunity  to  advantage  —  and  finally,  by  taking  the 
mean  or  average  of  the  results  obtained,  this  class  of  errors  may  be  so 
far  sithdued,  by  setting  them  to  destroy  one  another,  as  no  longer  sensibly 
to  vitiate  any  theoretical  or  practical  conclusion.  This  is  the  great  and 
indeed  only  resource  against  tjch  errors,  not  merely  to  the  astronomer, 
but  to  the  investigator  of  numerical  results  in  every  department  of 
physical  research. 

(138.)  With  regard  to  errors  of  adjustment  and  workmanship,  not 
only  the  posdhility,  but  the  certainty  of  their  existence,  in  every  ima- 
ginable form,  in  all  instruments,  must  be  contemplated.  Human  hands 
or  machines  never  formed  a  circle,  drew  a  straight  line,  or  erected  a  per- 
pendicular, nor  ever  placed  an  instrument  in  perfect  adjustment,  unless 
accidentally ;  and  then  only  during  an  instant  of  time.  This  does  not 
prevent,  however,  that  a  great  approximation  to  all  these  desiderata 
should  be  attained.  But  it  is  the  peculiarity  of  astronomical  observation 
to  be  the  idtim/ite  means  of  dHection  of  all  mechanical  defects  which 
elude  by  their  minuteness  every  other  mode  of  detection.  What  the  eye 
cannot  discern  nor  the  touch  perceive,  a  course  o^  a«*/onomical  obf-erva- 
tions  will  make  distinctly  evident.  The  imperfoc*  products  of  man's 
hands  are  here  tested  by  being  brought  into  comparisoo  wader  very  great 
magnifying  powersj  fcorresponding  in  effect  to  3  ^^at  increa*?  in  iK;ute- 
ness  of  percoptioTjy  with  the  perfect  workmanship  /  Datur«; ,  and  there 
is  none  which  will  boar  the  trial.  N(Ar,  it  may  se^inm  Ilk*  arguing  in  a 
vicious  circle,  to  deduce  theoretical  conclui»*on8  aiKl  laws  from  f/oservation, 
and  then  to  turn  round  upon  the  in^ti-uments  witii  whicK>  those  observa- 
tions were  made,  accuse  thorn  <4  imperfection,  and  attem}/  U)  'J*'t«ct  aiid 
rectify  their  errors  by  means  of  the  very  laws  and  theorivi*  which  they 
have  helped  us  to  a  knowledge  of.  A  little  consideration,  however,  will 
suffice  to  show  that  such  a  course  of  proceeding  is  perfeeCJ-/  logitimi-te. 

(139  )  The  steps  by  which  we  arrive  at  the  laws  of  uatur  '  -  '\eaomena, 


: 


and  especia! 
determinatic 
lavs  are  ar 
without  any 
not  to  be  coi 
latitude  com 
These  '"'sulti 
delicate  mea 
them  are  pei 
is  corrected, 
until  the  ne 
improved  st^ 
subordinate  . 
the  verbal  st 
themselves  tc 
certainty,  oth 
become  subje 
the  reason  is 
laws  —  the  fii 
— is  that  of  e 
and  what  we 
bute  to  accide 
our  instrumec 
minations  car 
e.\ceed  the  ob 
set  about  imj 
deviations  occ 
better  defined 
of  a  law  of  ni 
statement,  ani 
of  circumstani 
(140.)  Noi 
that  other  disc 
the  existence 
Jraw  out  in  o 
'his  synoptic  i 
^ion.     Again 
of  this  suppos 
other,  of  a  to 
instrumental 
the  th'.ory  of 
6 


INSTRUMENTAL  SOURCES   OF   ERROR. 


81 


not 


I  ; 


and  especially  those  which  depend  for  their  verification  on  numerical 
determinatioas,  are  necessarily  successive.  Gross  results  and  palpable 
la^y'S  are  arrived  at  by  rude  observation  with  coarse  instruruents,  or 
without  any  instruments  at  all,  a.id  are  expressed  in  language  which  is 
not  to  be  considered  as  absolute,  but  is  to  be  interpreted  with  a  degree  of 
latitude  commensurate  to  the  imperfection  of  the  observations  themselves. 
These  '•"suits  are  corrected  and  refined  by  nicer  scrutiny,  and  with  more 
delicate  mean£.  The  first  rude  expressions  of  the  laws  which  embody 
theiu  are  perceived  to  be  inexact.  The  language  used  in  their  expression 
is  corrected,  its  terms  more  rigidly  defined,  or  i.tsh  terms  introduced, 
until  the  new  state  of  language  and  terminology  is  brought  to  fit  the 
improved  st\te  of  knowledge  of  facts.  In  the  progress  of  this  scrutiny 
subordinate  .aws  are  brought  into  view  which  still  further  modify  both 
the  verbal  statement  and  numerical  results  of  those  which  first  offered 
themselves  to  our  notice ;  and  when  these  are  traced  out  and  reduced  to 
certainty,  others,  again,  subordinate  to  them,  make  their  appearance,  and 
become  subjects  of  further  inquiry.  Now,  it  invariably  happens  (and 
the  reason  is  evident)  that  the  first  glimpse  we  catch  of  such  subordinate 
laws  —  the  first  form  in  which  they  are  dimly  shadowed  out  to  our  minds 
— is  that  of  errors.  We  perceive  a  discordance  between  what  we  expect, 
and  what  we  find.  The  first  occurrence  of  such  a  discordance  we  attri- 
bute to  accident.  It  happens  again  and  again ;  and  we  begin  to  suspect 
our  instruments.  We  then  inquire,  to  what  amount  of  error  their  deter- 
minations can,  hy  pomhility,  be  liable.  If  their  limit  of  possible  error 
e.xceed  the  observed  deviation,  we  at  once  condemn  the  instrument,  and 
set  about  improving  its  construction  or  adjustments.  Still  the  same 
deviations  occur,  and,  so  far  from  being  palliated,  are  more  marked  and 
better  defined  than  before.  We  are  now  sure  that  we  are  on  the  traces 
of  a  law  of  nature,  and  wo  pursue  it  till  we  have  reduced  it  to  a  definite 
statement,  and  verified  it  by  repeated  observation,  under  every  variety 
of  circumstances. 

(140.)  Now,  in  the  course  of  this  inquiry,  it  will  not  fail  to  happen 
that  other  discordances  will  strike  us.  Taught  by  experience,  we  suspect 
the  existence  of  some  natural  law,  before  unknown ;  we  tabulate  (i.  e. 
draw  out  in  order)  the  results  of  our  observations ;  and  we  perceive,  in 
'his  synoptic  statement  of  them,  distinct  indications  of  a  regular  progres- 
m\\.  Again  we  improve  or  vary  our  instruments,  and  we  now  lose  sight 
of  this  supposed  new  law  of  nature  altogether,  or  find  it .  3placed  by  some 
other,  of  a  totally  different  character.  Thus  we  are  led  to  suspect  an 
instrumental  cause  for  what  we  have  noticed.  We  examine,  therefore, 
the  th'ory  of  our  instrument ;  we  puppose  defects  in  its  structure,  and,  by 
6 


I 

m 

tA 

o 


n 

o 
a 

C 

2 


82 


OUTLINES   OF   ASTRONOMY. 


t  i 


the  aid  of  geometry,  we  trace  their  influence  in  introducing  actnnl  errors 
into  its  indications.  These  errors  have  their  laics,  which,  so  long  as  we 
have  no  knowledge  of  causes  to  guide  us,  may  be  confounded  with  laws 
of  nature,  as  they  are  mixed  up  with  them  in  their  effects.  They  are  not 
fortuitous,  like  errors  of  observation,  but,  as  they  arise  from  sources 
inherent  in  the  instrument,  and  anchungeable  while  it  and  its  adjustments 
remain  unchanged,  they  are  reducible  to  fixed  and  ascertainable  forms ; 
each  particular  defect,  whether  of  structure  or  adjustment,  producing  its 
own  appropriate  form  of  error.  When  these  are  thoroughly  investigated, 
we  recognize  among  them  one  which  coincides  in  its  nature  and  progression 
with  that  of  our  observed  discordances.  The  mystery  is  at  once  solved. 
We  have  detected,  by  direct  observation,  an  ins'cruinental  defect. 

(141.)  It  is,  therefore,  a  chief  requisite  fov  the  practical  astronomer  to 
make  himself  completely  familiar  with  the  theorj/  of  his  instruments.  By 
this  alone  is  he  enabled  at  once  to  decide  what  effect  on  his  observations  any 
given  imperfection  of  structure  or  adjustment  will  produce  in  any  given 
circumstances  under  which  an  observation  can  Lo  made.  This  alone  also 
can  place  him  in  a  condition  to  derive  available  and  practical  means  of 
destroying  and  eliminating  altogether  the  influence  of  such  imperfections, 
by  so  arranging  his  observations,  that  it  shall  affect  their  results  in  oppo- 
site ways,  and  that  its  influence  shall  thus  disappear  from  their  mean, 
which  is  one  of  the  chief  modes  by  which  precision  is  attained  in  practical 
astronomy.  Suppose,  for  example,  the  principle  of  an  instrument  required 
that  a  circle  should  be  concentric  with  the  axis  on  which  it  is  made  to 
turn.  As  this  is  a  condition  which  no  workmanship  can  exactly  fulfil,  it 
becomes  necessary  to  ii>quire  what  errors  will  be  produced  in  observations 
made  and  registered  on  the  faith  of  such  an  instrument,  by  any  assigned 
deviation  in  this  respect ;  that  :s  to  say,  what  would  be  the  disagreement 
between  observations  made  with  it  and  with  one  absolutely  perfect,  could 
such  be  obtained.  Now,  simple  geometrical  considerations  suffice  to  show 
—  1st.  that  if  the  axis  be  excentric  by  a  given  fraction  (say  one  thou- 
sandth part)  of  the  radius  of  the  circV\  all  angles  read  off  on  that  part 
of  the  circle  towards  which  the  excentricity  lies,  will  appear  by  that  frac- 
tional amount  too  small,  and  all  on  the  opposite  side  too  large.  And, 
2dly,  that  lohatcver  be  the  amount  of  the  excentricity,  and  on  tchntcvcr 
part  of  the  circle  any  proposed  angle  is  measured,  the  effect  of  the  error 
in  question  on  the  result  of  observations  depending  on  the  graduation  of 
its  circumference  (or  limb,  as  it  is  technically  called)  will  b^  completely 
annihilated  by  the  very  easy  method  of  always  reading  off  the  divisions 
on  two  diametrically  opposite  points  of  the  circle,  and  taking  a  mean  ;  for 
the  effect  of  excentricity  is  always  to  increase  the  arc  representing  the 


M 


angle  in 
which  it 
use  of  th 
that  of  tl 
question, 
deviation, 
tion.      Si 
theory  of 
knowledg( 
often  to  al 
the  most  j 
turns  aim 
the  most 
further  con 
to  describe 
tion  and  ad 

(142.) 

ing  of  tho 

methods,  w 

Observant 

already  con< 

formed  in  ci 

going  chapt 

entirely  ovei 

in  the  imme( 

irregularity, 

as  the  diurna 

ments,  even  i 

exact  circles 

the  phenome 

apparent  diui 

oval  form,  its 

tion  being  gre 

being  the  sam 

and  the  lower 

soon  found  to 

sary  to  seek  a 


*  The  principlt 
and  common  insi 
formed,  are,  how 
struments  withou 


ILLUSTRATION   BY   EXAMPLES.  —  REFRACTION. 


83 


rrors 
IS  wo 
laws 
•e  not 
jurces 
ments 
orms ; 
ng  its 
gated, 
ression 
solved. 


•mer  to 
s.    By 
Dns  any 
y  given 
)ne  also 
cans  of 
fections, 
in  oppo- 
mean, 
ractical 
equired 
Imade  to 
[fulfil,  it 
irvations 
ssigncd 
Ireement 
pt,  could 
to  sbow 
e  thou- 
iiat  part 
at  frac- 
And, 
hatevcr 
[he  error 
tion  of 
)pletoly 
iivisions 
?an ;  for 
tmg  the 


angle  in  question  on  one  side  of  the  circle,  by  just  the  same  quantity  by 
which  it  diminishes  that  on  the  other.  Again,  suppose  that  the  proper 
use  of  the  instrument  required  that  this  axis  should  be  exactly  parallel  to 
that  of  the  earth.  As  it  never  can  be  placed  or  remain  so,  it  becomes  a 
question,  what  amount  of  error  will  arise,  in  its  use,  from  any  assigned 
deviation,  whether  in  a  horizontal  or  vertical  plane,  from  this  precise  posi- 
tion. Such  inquiries  constitute  the  theory  of  instrumental  errors ;  a 
theory  of  the  utmost  importance  to  practice,  and  one  of  which  a  complete 
knowledge  will  enable  an  observer,  with  moderate  instrumental  means, 
often  to  attain  a  degree  of  precision  which  might  seem  to  belong  only  to 
the  most  refined  and  costly.  This  theory,  as  will  readily  be  apprehended, 
turns  almost  entirely  on  considerations  of  pure  geometry,  and  those  for 
the  most  part  not  difficult.  In  the  present  work,  however,  we  have  no 
further  concern  with  it.  The  Astronomical  instruments  we  propose  briefly 
to  describe  in  this  chapter  will  be  considered  as  perfect  both  in  construc- 
tion and  adjustment.' 

(142.)  As  the  above  remarks  are  very  essential  to  a  right  understand- 
ing of  tho  philosophy  of  our  subject  and  the  spirit  of  astronomical 
methods,  we  shall  elucidate  them  by  taking  one  or  two  special  cases. 
Observant  persons,  before  the  invention  of  astronomical  instruments,  had 
already  concluded  the  apparent  diurnal  motions  of  the  stars  to  be  per- 
formed in  circles  abcut  fixed  poles  in  the  heaveas,  as  shown  in  the  fore- 
going chapter.  In  drawing  this  conclusion,  however,  refraction  was 
entirely  overlooked,  or,  if  forced  on  their  notice  by  its  great  magnitude 
in  the  immediate  neighbourhood  of  the  horizon,  was  regarded  as  a  local 
irregularity,  and,  as  such,  neglected,  or  slurred  over.  As  soon,  however, 
as  the  diurnal  paths  of  the  stars  were  attempted  to  be  traced  by  instru- 
ments, even  of  the  coarsest  kind,  it  became  evident  that  the  notion  of 
exact  circles  described  about  one  and  the  same  pole  would  not  represent 
the  phenomena  correctly,  but  that,  owing  to  some  cause  or  other,  the 
apparent  diurnal  orbit  of  every  star  is  distorted  from  a  circular  into  an 
oval  form,  its  lower  segment  being  flatter  than  its  upper ;  and  the  devia- 
tion being  greater  the  nearer  the  star  approached  the  horizon,  the  effect 
being  the  same  as  if  the  circle  had  been  squeezed  upwards  from  below, 
and  the  lower  parts  more  than  the  higher.  For  such  an  effect,  as  it  was 
soon  found  to  arise  from  no  casual  or  instrumental  cause,  it  became  neces- 
sary to  seek  a  natural  one ;  and  refraction  readily  occurred,  to  solve  the 

'  The  principle  on  which  the  chief  adjustments  of  two  or  three  of  the  most  useful 
and  common  instruments,  such  as  the  transit,  the  equatorial,  and  the  sextant,  are  per- 
Ibrmed,  are,  however,  noticed,  for  the  convenience  of  readers  who  may  use  such  in- 
struments without  going  farther  into  the  arcana  of  practical  astronomy. 


G 

I 
i 

turn* 

< 

O 


r 

o 
a 


r 


84 


OUTLINES   OF  ASTRONOMY. 


i  ;* 


difficulty.  In  fact,  it  is  a  case  precisely  analogous  to  what  we  have 
already  noticed  (art.  47),  of  the  apparent  distortion  of  the  sun  near  the 
horizon,  only  on  a  larger  scale,  and  traced  up  to  greater  altitudes.  This 
new  law  once  established,  it  became  necessary  to  modify  the  expression  of 
that  anciently  received,  by  inserting  in  it  a  salvo  for  the  effect  of  refrac- 
tion, or  by  making  a  distinction  between  the  ajyparent  diurnal  orbits,  as 
affected  by  refraction,  and  the  true  ones  cleared  of  that  effect.  This  dis- 
tinction between  the  apparent  and  the  true — between  the  uncorrected 
and  corrected — between  the  rough  and  obvious,  and  the  refined  and  ulti- 
mate— is  of  perpetual  occurrence  in  every  part  of  astronomy. 

(143.)  Again.  The  first  impression  produced  by  a  view  of  the  diurnal 
movement  of  the  heavens  is  that  all  the  heavenly  bodies  perform  this 
revolution  in  one  common  period,  viz.  a  day,  or  24  hours.  But  no  sooner 
do  we  come  to  examine  the  matter  instrumentally,  i.  e.  by  noting,  by 
time-keepers,  their  successive  arrivals  on  the  meridian,  than  we  find  dif- 
ferences which  cannot  be  accounted  for  bj  any  error  of  observation.  All 
the  stars,  it  is  true,  occupy  the  same  interval  of  time  between  their  suc- 
cessive appulses  to  the  meridian,  or  to  any  vertical  circle ;  but  this  is  a 
very  different  one  from  that  occupied  by  the  cun.  It  is  palpably  shorter; 
being,  in  fact,  only  23''  56'  409",  instead  of  24  hours,  such  hours  as 
our  common  clocks  mark.  Here,  then,  we  have  already  txco  different 
days,  a  sidereal  and  a  solar;  and  if,  instead  of  the  sun,  we  observe  the 
moon,  we  find  a  third,  much  longer  than  either, — a  lunar  day,  whose 
average  duration  is  24''  54""  of  our  ordinary  time,  which  last  is  solar  time, 
being  of  necessity  conformable  to  the  sun's  successive  re-appearances,  on 
which  all  the  business  of  life  depends. 

(144.)  Now,  all  the  stars  are  found  to  be  unanimous  in  giving  the 
same  exact  duration  of  23"  56'  4-09  ",  for  the  sidereal  day;  which,  there- 
fore, we  cannot  hesitate  to  receive  as  the  period  in  which  the  earth  makes 
one  revolution  on  its  axis.  We  are,  therefore,  compelled  to  look  on  the 
sun  and  moon  as  exceptions  to  the  general  law ;  as  having  a  different 
nature,  or  at  least  a  different  relation  to  us,  from  the  stars ;  and  as  having 
motions,  real  or  apparent,  of  their  own,  independent  of  the  rotation  of 
the  earth  on  its  axis.  Thus  a  jpreat  and  most  important  distinction  is 
disclosed  to  us. 

(145.)  To  establish  these  facts,  almost  no  apparatus  is  required.  An 
ob--orver  need  only  station  himself  to  the  north  of  .-^ome  well-defined  ver- 
tical object,  as  the  angle  of  a  building,  and,  placing  his  eye  exactly  at  a 
certain  fixed  point  (such  as  a  small  hole  in  a  plate  of  metal  nailed  to  some 
immoveable  support),  notice  the  successive  disappearances  of  any  star  be- 


8ID£KEAL  AND   SOLAR  TIME. 


85 


lavc 

the 

rhis 

Q  of 

fiac- 
s,  as 

dis- 
ccted 

ulti- 

urnal 
1  this 
looner 

g,  ^y 

id  dif- 
AU 
ir  suc- 
ds  is  a 
aorter; 
lurs  as 
^ffcirnt 
Ive  the 

whose 
time, 

!es,  on 

ing  the 

there- 

I  makes 

Ion  the 

IfFerent 

laving 

ton  of 

don  is 


hind  the  building,  by  a  watch.'  When  he  observes  the  sun,  he  must 
shade  his  eye  with  a  dark-coloured  or  smoked  glass,  and  notice  the  moments 
when  its  western  and  eastern  edges  successively  come  up  to  the  wall,  from 
which,  by  taking  half  the  interval,  he  will  ascertain  (what  he  cannot  di- 
rectly observe)  the  moment  of  disappearance  of  its  centre. 

(146.)  When,  in  pursuing  and  establishing  this  general  fact,  we  are 
led  to  attend  more  nicely  to  the  times  of  the  daily  arrival  of  the  sun  on 
the  meridian,  irregularities  (such  they  first  seem  to  be)  begin  to  make  their 
appearance.    The  intervals  between  two  successive  arrivals  are  not  iho  same 
at  all  times  of  the  year.   They  are  sometimes  greater,  sometimes  less,  than 
24  hours,  as  shown  by  the  clock ;  that  is  to  say,  the  solar  day  is  not  always 
of  the  same  length.    About  the  21st  of  December,  for  example,  it  is  half 
a  minute  longer,  and  about  the  same  day  of  September  nearly  as  much 
shorter,  than  its  average  duration.   And  thus  a  distinction  is  again  press- 
ed upon  our  notice  between  the  actual  solar  day,  which  is  never  two  days 
in  succession  alike,  and  the  mean  solar  day  of  24  hours,  which  is  an  ave- 
rage of  all  the  solar  days  throughout  the  year.    Here,  then,  a  new  source 
of  inquiry  opens  to  us.     The  sun's  apparent  motion  is  not  only  not  the 
same  with  the  stars,  but  it  is  not  (     ine  latter  is)  uniform.     It  is  subject 
to  fluctuations,  whose  laws  become  mafier  of  investigation.     But  to  pur- 
sue these  laws,  we  require  nicer  means  of  observation  than  what  we  have 
described,  and  are  obliged  to  call  in  to  our  aid  an  instrument  called  the 
transit  instrument,  especially  destined  for  such  observations,  and  to  attend 
minutely  to  all  the  causes  of  irregularity  in  the  going  of  clocks  and  watches 
which  may  affect  our  reckoning  of  time.     Thus  we  become  involved  by 
degrees  in  more  and  more  delicate  instrumental  inquiries ;  and  we  speed- 
ily find  that,  in  proportion  as  we  ascertain  the  amount  and  law  of  one 
great  or  leading  fluctuation,  or  inequality,  as  it  is  called,  of  the  sun's 
diurnal  motion,  we  bring  into  view  others  continually  smaller  and  smaller, 
which  were  before  obscured,  or  mixed  up  with  errors  of  observation  and 
instrumental  imperfections.     In  short,  we  may  not  inaptly  compare  the 
mean  length  of  the  solar  day  to  the  mean  or  average  height  of  water  in 
a  harbour,  or  the  general  level  of  the  sea  unagitated  by  tide  or  waves. 
The  great  annual  fluctuation  above  noticed  may  be  compared  to  the  daily 


i 

0 

< 

o 


An 
pd  ver- 
ily at  a 
some 
Itar  be- 


*  This  is  an  excellent  practical  method  of  ascertaining  the  rate  of  a  clock  or  watch, 
being  exceeding  accurate  if  a  few  precautions  are  attended  to ;  the  chief  of  which  is, 
to  take  care  that  that  part  of  the  edge  behind  which  the  star  (a  bright  one,  not  a  planet) 
disappears  shall  be  quite  smooth ;  as  otherwise  variable  refraction  may  transfer  the 
point  of  disappearance  from  a  protuberance  to  a  notch,  and  thus  vary  the  moment  of 
observation  unduly.  This  is  easily  secured,  by  nailing  up  a  smooth-edged  board. 
The  verticality  of  its  edge  should  be  insured  by  the  use  of  a  plumb-line. 


86 


OUTLINES   OP   ASTRONOMY. 


variations  of  level  produced  by  the  tides,  which  are  nothing  but  enormous 
waves  rxtendiug  ovu  the  whole  ocean,  while  the  suialler  subordinate  ine- 
qualities may  be  assimilated  to  waves  ordinarily  so  called,  c  ,fhich,  when 
largo,  we  perceive  lesser  undulations  to  ride,  and  ou  the:^u,  again,  minuter 
ripplings,  to  the  series  of  whose  subordination  wo  can  perceive  no  end. 

(147.)  With  the  causes  of  these  irregularities  in  the  solar  motion  wc 
have  no  concern  at  present ;  their  explanation  belongs  to  a  more  advanced 
part  of  our  subject;  but  the  distinction  between  the  solar  and  sidereal 
days,  as  it  pervades  every  part  of  astronomy,  requires  to  be  early  intro- 
duced, and  never  lost  sight  of.  It  is,  as  already  observed,  the  mean  or 
average  length  of  the  solar  day,  which  is  used  in  the  civil  reckoning  of 
time.  It  commences  at  midnight,  but  astronomers,  even  when  they  use 
mean  solar  time,  depart  from  the  civil  reckoning,  commencing  their  day 
at  noon,  and  reckoning  the  hours  from  0  round  to  24.  Thus,  11  o'clock 
in  the  forenoon  of  the  second  of  January,  in  the  civil  reckoning  of  time, 
corresponds  to  January  1  day  23  hours  in  the  astronomical  reckoning ; 
and  one  o'clock  in  the  afternoon  of  the  former,  to  January  2  days  1  hour 
of  the  latter  reckoning.  This  usage  has  its  advantages  and  disadvantages, 
but  the  latter  seem  to  preponderate  j  and  it  would  be  well  if,  in  conse- 
quence, it  could  be  broken  through,  and  the  civil  reckoning  substituted. 
Uvtformitt/  i.-i  'j,<  aenclature  and  modes  of  rechoning  in  all  matters  relat- 
ing io  timi\  ij/'wc'  weight,  measi't'e,  t&c,  is  of  such  vast  and  paramount 
imjortaii!'.  iti,  eiy  ry  relation  of  life  as  to  outweigh  every  consideration  of 
technical  convi  n/ince  or  custom,^ 

(148.)  Both  astronomers  and  civilians,  however,  who  inhabit  different 
points  of  the  earth's  surface,  differ  from  each  other  in  their  reckoning  of 
time ;  as  it  is  obvious  they  must,  if  we  consider  that,  when  it  is  noon  at 
one  place,  it  is  midnight  at  a  place  diametrically  opposite;  sunrise  at 
another;  and  sunset,  again,  at  a  fourth.  Hence  arises  considerable  in- 
convenience, especially  as  respects  places  differing  very  widely  in  situation, 
and  which  may  even  in  some  crUJoal  cases  involve  the  mistake  of  a  whole 
day.  To  obviate  this-  inconvenience,  there  has  lately  been  introduced  a 
system  of  reckoning  time  by  mean  solar  days  and  parts  of  a  day  counted 
from  a  fixed  instant,  common  to  all  the  world,  and  determined  by  no  local 

>  The  only  disadvantage  to  astronomers  of  using  the  civil  reckoning  is  this — that 
their  observations  being  chiefly  carried  on  during  the  night,  the  day  of  their  date  will, 
in  this  reckoning,  always  have  to  be  changed  at  midnight,  and  the  former  and  latter 
portion  of  every  night's  observations  will  be'oiig  to  two  diflerently  numbered  civil  days 
of  the  month.  There  is  no  denying  this  to  be  an  inconvenience.  Habit,  however, 
would  alleviate  it;  and  some  inconveniences  must  be  cheerfully  submitted  to  by  all  who 
resolve  to  act  on  general  principles.  All  other  classes  of  men,  whose  occupation  ex- 
extends  to  the  night  as  well  as  day,  submit  to  it,  and  find  their  advantage  in  doing  so. 


circumstance 
among  the  si 
numerically  i 
Its  oi  igin  wi] 
work. 

(149.;    Til 

twofold  poinl 

The  ,  arth's  d 

circle  uniform 

in  succession 

direct  measui 

fundamemal  i 

guage  of  geoti 

tronomy  is  tl 

their  reference 

of  the  law  of 

than  a  propos 

apparent  situai 

compare  such  1 

of  the  observec 

they  were  obsc 

(150.)  The 

clepsydras,  and 

astronomy.     T 

ing,  or  rather  c 

The  clepsydra, 

vessel  of  water 

ble  exactness, 

invention  of  cl( 

the  greater  com 

case  only  has  tl 

measurement  o 

cury  from  a  smt 

to  a  fixed  heigh 

any  event,  and  ^ 

run,  till  the  mc 

cause  is  sudden 

ceases  to  run  ir 

pared  with  the 

clock,  gives  the 

and  simple  metl 


MEASUREMENT  OP  TIME. 


87 


passage  of  the  stars 

nes,  therefore,  a 

..     2dly,  As  the 

/<»/<//?,  to  use  the  lan- 


circumstnnce,  such  as  noon  or  midnight,  but  by  ;lio  motion  of  the  sun 
among  the  stars.  Time,  so  reckoned,  is  culled  equiuoctiul  time ;  and  is 
numerically  the  same,  at  the  same  instant,  in  every  part  of  the  globe. 
Its  origin  will  be  explained  more  fully  at  a  more  advanced  stage  of  our 
work. 

(140.;  Time  is  an  essential  element  in  astronomical  observation,  in  a 
twofold  point  of  view:  —  1st,  As  the  representative  of  angular  motion. 
The  earth's  diurnal  motion  being  uniform,  everv  'ar  describes  its  diurnal 
circle  uniformly;  and  the  time  elapwing  bef^ 
in  succession  across  the  meridian  of  un^ 
direct  measure  of  their  differences  of  rigl. 
fundameuial  element  (or  natural  indrprndeui  . 
guagc  of  geometers)  in  all  dynamical  theories.  Tlio  great  object  of  as- 
tronomy is  the  determination  of  the  laws  of  the  celestial  motions,  and 
their  reference  to  their  proximate  or  remote  causes.  Now,  the  statement 
of  the  law  of  any  observed  motion  in  a  celestial  object  can  be  no  other 
than  a  proposition  declaring  what  has  been,  is,  and  will  be,  the  real  or 
apparent  situation  of  that  object  <'t  ani/  time,  past,  present,  or  future.  To 
conipare  such  laws,  therefore,  with  observation,  we  must  possess  a  register 
of  the  observed  situations  of  the  object  in  question,  and  of  the  times  when 
they  were  observed. 

(150.)  The  measurement  of  time  is  performed  by  clocks,  chronometers, 
clepsydras,  and  hour-glasses.  The  two  former  are  alone  used  in  modern 
astronomy.  The  hour-glass  is  a  coarse  and  rude  contr  vauce  for  measur- 
ing, or  rather  counting  out,  fixed  portions  of  time,  and  is  entirely  disused. 
The  clepsydra,  which  measured  time  by  the  gradual  emptying  of  a  largo 
vessel  of  water  through  a  determinate  orifice,  is  susceptible  of  considera- 
ble exactness,  and  was  the  only  dependence  of  astronomers  before  the 
invention  of  clocks  and  watches.  At  present  it  is  abandoned,  owing  to 
the  greater  convenience  and  exactness  of  the  latter  instruments.  In  one 
case  only  has  the  revival  of  its  use  been  proposed  j  viz.  for  the  accurate 
measurement  of  very  small  portions  of  time,  by  the  flowing  out  of  mer- 
cury from  a  small  orifice  in  the  bottom  of  a  vessel,  kept  constantly  full 
to  a  fixed  height.  The  stream  is  intercepted  at  the  moment  of  noting 
any  event,  and  directed  aside  into  a  receiver,  into  which  it  continues  to 
run,  till  the  moment  of  noting  any  other  event,  when  the  intercepting 
cause  is  suddenly  removed,  the  stream  flows  in  its  original  course,  and 
ceases  to  run  into  the  receiver.  The  weight  of  mercury  received,  com- 
pared with  the  weight  received  in  an  interval  of  time  observed  by  the 
clock,  gives  the  interval  between  the  events  observed.  This  ingenious 
and  simple  method  of  resolving,  with  all  possible  precision,  a  problem 


I 

O 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


?■ 


^/ 


4r 


^ 


1.0 


1*5 


■21    125 

|»0     ^^"       ■■■ 


I.I 


lU 

u 


liC 


^ 


^/^^" 

"k 


** 


Fhotographic 

Sdenoes 
Corporation 


23  WIST  MAM  STRHT 

WltSTIR,N.Y.  USM 

(7H)t72-4S03 


;\ 


88 


OUTLINES  OF  ASTRONOMY. 


11   • 


of  much  importance  in  many  physical  inquiries,  is  due  to  the  late  Captain 
Katcr. 

(151.)  The  pendulum  clock,  however,  and  the  balance  watch,  with 
those  improvements  and  refinements  in  its  structure  which  constitute  it 
emphatically  a  chronometer,^  are  the  instruments  on  which  the  astronomer 
depends  for  his  knowledge  of  the  lapse  of  time.  These  instruments  are 
now  brought  to  such  perfection,  that  an  habitual  irregularity  in  the  rate 
of  going,  to  the  extent  of  a  single  second  in  twenty-four  hours  in  two 
consecutive  days,  is  not  tolerated  in  one  of  good  character ;  so  that  any 
interval  of  time  less  than  twenty-four  hours  may  be  certainly  ascertained 
within  a  few  tenths  of  a  second,  by  their  use.  In  proportion  as  intervals 
are  longer,  the  risk  of  error,  as  well  as  the  amount  of  error  risked,  be- 
comes greater,  because  the  accidental  errors  of  many  days  may  accumu- 
late ;  and  causes  producing  a  slow  progressive  change  in  the  rate  of  going 
may  subsist  unporceived.  It  is  not  safe,  therefore,  to  trust  the  determi- 
nation of  time  to  clocks,  or  watches,  for  many  days  in  succession,  without 
checking  them,  and  ascertaining  their  errors  by  reference  to  natural  events 
which  we  know  to  happen,  day  after  day,  at  equal  intervals.  But  if  this 
be  done,  the  longest  intervals  may  be  fixed  with  the  same  precision  as  the 
shortest;  since,  in  fact,  it  is  then  only  the  times  intervening  between  the 
first  and  the  last  moments  of  such  long  intervals,  and  such  of  those 
periodically  recurring  events  adopted  for  our  points  of  reckoning,  as  occur 
within  twenty-four  hours  respectively  of  either,  that  we  measure  by  arti- 
ficial means.  The  whole  days  are  counted  out  for  us  by  nature ;  the  frac- 
tional parts  only,  at  either  end,  are  measured  by  our  clocks.  To  keep  the 
reckoning  of  the  integer  days  correct,  so  that  none  shall  be  lost  or  counted 
twice,  is  the  object  of  the  calendar.  Chronology  marks  out  the  oi-der  of 
succession  of  events,  and  refers  them  to  their  proper  years  and  days; 
while  chronometry,  grounding  its  determinations  on  the  precise  observa- 
tion of  such  regularly  periodical  events  as  can  be  conveniently  and  exactly 
subdivided,  enables  us  to  fix  the  moments  in  which  phenomena  occur,  with 
the  last  degree  of  precision. 

(152.)  In  the  culmination  or  transit  (i.  e.  the  passage  across  the 
meridian  of  an  observer,)  of  every  star  in  the  heavens,  he  is  furnished 
with  such  a  regularly  periodical  natural  event  as  we  allude  to.  Accord- 
ingly, it  is  to  the  transits  of  the  brightest  and  most  conveniently  situated 
fixed  stars  that  astronomers  resort  to  ascertain  their  exact  time,  or,  which 
comes  to  the  same  thing,  to  determine  the  exact  amount  of  error  of  their 
docks. 

(153.)  Before  we  describe  the  instrument  destined  for  the  purpose  of 
*»" '  '  Xpovos,  time ;  iitrpuv,  to  moosuro. 


observing 
ment  of  a 
before  the 
nomy  to  tl 
of  the  visi 

(154.) 
poses  is  t 
single,  or 
optica,  an 
cell  of  the 


often  substi 
fying  powei 
according  t< 
This  also  is 
the  tube,  e 
forming  om 

(155)  Tl 
and  produce 
And  it  is  ev 
the  tube  anc 
their  fixity  i 

(156.)  \^ 
picture  or  in 
optics),  in  tl 
were  a  real  > 
bles  us  to  m 
in  the  same 

(157.)  N( 
immaterial  a 
place  F  in  I 
definite  form 
needle  —  or 
lines),  thin  i 
at  right  angi 
If  such  a  po: 


PRINCIPLE  OP  TELBSOOPIO  SIGHTS. 


89 


observing  such  culmiDations,  however,  or  those  intended  for  the  measure- 
ment  of  angular  intervals  in  the  sphere,  it  is  requisite  to  place  clearly 
before  the  reader  the  principle  on  which  the  telescope  is  applied  in  astro- 
nomy to  the  precise  determination  of  a  direction  in  space,  —  that,  namely, 
of  the  visual  ray  by  which  we  see  a  star  or  any  other  distant  object. 

(154.)  The  telescope  most  commonly  used  in  astronomy  for  these  pur- 
poses is  the  refracting  telescope,  which  consists  of  an  object-glass  (either 
single,  or  as  is  now  almost  universal,  double,  forming  what  is  called  in 
optics,  an  acromatic  combination)  A ;  a  tube  A  B,  into  which  the  brass 
cell  of  the  object-glass  b  firmly  screwed,  and  an  eye-lens  C,  for  which  is 


Fig.  14. 


ffi 


£ 

— 1_ 


f 


— 1 


often  substituted  a  combination  of  glasses  designed  to  increase  the  magni- 
fying power  of  the  telescope,  cr  otherwise  give  more  distinctness  of  vision 
according  to  optical  principles  which  we  have  no  occasion  here  to  refer  to. 
This  also  is  fitted  into  a  cell,  which  is  screwed  firmly  into  the  end  B  of 
the  tube,  so  that  object-glass,  tube,  and  eye-glass  may  be  considered  as 
forming  one  piece,  invariable  in  the  relative  position  of  its  parts. 

(155)  The  line  PQ  joining  the  centres  of  the  object  and  eye-glasses 
and  produced,  is  called  the  axis,  or  line  of  colKmation  of  the  telescope. 
And  it  is  evident,  that  the  situation  of  this  line  holds  a  fixed  relation  to 
the  tube  and  its  appendages,  so  long  as  the  object  and  eye-glasses  maintain 
tJieir  fixity  in  this  respect. 

(156.)  Whatever  distant  object  E,  this  line  is  directed  to,  an  inverted 
picture  or  image  of  that  object  F  is  formed  (according  to  the  principles  of 
optics),  in  the  focus  of  the  object-glass,  and  may  there  be  viewed  as  if  it 
were  a  real  object,  through  the  eye-lens  C,  which  (if  of  short  focus)  ena- 
bles us  to  magnify  it  just  as  such  a  lens  would  magnify  a  material  object 
in  the  same  place. 

(157.)  Now  as  this  image  is  formed  and  viewed  in  the  air,  being  itself 
immaterial  and  impalpable  —  nothing  prevents  our  placing  in  that  very 
place  F  in  the  axis  of  the  telescope,  a  real,  substantial  object  of  very 
definite  form  and  delicate  make,  such  as  a  fine  metallic  point,  as  of  a 
needle  —  or  better  still,  a  cross  formed  by  two  very  fine  threads  (spider- 
lines),  thin  metallic  wires,  or  lines  drawn  on  glass  intersecting  each  other 
at  right  angles  —  and  whose  intersection  is  all  but  a  mathematical  point. 
If  such  a  point,  wire,  or  cross  be  carefully  placed  and  firmly  fixed  in  the 


c 

I 

a 

(/) 

3 
-< 


o 

o 
o 


s 


90 


OUTLINES  OF  ASTRONOMY. 


exact  focus  F,  both  of  the  object  and  eje-glass,  it  will  be  seen  through  the 
latter  at  the  same  time,  and  occupying  the  same  precise  place  as  the  image 
of  the  distant  star  E.  The  magnifying  power  of  the  lens  renders  percep- 
tible the  smallest  deviation  from  perfect  coincidence,  which,  should  it  exist, 
is  a  proof,  that  the  axis  Q  P  is  not  directed  rigorously  towards  E.  In  that 
case,  a  fine  motion  (by  means  of  a  screw  duly  applied),  communicated  to 
the  telescope,  will  be  necessary  to  vary  the  direction  of  the  axis  till  the 
coincidence  is  rendered  perfect.  So  precise  is  this  mode  of  pointing  found 
in  practice,  that  the  axis  of  a  telescope  may  be  directed  towards  a  star 
or  other  definite  celestial  object  without  an  error  of  more  than  a  few  tenths 
of  a  second  of  angular  measure. 

(158.)  This  application  of  the  telescope  may  be  considered  as  completely 
annihilating  that  part  of  the  error  of  observation  which  might  otherwise 
arise  from  an  erroneous  estimation  of  the  direction  in  which  an  object  lies 
from  the  observer's  eye,  or  from  the  centre  of  the  instrument.  It  is,  in  fact, 
the  grand  source  of  all  the  precision  of  modern  astronomy,  without  which  all 
other  refinements  in  instrumental  workmanship  would  be  thrown  away ; 
the  errors  capable  of  being  committed  in  pointing  to  an  object,  without 
such  assistance,  being  far  greater  than  what  could  arise  from  any  but  the 
very  coarsest  graduation.'  In  fact,  the  telescope  thus  applied  becomes, 
with  respect  to  angular,  what  the  microscope  is  with  respect  to  linear 
dimension.  By  concentrating  attention  on  its  smallest  parts,  and  magni- 
fying into  palpable  intervals  the  minutest  difierences,  it  enables  us  not 
only  to  scrutinise  the  form  and  stru^'  "e  of  the  objects  to  which  it  is 


'  The  honour  of  this  capital  improvemeRl  .u.  oeen  successfully  vindicated  by  Der- 
ham  (Phil.  Trans,  xxx.  603)  to  our  young,  talented,  and  unfortunate  countryman  Gas- 
coigne,  from  his  correspondence  with  Crabtree  and  Horrockes,  in  his  (Derham's) 
possession.  The  passages  citetl  by  Derham  from  these  letters  leave  no  doubt  that,  so 
early  as  1640,  Gascoigne  had  applied  telescopes  to  his  quadrants  and  sextants,  with 
threads  in  the  common  focut  of  the  glatMen  ;  and  had  even  carried  the  invention  so  far 
as  to  illuminate  the  field  of  view  by  artificial  light,  which  he  found  "  very  helpful  when 
the  moon  appeareth  not,  or  it  i$  not  olherwite  light  enough."  These  inventions  were 
freely  communicated  by  him  to  Crabtree,  and  through  him  to  his  friend  Horrockes,  the 
pride  and  boast  of  British  astronomy  ;  both  of  whom  expressed  their  unbounded  admi- 
ration of  this  and  many  other  of  his  delicate  and  admirable  improvements  in  the  art 
of  observation.  Gascoigne,  however,  perished,  at  the  age  of  twenty-three,  at  the 
battle  of  Marston  Moor ;  and  the  premature  and  sudden  death  of  Horrockes,  at  a  yet 
earlier  age,  will  account  for  the  temporary  oblivion  of  the  invention.  It  was  revived, 
or  re-invented,  in  1667,  by  Picard  and  Auzout  (Lalandc,  Aslron.  2310),  after  which  its 
use  became  universal.  Morin,  even  earlier  than  Gascoigne  (in  1633),  had  proposed  to 
substitute  the  telescope  for  plain  sights ;  but  it  is  the  thread  or  wire  stretched  in  the 
focus  with  which  the  image  of  a  star  can  be  brought  to  exact  coincidence,  which 
gives  the  telescope  its  advantage  in  practice  ;  and  the  idea  of  this  does  not  seem  to  have 
occurred  to  Morin.    See  Lalande,  vbri  $uprvt. 


THE  TRANiJiT  INSTRUMENT. 


pointed,  but  to  refer  their  appavent  places,  with  all  but  geometrical  pre- 
cision,  to  the  parts  of  any  seal  3  with  which  we  propose  to  compare  them. 
(159.)  We  now  return  to  our  subject,  the  determination  of  time  by  the 
transits  or  culminations  of  celestial  objects.  The  instrument  with  which 
such  culminations  are  observed  is  called  a  transit  instrument.  It  consists 
of  a  telescope  firmly  fastened  on  a  horizontal  axis  directed  to  the  east  and 
west  points  of  the  horizon,  or  at  right  angles  to  the  plane  of  the  meridian 
of  the  place  of  observation.  The  extremities  of  the  axis  are  formed  into 
cylindrical  pivots  of  exactly  equal  diameters,  which  rest  in  notches  formed 
in  metallic  supports,  bedded  (in  the  case  of  large  instruments)  on  strong 
pieces  of  stone,  and  susceptible  of  nice  adjustment  by  screwr,  both  in  a 
vertical  and  horizontal  direction.     By  the  former  adjustment,  the  axis  can 

Fig-  16.  !     : 


k..  1? 


be  rendered  precisely  horizontal,  by  leveUmg  it  with  a  level  made  to  rest 
on  the  pivots.  By  the  latter  adjustment  the  axis  is  brought  precisely  into 
the  east  and  west  directions,  the  criterion  of  which  is  furnished  by  the 
observations  themselves  made  with  the  instrument,  in  a  manner  presently 
to  be  explained,  or  by  a  well-defined  object,  called  a  meridian-mark,  origi- 
nally determined  by  such  observations,  and  then,  for  convenience  of  ready 
reference,  permanently  established,  at  a  great  distance,  exactly  in  a  meri- 
dian line  passing  through  the  central  point  of  the  whole  instrument.  It 
is  evident,  from  this  description,  that,  if  the  axis,  or  line  of  collimation 
of  the  telescope  be  once  well  adjusted  at  right  angles  to  the  axis  of  the 
transit,  it  will  never  quit  the  plane  of  the  meridian,  when  the  instrument 
is  turned  round  on  its  axis  of  rotation. 

(160.)  In  the  focus  of  the  eye-piece,  and  at  right  angles  to  the  length 
of  the  telescope,  is  placed,  not  a  single  cross,  as  in  our  general  explanation 
in  art.  157,  but  a  system  of  one  horizontal  and  several  equidistant  vertical 
threads  or  wires,  (five  or  seven  are  more  usually  employed,)  as  represented 
in  the  annexed  figure,  which  always  appear  in  the  field  of  vieio,  when 
properly  illuminated,  by  day  by  the  light  of  the  sky,  by  night  by  that  of 
a  lamp  introduced  by  a  contrivance  not  necessary  here  to  explain.     The 


G 

I 
i 

O 


o 
a 


C 

1^ 


90 


OUTLINES  OF  ASTRONOMY. 


Fig.  16. 


'■'■    >   '<4V,!>''»'.""     f"\ 


It  (' 

h 


i'l 


I, 


:M 


place  of  this  system  of  wires  may  be  altered  by  adjusting  screws,  giving 
it  a  lateral  (horizontal)  motion ;  and  it  is  by  this  means  brought  to  such 
a  position,  that  the  middle  one  of  the  vertical  wires  shall  intersect  the  line 
of  colUmation  of  the  telescope,  where  it  is  arrested  and  permanently 
fastened.'  In  this  situation  it  is  evident  that  the  middle  thread  will  be  a 
visible  representation  of  that  portion  of  the  celestial  meridian  to  which 
the  telescope  is  pointed ;  and  when  a  star  is  seen  to  cross  this  wure  in 
the  telescope,  it  is  in  the  act  of  culminating,  or  passing  the  celestial  meri- 
dian. The  instant  of  this  event  is  noted  by  the  clock  or  chronometer, 
which  forms  an  indispensable  accompaniment  of  the  transit  instrument. 
For  greater  precision,  the  moment  of  its  crossing  all  the  vertical  threads 
is  noted,  and  a  mean  taken,  which  (since  the  threads  are  equidistant) 
would  give  exactly  the  same  result,  were  all  the  observations  perfect,  and 
will,  of  course,  tend  to  subdivide  and  destroy  their  errors  in  an  average  of 
the  whole  in  the  contrary  case. 

(161.)  For  the  mode  of  executing  the  adjustments,  aikd  allowing  for 
the  errors  unavoidable  in  the  use  of  this  simple  and  elegant  instrument, 
the  reader  must  consult  works  especially  devoted  to  this  department  of 
pi'actical  astronomy.'  We  shall  here  only  mention  one  important  verifica- 
tion of  its  correctness,  which  consists  in  reversing  the  ends  of  the  axis,  or 
turning  it  east  for  west.  If  this  be  done,  and  it  continue  to  give  the 
same  results,  and  intersect  the  same  point  on  the  meridian  mark,  we  may 
be  sure  that  the  line  of  collimation  of  the  telescope  is  truly  at  right  angles 
to  the  axis,  and  describes  strictly  a  plane,  %.  e.  marks  out  in  the  heavens 
a  great  circle.  In  good  transit  observations,  an  error  of  two  or  three 
tenths  of  a  second  of  time  in  the  moment  of  a  star's  culmination  is  the 
utmost  which  need  be  apprehended,  exclusive  of  the  error  of  the  clock :  in 

*  There  is  no  way  of  bringing  the  trut  optic  axit  of  the  object-glass  to  coincide 
exactly  with  the  line  of  collimation,  but,  so  long  as  the  object-glass  does  not  shift  or 
shake  in  its  cell,  any  line  holding  an  invariable  position  with  respect  to  that  axis,  may 
be  taken  for  (he  conventional  or  astronomical  axis  with  equal  eflect. 

■  See  Dr.  Pearson's  Treatise  on  Practical  Astronomy.  Also  Bianchi  Sopra  lo 
Stromento  do'  Passagi.    Ephem.  di  Milano,  1824.  ""  --i- 


MEASUREMENT  OF  ANGULAR  INTERVALS. 


other  words,  a  dock  may  be  compared  with  the  earth's  diurnal  motion  by 
a  single  observation,  without  risk  of  greater  error.  By  multiplying 
observations,  of  course,  a  vet  greater  degree  of  precision  may  be  obtained. 

(162.)  The  plane  described  by  the  line  of  coUimation  of  a  transit  ought 
to  be  that  of  the  meridian  of  the  place  of  obsorvfytion.  To  ascertain 
whether  it  is  so  or  not,  celestial  observation  must  be  resorted  to.  Now,  as 
the  meridian  is  a  great  circle  passing  through  the  pole,  it  necessarily 
bisects  the  diurnal  circles  described  by  all  the  stars,  all  which  describe  the 
two  semicircles  so  arising  in  equal  intervals  of  12  sidereal  hours  each. 
Hence,  if  we  choose  a  star  whose  whole  diurnal  circle  is  above  the  horizon, 
or  which  never  sets,  and  observe  the  moments  of  its  upper  and  lower  tran- 
sits across  the  middle  wire  of  the  telescope,  if  we  find  the  two  semidiurnal 
portions  east  and  west  of  the  plane  described  by  the  telescope  to  be 
described  in  precisely/  equal  times,  we  may  be  sure  that  plane  is  the  meridian. 

(163.)  The  angular  intervals  measured  by  means  of  the  transit  instru- 
ment and  clock  are  arcs  of  the  equinoctial,  intercepted  between  circles  of 
declination  passing  through  the  objects  observed ;  and  their  measurement, 
in  this  case,  is  performed  by  no  artificial  graduation  of  circles,  but  by  the 
help  of  the  earth's  diurnal  motion,  which  carries  equal  arcs  of  the  equi- 
noctial across  the  meridian,  in  equal  times,  at  the  rate  of  15°  per  sidereal 
hour.    In  all  other  oases,  when  we  would  measure  angular  intervals,  it  is 

Fig.  17.  ,      ,,     ,; 


a    S 


necessary  to  have  recourse  to  circles,  or  portions  of  circles,  constructed  of 
metal  or  other  firm  and  durable  material,  and  mechanically  subdivided  into 
equal  parts,  such  as  degrees,  minutes,  &o.  The  simplest  and  most  obvious 
mode  in  which  the  measurement  of  the  angular  interval  between  two 
directions  in  space  can  be  performed  is  as  follows.  Let  ABCB  be  a 
circle,  divided  into  360  degrees,  (numbered  in  order  from  any  point  0°  in 
the  circumference,  round  to  the  same  point  again,)  and  connected  with  its 
centre  by  spokes  or  rays,  x,  y^  z,  firmly  united  to  its  circumference  or 


e 
5! 

(A 

O 


V«'.«i 

m 

r 

c 
o 


r 

C9 


94 


OUTLINES  OF  iiSTRONOMT. 


Umb.  At  the  centre  let  a  circular  hole  be  pierced,  in  which  shall  move 
a  pivot  ezaciily  fitting  it,  carrying  a  tube,  whose  axis,  ah,  is  exactly 
parallel  to  the  plane  of  the  circle,  or  perpendicular  to  the  pivot ;  and  also 
two  arras,  m,  n,  at  right  angles  to  it,  and  forming  one  piece  with  the  tube 
and  the  axis ;  so  that  the  motion  of  the  axis  on  the  centre  shall  carry  the 
tube  and  arms  smoothly  round  the  circle,  to  be  arrested  and  fixed  at  any 
point  we  please,  by  a  contrivance  called  a  clamp.  Suppose,  now,  we 
would  measure  the  angular  interval  between  two  fixed  objects,  S,  T.  The 
plane  of  the  circle  must  first  be  adjusted  so  as  to  pass  through  them  both, 
and  immoveably  fixed  and  maintained  in  that  position.  This  done,  let  the 
axis  ab  of  the  tube  be  directed  to  one  of  them,  S,  and  clamped.  Then 
will  a  mark  on  the  arm  m  point  either  exactly  to  some  one  of  the  divisions 
on  the  limb,  or  between  two  of  them  adjacent.  In  the  former  case,  the 
division  must  be  noted  as  tJie  reading  of  the  arm  m.  In  the  latter,  the 
fractional  part  of  one  whole  interval  between  the  consecutive  divisions  by 
which  the  mark  on  m  surpassea  the  last  inferior  division  must  be  estimated 
or  measured  by  some  mechanical  or  optical  ra>!an£  (See  art.  165.)  The 
division  and  fractional  part  thus  noted,  and  reduced  into  degrees,  minutes, 
and  seconds,  is  to  be  set  down  as  the  reading  of  the  Umb  corresponding 
to  that  position  of  the  tube  a  &,  where  it  points  to  the  object  S.  The 
same  must  then  be  done  for  the  object  T ;  the  tube  pointed  to  it,  and  the 
limb  "  read  off,"  the  position  of  the  circle  remaining  meanwhile  unaltered. 
It  is  manifest,  then,  that,  if  the  lesser  of  these  readings  be  subtracted 
from  the  greater,  their  difference  will  be  the  angular  interval  between  S 
and  T,  as  seen  from  the  centre  of  the  circle,  at  whatever  point  of  the  limb 
the  commencement  of  the  graduations  or  the  point  0°  be  situated. 
(1G4.)  The  very  same  result  will  be  obtained,  if,  instead  of  making  the 

Fig.  18. 


,!•      It 


;jy 


tube  moveable  upon  the  circle,  we  connect  it  invariably  with  the  latter, 
and  make  both  revolve  together  on  an  axis  concentric  with  the  circle,  and 
forming  one  piece  with  it,  working  in  a  hollow  formed  to  receive  and  fit 
it  in  some  fixed  support.  Such  a  combination  is  represented  in  section  in 
the  annexed  sketch.  T  is  the  tube  or  sight,  fastened,  tit  pp,  on  the  circle 
A  B,  whose  axis,  D,  works  in  the  solid  metallic  centring  E,  from  which 


■v\ 


METHODS   OF   READING  OFF. 


95 


originates  an  arm,  F,  carrying  at  its  extremity  an  index,  or  other  proper 
mark,  to  point  out  and  read  otT  the  exact  division  of  the  circle  at  B,  the 
point  close  to  it.  It  ia  evident  that,  as  the  telescope  and  circle  revolve 
through  any  angle,  the  part  of  the  limb  of  the  latter,  which  by  such 
revolution  is  carried  past  the  index  F,  will  measure  the  angle  described. 
This  is  the  most  usual  mode  of  applying  divided  circles  in  astronomy. 

(165.)  The  index  F  may  either  be  a  simple  pointer,  like  a  clock  hand 
{jig.  a);  or  a  vernier  {Jig.  h) )  or,  lastly,  a  compound  microscope  {fig. 


Fig.  10. 


,11-"       I 


C 


d  n 


^ 


P^ 


c),  represented  in  section  \nfig.  d,  and  furnished  with  a  cross  in  the  com- 
mon focus  of  its  object  and  eye-glass,  moveable  by  a  fine-threaded  screw, 
by  which  the  intersection  of  the  cross  may  be  brought  to  exact  coincidence 
with  the  image  of  the  nearest  of  the  divisions  of  the  circle  formed  in  the 
focus  of  the  object  lens  upon  the  very  same  principle  with  that  explained, 
art.  157  for  the  pointing  of  the  telescope,  only  thct  here  the  fiducial  cross 
is  made  moveable ;  and  by  the  turns  and  parts  of  a  turn  of  the  screw 
required  for  this  purpose  the  distance  of  that  division  from  the  original  or 
zero  point  of  the  microscope  may  be  estimated.  This  simple  but  delicate 
contrivance  gives  to  the  reading  off  of  a  circle  a  degree  of  accuracy  only 
limited  by  the  power  of  the  microscope,  and  the  perfection  with  which  a 
screw  can  be  executed,  and  places  the  subdivision  of  angles  on  the  same 
footing  of  optical  certainty  which  is  introduced  into  their  measurement  by 
the  use  of  the  telescope. 

(166.)  The  exactness  of  the  result  thus  obtained  must  depend,  1st,  on 
the  precision  with  which  the  tube  a  h  can  be  pointed  to  the  objects ;  2dly, 
on  the  accuracy  of  graduation  of  the  limb ;  3dly,  on  the  accuracy  with 
which  the  subdivision  of  the  intervals  between  any  two  consecutive  gradu- 
atious  can  be  performed.  The  mode  of  accomplishing  the  latter  object 
with  any  required  exactness  has  been  explained  in  the  last  article.  With 
regard  to  the  graduation  of  the  limb,  being  merely  of  a  mechanical  nature. 


e 

I 

s 

-< 
o 

o 
o 

i 


i 


06 


OUTLINES  OF  ASTRONOMT. 


we  shall  pass  it  without  remark,  further  than  this,  that,  in  the  present 
state  of  instrument-making,  the  amount  of  error  from  this  source  of  inao- 
curaoy  is  reduced  within  very  narrow  limits  indeed.'  With  regard  to  the 
first,  it  must  be  obvious  that,  if  the  sights  a  b  be  nothing  more  than 
simple  crosses,  or  pin-holes  at  the  ends  of  a  hollow  tube,  or  an  ejre-hole 
at  one  end,  and  a  cross  at  the  other,  no  greater  nicety  in  pointing  can  be 
expected  than  what  simple  vbion  with  the  naked  eye  can  command.  But 
if,  in  place  of  these  simple  but  coarse  contrivances,  the  tube  itself  be  con- 
verted into  a  telescope,  having  an  object-glass  at  h,  an  eye-piece  at  a,  and 
a  fiducial  cross  in  their  common  focus,  as  explained  in  art.  1 57 ;  and  if 
the  motion  of  the  tube  on  the  limb  of  the  circle  be  arrested  when  the 
object  is  brought  just  into  coincidence  with  the  interseotional  point  of 
that  cross,  it  is  evident  that  a  greater  degree  of  exactness  may  be  attained 
in  the  pointing  of  the  tube  than  by  the  unassisted  eye,  in  proportion  to 
the  magnifying  power  and  distinctness  of  the  telescope  used. 

(167.)  The  simplest  mode  in  which  the  measurement  of  an  angular  in- 
terval can  be  executed,  is  what  we  have  just  described ;  but,  in  strictness, 
this  mode  is  applicable  only  to  terrestrial  angles,  such  as  those  occupied 
on  the  sensible  horizon  by  the  objects  which  surround  our  station,  —  be- 
cause these  only  remain  stationary  during  the  interval  while  the  telescope 
is  shifted  on  the  limb  from  one  object  to  the  other.  But  the  diurnal 
motion  of  the  heavens,  by  destroying  this  essential  condition,  renders  the 
direct  measurement  of  angular  distance  from  object  to  object  by  this  means 
impossible.  The  same  objection,  however,  does  not  apply  if  we  seek  only 
to  determine  the  interval  between  the  diurnal  circles  described  by  any 
two  celestial  objects.  Suppose  every  star,  in  its  diurnal  revolution,  were 
to  leave  behind  it  a  visible  trace  in  the  heavens, — a  fine  line  of  light,  for 
instance, — then  a  telescope  once  pointed  to  a  star,  so  as  to  have  its  image 
brought  to  coincidence  with  the  intersection  of  the  wires,  would  constantly 
remain  pointed  to  some  portion  or  other  of  this  line,  which  would  there- 
fore continue  >.o  appear  in  its  field  as  a  luminous  lino,  permanently  inter- 
secting the  same  point,  till  the  star  came  round  again.  From  one  such 
line  to  another  the  telescope  might  be  shifted,  at  leisure,  without  error ; 
and  then  the  angular  interval  between  the  two  diurnal  circles,  in  the  plane 
of  the  telescope's  rotation,  might  be  measured.  Now,  though  we  cannot 
see  the  path  of  a  star  in  the  heavens,  we  can  wait  till  the  star  itself  crosses 
the  field  of  view,  and  seize  the  moment  of  its  passage  to  place  the  inter- 
section of  its  wires  so  that  the  star  shall  traverse  it ;  by  which,  when  the 

*  In  the  great  Ertel  circle  at  Pulkova,  the  probable  amount  of  the  accidental  error 
of  division  is  stated  by  M.  Struve  not  to  exceed  V'26i.  Desc.  do  I'Obs.  centrale  de 
Pulkova,  p.  147. 


OF  THE   MURAL  CIRCLE. 


w? 


telesoopo  ia  well  damped,  wo  equally  well  secure  the  position  of  its  diurnal 
circle  us  if  wo  continued  to  see  it  ever  so  long.  The  reading  off  of  the 
limb  may  then  bo  performed  at  leisure ;  and  when  another  star  comes 
round  into  the  plana  of  the  circle,  wo  may  unclamp  the  telescope,  and  a 
similar  observation  will  enable  us  to  assign  the  place  of  its  diurnal  circle 
on  the  limb :  and  the  observations  may  be  repeated  alternately,  every  day, 
as  the  stars  pass,  till  wo  are  satisfied  with  their  result. 

(168.)  This  is  the  principle  of  the  mural  circle,  which  is  nothing  more 
than  such  a  circle  as  wo  have  described  in  art.  163,  firmly  supported,  in 
the  plane  of  the  meridian,  on  a  long  and  powerful  horizontal  axis.  This 
axis  is  let  into  a  massive  pier,  or  wall,  of  stone  (whence  the  name  of  tho 
instrument),  and  so  secured  by  screws  as  to  be  capable  of  adjustment 
both  in  a  vertical  and  horizontal  direction )  so  that,  like  the  axis  of  the 
transit,  it  can  be  maintained  in  tho  exact  direction  of  tho  east  a!id  west 
points  of  the  horizon,  tho  plane  of  tho  circle  being  consequently  truly 
meridional. 

(160.)  Tho  meridian,  being  at  right  angles  to  all  the  diurnal  circles 
described  by  tho  stars,  its  arc  intercepted  between  any  two  of  them  will 
measure  tho  least  distance  between  these  circles,  and  will  be  equal  to  tho 
difference  of  the  declinations,  os  also  to  the  difference  of  tho  nwridian 
altitudes  of  tho  objects — at  least  when  corrected  for  refraction.  These 
differences,  then,  are  tho  angular  intervals  directlif  measured  by  the  mural 
circle.  But  from  these,  supposing  tho  law  and  amount  of  refraction 
known,  it  is  easy  to  conclude,  not  their  differences  only,  but  the  quantities 
themselves,  as  wo  shall  now  explain. 

(170.)  Tho  declination  of  a  heavenly  body  is  tho  complement  of  its 
distance  from  the  polo.  The  pole,  being  a  point  in  tho  meridian,  might 
be  directly  observed  on  the  limb  of  the  circle,  if  any  star  stood  exactly 
therein ;  and  thence  the  polar  distances,  and,  of  course,  the  declinations 
of  all  the  rest,  might  be  at  once  determined.  But  this  not  being  the 
case,  a  bright  star  as  near  tho  pole  as  can  be  found  is  selected,  and  observed 
in  its  iippcr  and  Imccr  culminations ;  that  is,  when  it  passes  the  meridian 
ahove  and  beloio  the  pole.  Now,  as  its  distance  from  the  pole  remains 
the  same,  the  difference  of  reading  off  the  circle  in  tho  two  cases  is,  of 
course  (when  corrected  for  refraction),  equal  to  twice  the  polar  distance 
of  the  star;  the  arc  intercepted  on  the  limb  of  the  circle  being,  in  this 
case,  equal  to  the  angular  diameter  of  the  star's  diurnal  circle.  In  tho 
annexed  diugi'am,  II  P  0  represents  the  celestial  meridian,  P  the  pole, 
B 11,  A  Q,  C  D  the  diurnal  circles  of  stars  which  arrive  on  the  meridian  at 
B,  A,  and  C  in  their  upper  and  at  R,  Q,  D  in  their  lower  culminations, 
of  which  D  and  Q  happen  above  tho  horizon  HO.  P  is  the  pole ;  and  if 
7 


H 


G 

I 

i 

=i 

•< 

O 

•VI 

pi 

g 

a 

C 

09 


9 


OUTLINES  OF  ASTRONOMY. 

Fig.  20. 
A^ ^B 


■•I 


we  suppose  hpo  to  be  the  mural  circle,  having  S  for  its  centre,  hacpd 
will  be  the  points  on  its  circumference  corresponding  to  B  AOPD  in  the 
heavens.  Now  the  arcs  ha,  bc,bd,  and  cd  are  given  immediately  by  ob- 
servation ;  and  since  C  P  =  P  D,  we  have  also  cp=pd,  and  each  of  them 
=  ^cd,  consequently  the  place  of  tJie  polar  point,  as  it  is  called,  upon 
the  limb  of  the  circle  becomes  known,  and  the  arcs  pb,  pa,  pc,  which 
represent  on  the  circle  the  polar  distances  required,  become  also  known. 

(171.)  The  situation  of  the  pole  star,  which  is  a  very  brilliant  one,  is 
eminently  favourable  for  this  purpose,  being  only  about  a  degree  and  an  half 
from  the  pole ;  it  is,  therefore,  the  star  usually  and  almost  solely  chosen 
for  this  important  purpose ;  the  more  especially  because,  both  its  culmina- 
tions taking  place  at  great  and  not  very  different  altitudes,  the  refractions 
by  which  they  are  affected  are  of  small  amount,  and  differ  but  slightly 
from  each  other,  so  that  their  correction  is  easily  and  safely  applied.  The 
brightness  of  the  pole  star,  too,  allows  it  to  be  easily  observed  in  the  day- 
time. In  consequence  of  these  peculiarities,  this  star  is  one  of  constant 
resort  with  astronomers  for  the  adjustment  and  verification  of  instruments 
of  almost  every  description.  In  the  case  of  the  transit,  for  instance,  it 
furnishes  an  excellent  object  for  the  application  of  the  method  of  testing 
the  meridional  situation  of  the  instrument  described  in  art.  162,  in  fact, 
the  most  advantageous  of  any  for  that  purpose,  owing  to  its  being  the 
most  remote  from  the  zenith,  at  its  upper  culmination,  of  all  bright  stars 
observable  both  above  and  below  the  pole. 

(172.)  The  place  of  the  polar  point  on  the  limb  of  the  mural  circle 
once  determined,  becomes  an  origin,  or  zero  point,  from  which  the  polar 
distances  of  all  objects,  referred  to  other  points  on  the  same  limb,  reckon. 
It  matters  not  whether  the  actual  commencement  0"  of  the  graduations 
stand  there,  or  not  j  since  it  is  only  by  the  differences  of  the  readings 
tihat  the  area  on  the  limb  are  determined ;  and  hence  a  great  advantage  is 


OF  TUE   MERIDIAN   CIRCLE. 


99 


obtained  in  the  powor  of  oommonoing  ■itinw  a  frosh  series  of  obscrvatioDs, 
in  which  a  different  part  of  the  oiroumferouco  of  the  circle  shall  be 
employed,  and  different  graduations  brought  into  use,  by  which  inequalities 
of  division  may  be  detected  and  neutralized.  This  is  accomplished  prao> 
tioally  by  detaching  the  telescope  fror  its  old  bearings  on  the  circle,  and 
fixing  ii  afresh,  by  screws  or  clamps,  on  a  different  part  of  the  circum- 
ference. 

(178.)  A  point  on  the  limb  of  the  mural  circle,  not  less  important 
than  the  polar  point,  is  the  tu>nzontal  point,  which,  being  once  known, 
becomes  in  like  manner  an  origin,  or  zero  point,  from  which  altitudes  are 
reckoned.  The  principle  of  its  determination  is  ultimately  nearly  the 
same  with  that  of  the  polar  point.  As  no  star  exists  in  the  celestial 
horizon,  the  observer  muist  seek  to  determine  two  points  on  the  limb, 
the  9ne  of  which  shall  be  precisely  as  far  hehw  the  horizontal  point  as 
the  other  is  above  it.  For  this  purpose,  a  star  is  observed  ai  its  oulmina- 
nation  on  one  night,  by  pointing  the  telescope  directly  to  it,  and  the  next, 
by  pointing  to  the  image  of  the  same  star  reflected  in  the  still,  unruffled 
surface  of  a  fluid  at  perfect  rest.  Mercury,  as  the  most  reflective  fluid 
known,  is  generally  chosen  for  that  use.  As  the  surface  of  a  fluid  at  rest 
is  necessarily  horizontal,  and  as  the  angle  of  reflection,  by  the  laws  of  optics, 
is  equal  to  that  of  incidence,  this  image  will  be  just  as  much  depressed 
below  the  horizon  as  a  star  itself  is  above  it  (allowing  for  the  difference 
of  refraction  at  the  moment  of  observation).  The  arc  intercepted  on  the 
limb  of  the  circle  between  the  star  and  its  reflected  image  thus  consecu- 
tively observed,  when  corrected  for  refraction,  is  the  double  altitude  of 
the  star,  and  its  point  of  bisection  the  horizontal  point.  The  reflecting 
surface  of  a  fluid  so  used  for  the  determination  of  the  altitudes  of  objeoto 
is  called  an  artificial  horizon.^ 

(174.)  The  mural  circle  is,  in  fact,  at  the  same  time,  a  transit  instru- 
ment; and,  if  furnished  with  a  proper  system  of  vertical  wires  in  the 
focus  of  its  telescope,  may  bo  used  aa  such.  As  the  axis,  however,  is 
only  supported  at  one  end,  it  has  not  the  strength  and  permanence  neces> 
sary  for  the  more  delicate  purposes  of  a  transit;  nor  can  it  be  verified,  as 
a  transit  may,  by  the  reversal  of  the  two  ends  of  its  axis,  east  or  west. 

I  By  a  peculiar  and  delicate  manipulation  and  management  of  the  setting  bisection 
and  reading  off  of  the  circle,  aided  by  the  use  of  a  moveable  horizontal  micrometio 
wire  in  the  focus  of  the  object-glass,  it  is  found  practicable  to  observe  a  slow  moving 
star  (as  the  pole  star)  on  one  and  the  tame  night,  both  by  reflection  and  durect  vision, 
sufficiently  near  to  either  culmination  to  give  the  horizontal  point,  without  tisking  the 
change  of  refraction  in  twenty- four  hours;  so  that  this  source  of  error  is  thus  com- 
pletely eliminated. 


e 

I 

s 

(A 


■IVI 

r 
o 
a 


S 

09 


9 

S 


100 


OUTLINES   OF  ASTRONOMY. 


It 


r  fi 


Nothing,  however,  prevents  a  divided  circle  being  permanently  fastened 
on  the  axis  of  a  transit  instrument,  either  near  to  one  of  its  extremities, 
or  close  to  tbo  telescope,  so  as  to  revolve  with  it,  the  reading  oflF  being 
performed  by  one  or  more  microscopes  fixed  on  one  of  its  piers.  Such  an 
instrument  is  called  a  transit  circle,  or  a  mehidian  circle,  and  serves 
for  the  simultaneous  determination  of  the  right  ascensions  and  polar  dis- 
tances of  objects  observed  with  it ;  the  time  of  transit  being  noted  by  the 
clock,  and  the  circle  being  read  off  by  the  lateral  microscopes.  There  is 
much  advantage,  when  extensive  catalogues  of  small  stars  have  to  be 
formed,  in  this  simultaneous  determination  of  both  their  celestial  co-ordi- 
nates :  to  which  may  be  added  the  facility  of  applying  to  the  meridian 
circle  a  telescope  of  any  length  and  optical  power.  The  constniction  of 
the  mural  circle  renders  this  highly  inconvenient,  and  indeed  impracticable 
beyond  very  moderate  limits. 

(175.)  The  determination  of  the  horizontal  point  on  the  limb  of  an 
instrument  is  of  such  essential  importance  in  astronomy,  that  the  student 
should  be  made  acquainted  with  every  means  employed  for  this  purpose. 
These  are,  the  artificial  horizon,  the  plumb-lino,  the  level,  and  the  colli- 
mator. The  artificial  horizon  has  been  already  explained.  The  plumb- 
line  is  a  fine  thread  or  wire,  to  which  is  suspended  a  weight,  whose  oscil- 
lations are  impeded  and  quickly  reduced  to  rest  by  plunging  it  in  vater. 
The  direction  ultimately  assumed  by  such  a  line,  admittinn  its  perfixt 
flexibility^  is  that  of  gravity,  or  perpendicular  to  the  surface  of  still 
water.  Its  application  to  the  purposes  of  astronomy  is,  however,  so  deli- 
cate, and  difficult,  and  liable  to  error,  unless  extraordinary  precautions  are 
taken  in  its  use,  that  it  is  at  present  almost  universally  abandoned,  for 
the  more  convenient,  and  equally  exact  instrument  tlic  hvel. 

(176.)  The  level  is  a  glass  tube  nearly  filled  with  a  liquid,  (spirit  of 
wine,  or  sulphuric  ether,  being  thus  now  generally  used,  on  account  of 

Fig.  21. 


p  ?!W?^w^m<?^r..'^'2r;;>r»x'^r,r  :?>?. « 


their  extreme  mohility,  and  not  being  liable  to  freeze,)  the  bubble  in 
which,  when  the  tube  is  placed  horizontally,  would  rest  indifferently  in 
any  part  if  the  tube  could  be  mathematically  straight.     But  that  being 


DETERMINATION   OP   THE   HORIZONTAL   POINT. 


101 


impossible  to  execute,  and  every  tube  having  some  slight  curvature  j  if 
the  convex  side  be  placed  upwards  the  bubble  will  occupy  the  higher  part, 
as  in  the  figure  (where  the  curvature  is  purposely  exaggerated).  Suppose 
such  a  tube,  as  A  li,  firmly  fastened  on  a  straight  bar,  G  D,  and  marked 
at  a  hf  two  points  distant  by  the  length  of  the  bubble;  then,  if  the 
instrument  be  so  placed  that  the  bubble  shall  occupy  this  interval,  it  is 
clear  that  C  D  can  have  no  other  than  one  definite  inclination  to  the  hori- 
zon ;  because,  were  it  ever  so  little  moved  one  way  or  other,  the  bubble 
would  shift  its  place,  and  run  towards  the  elevated  side.  Suppose,  now, 
that  we  would  ascertain  whether  any  given  line  P  Q  be  horizontal  j  let 
the  base  of  the  level  C  D  be  set  upon  it,  and  note  the  points  a  h,  between 
which  the  bubble  is  exactly  contained;  then  turn  the  level  end  for  end, 
so  that  C  shall  rest  on  Q,  and  D  on  P.  If  then  the  bubble  continue  to 
occupy  the  same  place  between  a  and  i,  it  is  evident  that  P  Q  can  be  no 
otherwise  than  horizontal.  If  not,  the  side  towards  which  the  bubble 
runs  is  highest,  and  must  be  lowered.  Astronomical  levels  are  furnished 
with  a  divided  scale,  by  which  the  places  of  the  ends  of  the  bubble  can 
be  nicely  marked ;  ai^  it  is  said  that  they  can  be  executed  with  such 
delicacy,  as  to  indicate  a  single  second  of  angular  deviation  from  exact 
horizontality.  In  such  levels  accident  is  not  trusted  to  to  give  the  requi- 
site curvature.  They  are  ground  and  polished  internally  by  peculiar 
mechanical  processes  of  great  delicacy. 

(177.)  The  mode  in  which  a  level  may  be  applied  to  find  the  horizontal 
point  on  the  limb  of  a  vortical  divided  circle  may  be  thus  explained ;  let 
A  B  be  a  telescope  firmly  fixed  to  such  a  circle,  D  E  F,  and  moveable  iu 
one  with  it  on  a  horizontal  axis  C,  which  must  be  like  that  of  a  transit, 
susceptible  of  reversal  (sec  art.  101)  and  with  which  the  circle  is  insep- 
arably connected.  Direct  the  telescope  on  some  distant  well-defined  object 
S,  and  bisect  it  by  its  horizontal  wire,  and  in  this  position  clamp  it  fast. 
Let  L  be  a  level  fastened  at  right  angles  to  an  arm,  L  E  F,  furnished  with 
a  microscope,  or  vernier  at  F,  and,  if  wo  please,  another  at  E.  Let  this 
arm  be  fitted  by  grinding  on  the  axis  C,  but  capable  of  moving  smoothly 
on  it  without  carrying  it  round,  and  also  of  being  clamped  fast  on  it,  so  as 
to  prevent  it  from  moving  until  required.  While  the  tolesdbpe  is  kept 
fixed  on  the  object  S,  let  the  level  be  set  so  as  to  bring  its  bubble  to  the 
marks  a  h,  and  clamp  it  there.  Then  will  the  arm  L  C  F  have  some  cer- 
tain determinate  inclination  (no  matter  what)  to  the  horizon.  In  this. 
position  let  the  circle  be  read  off  at  F,  and  then  let  the  whole  apparatus 
bo  reversed  by  turning  its  horizontal  axis  end  for  end,  without  undamping 
the  level  arm  from  the  axis.  This  done,  by  the  motion  of  the  whole  in- 
strument (level  and  all)  on  its  axis,  restore  the  level  to  its  horizontal  posi- 


c 

I 

< 

"^1 


\ 


mm* 

o 
a 


90 


102 


OUTLINES   OF  ASTRONOMY. 


innumerable 
tal  point,  is 
tain  Kater,  I 
tenhouse,  in 
by  the  emer 
focus  of  a  £ 
small  telesco 
zontally,  or  t 
swim  on  me 
always  one  \ 
cross-wires  o; 
of  its  object 


11,  .< 
T' ' 

it 


tion  with  the  bubble  at  a  h.  Then  we  are  sure  that  the  telescope  has 
now  the  same  inclination  to  the  horizon  the  other  way,  that  it  had  when 
pointed  to  S,  and  the  reading  off  at  F  will  not  ha^e  been  changed.  Now 
unclamp  the  level,  and  keeping  it  nearl^  norizontal,  turn  round  the  circle 
on  the  axis,  so  as  to  carry  back  the  telescope  through  the  zenith  to  S,  and 
in  that  position  clamp  the  circle  and  telescope  fast.  Then  it  is  evident 
that  an  angle  equal  to  twice  the  zenith  distance  of  S  has  been  moved  over 
by  the  axis  of  the  telescope  from  its  last  position.  Lastly,  without  un- 
clamping  the  telescope  and  circle,  let  the  level  be  once  more  rectified. 
Then  will  the  arm  L  £  F  once  more  assume  the  same  definite  position 
with  respect  to  the  horizon ;  and,  consequently,  if  the  circle  be  again  read 
off,  the  difference  between  this  and  the  previous  reading  must  measure  the 
arc  of  its  circumference  which  has  passed  under  the  point  F,  which  may 
be  considered  as  having  all  the  while  retained  an  invariable  position. 
This  difference,  then,  will  be  the  double  zenith  distance  of  S,  and  its  half 
will  be  the  zenith  distance  simply,  the  complement  of  which  is  its  altitude. 
Thus  the  altitude  corresponding  to  a  given  reading  of  the  limb  becomes 
known,  or,  in  other  words,  the  horizontal  point  on  the  limb  is  ascertained. 
Circuitous  As  this  process  may  appear,  there  is  no  other  mode  of  employ- 
ing the  level  for  this  purpose  which  does  not  in  the  end  come  to  the  same 
thing.  Most  commonly,  however,  the  level  is  used  as  a  mere  fiducial  re- 
ference, to  preserve  a  horizontal  point  once  well  determined  by  other 
means,  which  is  done  by  adjusting  it  so  as  to  stand  level  when  the  tele- 
scope is  truly  horizontal,  and  thus  leaving  it,  depending  on  the  permanence 
of  its  adjustment. 

(178.)  The  last,  but  probably  not  the  least  exact,  as  it  certainly  is,  in 


fore  be  in  a 
other  telescc 
a  celestial  ol 
nation.  Thi 
served  as  if 
to  each  othei 
sel  of  mercui 
with  two  qui 
sides  of  the 
scope  of  the 
collimator  (f 
45"  inclined 
will  be  twice 
the  horizonts 
in  many  resp 
telescope  is  i 
is  described  i 
(179.)  Bj 
pie  of  collin 
which  afford 
of  the  nadir 


DETERMINATION  OF  THE   HORIZONTAL  POINT. 


108 


innumerable  cases,  the  most  convenient  means  of  ascertaining  the  Jiorizon- 
tal  point,  is  that  afforded  by  the  floating  collimator,  an  invention  of  Cap- 
tain Kater,  but  of  which  the  optical  principle  was  first  employed  by  Rit- 
tenhouse,  in  1785,  for  the  purpose  of  fixing  a  definite  direction  in  space 
by  the  emergence  of  parallel  rays  from  a  material  object  placed  in  the 
focus  of  a  fixed  lens.  This  elegant  instrument  is  nothing  more  than  a 
small  telescope  furnished  with  a  cross-wire  in  its  focus,  and  fastened  hori- 
zontally, or  as  nearly  so  as  may  be,  on  a  flat  iron  float,  which  is  made  to 
swim  on  mercury,  and  which,  of  course,  will,  when  left  to  itself,  assume 
always  one  and  the  same  invariable  inclination  to  the  horizon.  If  the 
cross-wires  of  the  collimator  be  illuminated  by  a  lamp,  being  in  the  focus 
of  its  object-glass,  the  rays  from  them  will  issue  parallel,  and  will  there- 
Fig.  23. 


fore  be  in  a  fit  state  to  be  brought  to  a  focus  by  the  object-glass  of  any 
other  telescope,  in  which  they  will  form  an  image  as  if  they  came  from 
a  celestial  object  in  their  direction,  i.  e.  at  an  altitude  equal  to  their  decli- 
nation. Thus  the  intersection  of  the  cross  of  the  collimator  may  be  ob- 
served as  if  it  were  a  star,  and  that,  however  near  the  two  telescopes  are 
to  each  other.  By  transferring  then,  the  collimator  still  floating  on  a  ves- 
sel of  mercury  from  the  one  side  to  the  other  of  a  circle,  we  are  furnished 
with  two  qiiasi-celestial  objects,  at  precisely  equal  altitudes,  on  opposite 
sides  of  the  centre ;  and  if  these  be  observed  in  succession  with  the  tele- 
scope of  the  circle,  bringing  its  cross  to  bisect  the  image  of  the  cross  of  the 
collimator  (for  which  end  the  wires  of  the  latter  cross  are  purposely  set 
45°  inclined  to  the  horizon),  the  difference  of  the  readings  on  its  limb 
will  be  twice  the  zenith  distance  of  either ;  whence,  as  in  the  last  article, 
the  horizontal  or  zenith  point  is  immediately  determined.  Another,  and, 
in  many  respects,  preferable  form  of  the  floating  collimator,  in  which  the 
telescope  is  vertical,  and  whereby  the  zenith  point  is  directly  ascertained) 
is  described  in  the  Phil.  Trans.  1828,  p,  257,  by  the  same  author. 

(179.)  By  far  the  neatest  and  most  delicate  application  of  i\iQ  princi- 
ple of  collimation  of  Rittenhouse,  however,  is  suggested  by  Benzenberg, 
which  affords  at  once,  and  by  a  single  observation,  an  exact  knowledge 
of  the  nadir  point  of  an  astronomical  circle.     In  this  combination,  tho 


;in| 


a 
a 


104 


■( 


Hi 


OUTLINES   OP  ASTRONOMY. 


Fig.  24. 


^^^ 


telescope  of  the  circle  is  its  own  collimator.  The  object  observed  is  the 
central  intersectional  cross  of  the  wires  in  its  own  focus  reflected  in  mer- 
cury. A  strong  illumination  being  thrown  upon  the  system  of  wires 
(art.  160)  by  a  lateral  lamp,  the  telescope  of  the  instrument  is  directed 
vertically  downwards  towards  the  surface  of  the  mercury,  as  in  the  figure 
annexed.  The  rays  diverging  from  the  wires  issue  in  parallel  pencils 
from  the  object-glass,  are  incident  on  the  mercury,  and  are  thence  re- 
flected back  (without  losing  their  parallel  character)  to  the  object-glass, 
which  is  therefore  enabled  to  collect  them  again  in  its  focus.  Thus  is 
formed  a  reflected  image  of  the  system  of  cross-wires,  which,  when 
brought  by  the  slow  motion  of  the  telescope  to  exact  coincidence  (inter- 
section upon  intersection)  with  the  real  system  as  seen  in  the  eye-piece 
of  the  instrument,  indicates  the  precise  and  rigorous  verticality  of  the 
optical  axis  of  the  telescope  when  directed  to  the  nadir  point. 

(180.)  The  transit  and  mural  circle  are  essentially  meridian  instru- 
ments, being  used  only  to  observe  the  stars  at  the  moment  of  their 
meridian  passage.  Independent  of  this  being  the  most  favourable  mo- 
ment for  seeing  them,  it  is  that  in  which  their  diurnal  motion  is  parallel 
to  the  horizon.  It  is  therefore  easier  at  this  time  than  it  could  be  at  any 
other,  to  place  the  telescope  exactly  in  their  true  direction ;  since  their 
apparent  course  in  the  field  of  view  being  parallel  to  the  horizontal  thread 
of  the  system  of  wires  therein,  they  may,  by  giving  a  fine  motion  to  the 


com: 

telescope,  b 
allowed  to  f 
hit,  which 
angular  niaj 
if  possible, 
nution ;   ha 
during  a  d 
repeat  and 
The  angle 
altitude  of 
meridian,  ar 
(181.)  T 
should  poss' 
meridian,  b 
present  itsel 
by  reference 
circles,  one 
the  languag 
ascertained : 
its  longitude 
ascension  an 
azimuth  and 
(182.)  To 
possess  the  n 
capable  of  m 
amount  of  it 
co-ordinate  t 
the  telescope 
effected  by  n 
other  at  righi 
the  other  ha 
entirely  by  t 
at  the  point 
the  simplest 
the  best  in  ] 
niers,  or  mi( 
carries  the  pr 
Both  circles 
attached  to  i 
reading  off  is 
(183.)  It  i 


COMPOUND  INSTRUMENTS  WITH  CO-ORDINATE  CIRCLES.     105 


telescope,  be  brought  to  exact  coincidence  with  it,  and  time  may  be 
allowed  to  examine  and  correct  this  coincidence,  if  not  at  first  accurately 
hit,  which  is  the  case  in  no  other  situation.  Generally  speaking,  all 
angular  magnitudes  which  it  is  of  importance  to  ascertain  exactly,  should, 
if  possible,  be  observed  at  their  maxima  or  minima  of  increase  or  dimi- 
nution; because  at  these  points  they  remain  not  perceptibly  changed 
during  a  time  'long  enough  to  complete,  and  even,  in  many  cases,  to 
repeat  and  verify,  our  observations  in  a  careful  and  leisurely  manner. 
The  angle  which,  in  the  case  before  us,  is  in  this  predicament,  is  the 
altitude  of  the  star,  which  attains  its  maximum  or  minimum  on  the 
meridian,  and  which  is  measured  on  the  limb  of  the  mural  circle. 

(181.)  The  purposes  of  astronomy,  however,  require  that  an  observer 
should  possess  the  means  of  observing  any  object  not  directly  on  the 
meridian,  but  at  any  point  of  its  diurnal  course,  or  wherever  it  may 
present  itself  in  the  heavens.  Now,  a  point  in  the  sphere  is  determined 
by  reference  to  two  great  circles  at  right  angles  to  each  other ;  or  of  two 
circles,  one  of  which  passes  through  the  pole  of  the  other.  These,  in 
the  language  of  geometry,  are  co-ordinates  by  which  its  situation  is 
ascertained:  for  instance, — on  the  earth,  a  place  is  known  if  we  know 
its  longitude  and  latitude ;  —  in  the  starry  heavens,  if  we  know  its  right 
ascension  and  declination ;  —  in  the  visible  hemisphere,  if  we  know  its 
azimuth  and  altitude,  &c. 

(182.)  To  observe  an  object  at  any  point  of  its  diurnal  course,  we  must 
possess  the  means  of  directing  a  telescope  to  it ;  which,  therefore,  must  be 
capable  of  motion  in  two  planes  at  right  angles  to  each  other ;  and  the 
amount  of  its  angular  motion  in  each  must  be  measured  on  two  circles 
co-ordinate  to  each  other,  whose  planes  must  be  parallel  to  those  in  which 
the  telescope  moves.  The  practical  accomplishment  of  this  condition  is 
effected  by  making  the  axis  of  one  of  the  circles  penetrate  that  of  the 
other  at  right  angles.  The  pierced  axis  turns  on  fixed  supports,  while 
the  other  has  no  connection  with  any  external  support,  but  is  sustained 
entirely  by  that  which  it  penetrates,  which  is  strengthened  and  enlarged 
at  the  point  of  penetration  to  receive  jt.  The  annexed  figure  exhibits 
the  simplest  form  of  such  a  combination,  though  very  far  indeed  from 
the  best  in  point  of  mechanism.  The  two  circles  are  read  off  by  ver- 
niers, or  microscopes;  the  one  attached  to  the  fixed  support  which 
carries  the  principal  axis,  the  other  to  an  arm  projecting  from  that  axis. 
Both  circles  also  are  susceptible  of  being  clamped,  the  clamps  being 
attached  to  the  same  ultimate  bearing  with  which  the  apparatus  for 
reading  off  is  connected. 

(188.)  It  is  manifest  that  such  a  combination,  however  its  principal 


c 

I 

£3 
;p 

(/> 
< 
o 


Vv.tai 


a 


106 


OUTLINES  OF  ASTRONOMY. 


axis  be  pointed  (provided  that  its  direction  be  invariable,)  will  enable  us 
to  ascertain  the  situation  of  any  object  with  respect  to  the  observer's 
station,  by  angles  reckoned  upon  two  great  circles  in  the  visible  hemi- 
sphere, one  of  which  has  for  its  poles  the  prolongations  of  the  principal 
axis  or  the  vanishing  points  of  a  system  of  lines  parallel  to  it,  and  the 
other  passes  always  through  these  poles :  for  the  former  great  circle  is 
the  vanishing  line  of  all  planes  parallel  to  the  circle  A  B,  while  the 
latter,  in  any  position  of  the  instrument,  is  the  vanishing  line  of  all  the 
planes  parallel  to  the  circle  G  H ;  and  these  two  planes  being,  by  the 
construction  of  the  instrument,  at  right  angles,  the  great  circles,  which 
are  their  vanishing  lines,  must  be  so  too.  Now,  if  two  great  circles  of 
a  sphere  be  at  right  angles  to  each  other,  the  one  will  always  pass 
through  the  other's  poles. 

(184.)  There  are,  however,  but  two  positions  in  which  such  an  appa- 
ratus can  be  mounted  so  as  to  be  of  any  practical  utility  in  astronomy. 
The  first  is,  when  the  principal  axis  C  D  is  parallel  to  the  earth's  axis, 
and  therefore  points  to  the  poles  of  the  heavens  which  are  the  vanishing 
points  of  all  lines  in  this  system  of  parallels ;  and  when,  of  course,  the 
plane  of  the  circle  A  B  is  parallel  to  the  earth's  equator,  and  therefore 
has  the  equinoctial  for  its  vanishing  circle,  and  measures,  by  its  arcs  read 
off,  hour  angles,  or  differences  of  right  ascension.  In  this  case,  the  great 
circles  in  the  heavens,  corresponding  to  the  various  positions,  which  the 
circle  G  H  can  be  made  to  ass  me,  by  the  rotation  of  the  instrument 
round  its  axis  C  D,  are  all  hour-circles ;  and  the  arcs  read  off  on  this 
oircle  will  be  declinations,  or  polar  distances,  or  their  differences. 


THE  EQUATORIAL  INSTRUMENT. 


107 


(185.)  In  this  position  the  apparatus  assumes  the  name  of  an  equato- 
rialf  or,  as  it  was  formerly  called,  a  parallactic  instrument.  It  is  a  most 
convenient  instrument  for  all  such  observations  as  .require  an  object  to  be 
kept  long  in  view,  because,  beiug  once  set  upon  the  object,  it  can  be  fol- 
lowed as  long  as  we  please  by  a  aingh  motion^  i.  e.  by  merely  turning  the 
whole  apparatus  round  on  its  polar  axis.  For  since,  when  the  telescope 
is  set  on  a  star,  the  angle  between  its  direction  and  that  of  the  polar  axis  is 
equal  to  the  polar  distance  of  the  star,  it  follows,  that  when  turned  about 
its  axis,  without  altering  the  position  of  the  telescope  on  the  circle  G  H, 
the  point  to  which  it  is  directed  will  always  lie  in  the  small  circle  of  the 
heavens  coincident  with  the  star's  diurnal  path.  In  many  observations 
this  is  an  inestimable  advantage,  and  one  which  belongs  to  no  other  instru- 
ment. The  equatorial  is  also  used  for  determining  the  place  of  an  un- 
known by  comparison  with  that  of  a  known  object,  in  a  manner  to  be 
described  in  the  fifth  chapter.  The  adjustments  of  the  equatorial  are 
somewhat  complicated  and  difficult.  They  are  best  performed  in  this 
manner: — 1st,  Follow  the  pole  star  round  its  whole  diurnal  course,  by 
which  it  will  become  evident  whether  the  polar  axis  is  directed  above  or 
below,  to  the  right  or  to  the  left,  of  the  true  pole, — and  correct  it  accord- 
ingly (without  any  attempt,  during  this  process,  to  correct  the  errors,  if 
any,  in  the  position  of  the  declination  axis).  2dly,  after  the  polar  axis  is 
thus  brought  into  adjustment,  place  the  plane  of  the  declination  circle  in 
or  near  the  meridian ;  and,  having  there  secured  it,  observe  the  transits 
of  several  known  stars  of  widely  different  declinations.  If  the  intervals 
between  these  transits  correspond  to  the  known  differences  of  right  ascen- 
sions of  the  stark,  we  may  be  sure  that  the  telescope  describes  a  true 
meridian,  and  that,  therefore,  the  declination  axis  is  truly  perpendicular 
to  the  polar  one  j  —  if  not,  the  deviation  of  the  intervals  from  this  law 
will  indicate  the  direction  and  amount  of  the  deviation  of  the  axis  in 
question,  and  enable  us  to  correct  it.*  > 

(l56.)  A  very  great  improvement  has,  within  a  few  years  of  the  present 
time,  been  introduced  into  the  construction  of  the  equatorial  instrument. 
It  consists  in  applying  a  clockwork  movement  to  turn  the  whole  instru- 
ment round  upon  its  polar  axis,  and  so  to  follow  the  diurnal  motion  of 
any  celestial  object,  without  the  necessity  of  the  observer's  manual  inter- 
vention.    The  driving  power  is  the  descent  of  a  weight  which  communi- 


c 

I 

n 

< 

o 

Vnsta 

b 
a 

C 

00 


'  See  Littrow  on  the  Adjustment  of  the  Equatorial  (Mem.  Ast.  Soc.  vol.  ii.  p.  iif), 
where  formula;  arc  given  for  ascertaining  the  amount  and  direction  of  all  the  misad- 
justments  simultaneously.    But  the  practical  observer,  who  wishes  to  avoid  bewilder 
ing  himself  by  doing  two  things  at  once,  had  better  proceed  aa  recommended  in  the 
text. 


■  if 


108 


OUTLINES   OF  ASTRONOMY. 


Ir.    I 

h' 


I! 


i 


(r:  fl 


catcs  motion  to  a  train  of  wheelwork,  and  thua,  ultimately,  to  tbo  polar 
axis,  while,  at  the  same  time,  its  too  swift  descent  is  controlled  and  regu- 
lated to  the  exact  and  uniform  rate  required  to  give  that  axis  one  turn  in 
24  hours,  by  connecting  it  with  a  regulating  clock,  or  (which  is  found 
preferable  in  practice)  by  exhausting  all  the  superfluous  energy  of  the 
driving  power,  by  causing  it  to  overcome  a  regulated  friction.  Artists 
have  thus  succeeded  in  obtaining  a  perfectly  smooth,  uniform,  and  rajula- 
hh  motion,  which,  when  so  applied,  serves  to  retain  any  object  on  which  the 
telescope  may  be  set,  commodiously,  in  the  centre  of  the  field  of  view  for 
whole  hours  in  succession,  leaving  the  attention  of  the  observer  undis- 
tracted  by  having  a  mechanical  movement  to  direct,  and  with  both  his 
bands  at  liberty. 

(187.)  The  other  position  in  which  such  a  compound  apparatus  as  we 
have  described  in  art.  182  may  be  advantageously  mounted,  is  that  in 
which  the  principal  axis  occupies  a  vertical  position,  and  the  one  circle,  A 
B,  consequently  corresponds  to  the  celestial  horizon,  and  the  other,  G  II, 
to  a  vertical  circle  of  the  heavens.  The  angles  measured  on  the  former 
are  therefore  azt'muths,  or  differences  of  azimuth,  and  those  of  the  latter 
zenith  distances,  or  altitudes,  according  as  the  graduation  commences  from 
the  upper  point  of  its  limb,  or  from  one  90°  distant  from  it.  It  is  there- 
fore known  by  the  name  of  an  azimuth  and  altitude  instrument.  The 
vertical  position  of  its  principal  axis  is  secured  either  by  a  plumb-line 
suspended  from  the  upper  end,  which,  however  it  be  turned  round,  should 
continue  always  to  intersect  one  and  the  same  fiducial  mark  near  its  lower 
extremity,  or  by  a  level  fixed  directly  across  it,  whose  bubble  ought  not 
to  shift  its  place,  on  moving  the  instrument  in  azimuth.  The  north  or 
south  point  on  the  horizontal  circle  is  ascertained  by  bringing  the  vertical 
circle  to  coincide  with  the  plane  of  the  meridian,  by  the  same  criterion  by 
which  the  azimuthal  adjustment  of  the  transit  is  performed  (art.  162), 
and  noting,  in  this  position,  the  reading  off  of  the  lower  circle ;  or  by  the 
following  process. 

(188)  Let  a  bright  star  be  observed  at  a  considerable  distance  to  the 
east  of  the  meridian,  by  bringing  it  on  the  cross  wires  of  the  telescope. 
In  this  position  let  the  horizontal  circle  be  read  off,  and  the  telescope 
securely  clamped  on  the  vertical  one.  When  the  star  has  passed  the 
meridian,  and  is  in  the  descending  point  of  its  daily  course,  let  it  be  fol- 
lowed by  moving  the  whole  instrument  round  to  the  west,  without,  how- 
ever, unclamping  the  telescope,  until  it  comes  into  the  field  of  view ;  and 
.  until,  by  continuing  the  horizontal  motion,  the  star  and  the  cross  of  the 
wires  come  once  more  to  coincide.  In  this  position  it  is  evident  the  star 
must  have  the  same  precise  altitude  above  the  icestern  horizon,  that  it  had 


at  the  mom( 

let  the  mot 

The  differen 

interval.     >j 

on  either  sid 

the  north  or 

—  cousequei 

azimuthal  ur 

(ISO.)  Tl 

horizontal  ci 

and  constant 

the  two  obs 

half-way  bet' 

which  may 

error  of  a  ch 

this  last  put 

vided  with  a 

be  measured 

arrives  at  cq 

course;  and, 

error  of  the  ^ 

(190.)  Th 

erected.     Foi 

the  horizontal 

actly  into  the 

This  done,  lei 

point  intersec 

there,  and  let 

these  points 

zontal  circle. 

(191.)  On( 
circle  is  appli( 
tion.  For,  b 
zenith,  and  an 
course,  the  ex 
which  their  c 
deviation  from 
observation  in 
in  altitude),  is 
(192.)  The 
of  the  altitudt 


ALTITUDE  AND.  AZIMUTH   INSTRUMENT. 


109 


at  tho  moment  of  the  first  observation  above  the  atslcm.  At  this  point 
let  the  motion  be  arrested,  and  the  horizontal  (;ircle  be  again  road  off. 
The  difference  of  the  readings  will  bo  the  azimuthal  arc  described  in  the 
interval.  Now,  it  ia  evident  that  when  the  altitudos  of  any  star  arc  equal 
on  either  side  of  tho  meridian,  its  azimnthn,  whether  reckoned  both  from 
the  north  or  both  from  the  south  point  of  the  hori/.on,  must  also  be  equal, 
—  consequently  the  north  or  south  point  of  tho  horizon  must  bisect  the 
azimuthal  arc  thus  determined,  and  will  therefore  l)ccomo  known. 

(ISO.)  This  method  of  determining  the  north  and  south  points  of  a 
horizontal  circle  is  called  the  "method  of  equal  altitudes,"  and  is  of  great 
and  constant  use  in  practical  astronomy.  If  we  note,  at  the  moments  of 
the  two  observations,  the  time,  by  a  clock  or  chronometer,  the  instant 
half-way  between  them  will  be  the  moment  of  the  star's  meridian  passage, 
which  may  thus  be  determined  without  a  transit;  and,  vice  vcrsd,  the 
error  of  a  clock  or  chronometer  may  by  this  process  be  discovered.  For 
this  last  purpose,  it  is  not  necessary  that  our  instrument  should  be  pro- 
vided with  a  horizontal  circle  at  all.  Any  means  by  which  altitudes  can 
be  measured  will  enable  us  to  determine  the  moments  when  the  same  star 
arrives  at  equal  altitudes  in  the  eastern  and  western  halves  of  its  diurnal 
course ;  and,  these  once  known,  the  instant  of  meridian  passage  and  the 
error  of  the  clock  become  also  known. 

(190.)  Thus  also  a  meridian  lino  may  be  drawn  and  a  meridian  mark 
erected.  For  the  readings  on  the  north  and  south  points  on  tho  limb  of 
the  horizontal  circle  being  known,  tho  vertical  circle  may  be  brought  ex- 
actly into  the  plane  of  the  meridian,  by  setting  it  to  that  precise  reading. 
This  done,  let  the  telescope  be  depressed  to  tho  north  horizon,  and  let  the 
point  intersected  there  by  its  cross-wires  be  noted,  and  a  mark  erected 
there,  and  let  the  same  be  done  for  the  south  horizon.  The  line  joining 
these  points  is  a  meridian  line,  passing  through  the  centre  of  tho  hori- 
zontal circle.     The  marks  may  be  made  secure  and  permanent  if  required. 

(191.)  One  of  the  chief  purposes  to  which  the  altitude  and  azimuth 
circle  is  applicable  is  the  investigation  of  the  amount  and  laws  of  refrac- 
tion. For,  by  following  with  it  a  circunipolar  star  which  passes  tho 
zenith,  and  another  which  grazes  the  horizon,  through  their  whole  diurnal 
course,  the  exact  apparent  form  of  their  diurnal  orbits,  or  tho  ovals  into 
which  their  circles  arc  distorted  by  refraction,  can  be  traced ;  and  their 
deviation  from  circles,  being  at  every  moment  given  by  the  nature  of  the 
observation  in  the  direction  in  which  the  refraction  itself  takes  place  (i.  e. 
in  altitude),  is  made  a  matter  of  direct  observation. 

(192.)  The  zenith  sector  and  the  theodolite  are  peculiar  modifications 
of  the  altitude  and  azimuth  instrument.     Tho  former  is  adapted  for  the 


c 

I 

I 

-< 

o 


V^KO 


110 


OUTLINES   OF  ASTRONOMT. 


H^ 


very  exact  observation  of  stars  in  or  near  the  zenith,  by  giving  a  great 
length  to  the  vertical  axis,  and  suppressing  all  the  circuinforenco  of  tho 
vertical  circle,  except  a  few  degrees  of  its  lower  part,  by  which  a  groat 
length  of  radius,  and  a  consequent  proportional  enlargement  of  the  divi- 
sions of  its  arc,  is  obtained.  The  latter  is  especially  devoted  to  the  mea> 
sures  of  horizontal  angles  between  terrestrial  objects,  in  which  the  telescope 
uever  requires  to  be  elevated  more  than  a  few  degrees,  and  in  which, 
therefore,  the  vertical  circle  is  either  dispensed  with,  or  executed  on  a 
smaller  scale,  and  with  less  delicacy;  while,  on  the  other  hand,  great  care 
is  bestowed  on  securing  the  exact  perpendicularity  of  the  plane  of  the 
telescope's  motion,  by  resting  its  horizontal  axis  on  two  supports  like  the 
piers  of  a  transit-instrument,  which  themselves  are  firmly  bedded  on  the 
spokes  of  the  horizontal  circle,  and  turn  with  it. 

(193.)  The  next  instrument  we  shall  describe  is  one  by  whose  aid  the 
angular  distance  of  any  two  objects  may  be  measured,  or  the  altitude  of 
a  single  one  determined,  either  by  measuring  its  distance  from  the  visible 
horizon  (such  as  the  sea-offing,  allowing  for  its  dip),  or  from  its  own  reflec- 
tion on  the  surface  of  mercury.  It  is  the  sextant,  or  quadrant,  commonly 
called  ffadlei/'s,  from  its  reputed  inventor,  though  the  priority  of  inven- 
tion belongs  undoubtedly  to  Newton,  whose  claims  to  the  gratitude  of  the 
navigator  are  thus  doubled,  by  his  having  furnished  at  once  the  only 
theory  by  which  his  vessel  can  be  securely  guided,  and  the  only  instru- 
ment which  has  ever  been  found  to  avail,  in  applying  that  theory  to  its 
nautical  uses.' 

(194.)  The  principle  of  this  instrument  is  the  optical  property  of  re* 
fleeted  rays,  thus  announced :  — ''  The  angle  between  the  first  and  last 
directions  of  a  ray  which  has  suffered  two  reflections  in  one  plane  is  equal  to 
twice  the  inclination  of  the  reflecting  surfaces  to  each  other.  Let  A  B  be 
the  limb  or  graduated  arc,  of  a  portion  of  a  circle  60°  in  extent,  but 
divided  into  120  equal  parts.  On  the  radius  C  B  let  a  silvered  plane  glass 
D  be  fixed,  at  right  angles  to  the  plane  of  the  circle,  and  on  the  moveable 
radius  C  E  let  another  such  silvered  glass,  C,  be  fixed.  The  glass  D  is 
permanently  fixed  parallel  to  A  C,  and  only  one  half  of  it  is  silvered,  the 
other  half  allowing  objects  to  be  seen  through  it.  The  glass  C  is  wholly 
silvered,  and  its  plane  is  parallel  to  the  length  of  the  moveable  radius  C  E, 

*  Newton  communicated  it  to  Dr.  Halley,  who  suppressed  it.  The  description  of 
the  instrument  was  found,  after  the  death  of  Halley,  among  his  papers,  in  Newton's 
own  handwriting,  by  his  executor,  who  communicated  the  papers  to  the  Royal  Society, 
twenty-five  years  after  Newton's  death,  and  eleven  after  the  publication  of  Hadley'a 
invention,  which  might  be,  and  probably  was,  independent  of  any  knowledge  of  New- 
ton's,  though  Hutton  insinuates  the  contrary. 


at  tho  extr 
of  the  linil 
object,  Q,  I 
portion  of 
telescope,  \ 
silvered  pai 


telescope.  ^ 

view  at  onc( 

perpendicujj 

crating  eacl 

and  at  this 

ject,  and  F 

fixed  and  n 

being  purpo 

the  arc,  A I 

in  fact,  read 

will  express. 

the  objects. 

(195.)  T 

observation 

the  measure 

is  of  essenti 

but  can  be 

instrument  i 

plumb-line,  ( 

lesource;  an 

to  coincide  v 

altitude  abo^ 

hwizon  (art, 


THE   SEXTANT. 


Ill 


at  tbo  extremity  E  of  which  a  vernier  ia  placed  to  rend  off  the  divisions 
of  the  limb.  On  the  radius  A  (!  is  set  a  telescope  F,  through  which  any 
object,  Q,  may  be  seen  by  {liird  rays  which  pass  through  the  unsilvored 
portion  of  the  glass  D,  while  another  object,  P,  is  seen  through  the  same 
telescope,  by  rays,  which,  after  reflection  at  C,  have  been  thrown  upon  the 
silvered  part  of  D,  and  are  thence  directed  by  a  second  rofieetion  into  the 

Fig.  26. 


telescope.  The  two  images  so  formed  will  both  be  seen  in  the  field  of 
view  at  once,  and  by  moving  the  radius  C  E  will  (if  the  reflectors  be  truly 
perpendicular  to  the  plane  of  the  circle)  meet  and  pass  over,  without  oblit- 
erating each  other.  The  motion,  however,  is  arrested  when  they  meet, 
and  at  this  point  the  angle  included  between  the  direction  C  P  of  one  ob- 
ject, and  F  Q  of  the  other,  is  twice  the  angle  E  C  A  included  between  the 
fixed  and  moveable  radii  C  A,  C  E.  Now,  the  graduations  of  the  limb 
being  purposely  made  only  half  as  distant  as  would  correspond  to  degrees, 
the  arc,  A  E,  when  read  off,  as  if  the  graduations  were  whole  degrees,  will, 
in  fact,  read  double  its  real  amount,  and  therefore  the  numbers  so  read  off 
will  express,  not  the  angle  E  C  A,  but  its  double,  the  angle  subtended  by 
the  objects. 

(195.)  To  determine  the  exact  distances  between  the  stars  by  direct 
observation  is  comparatively  of  little  service ;  but  in  nautical  astronomy 
the  measurement  of  their  distances  from  the  moon,  and  of  their  altitudes, 
is  of  essential  importance ;  and  as  the  sextant  requires  no  fixed  support, 
but  can  be  held  in  the  hand,  and  used  on  ship-board,  the  utility  of  the 
instrument  becomes  at  once  obvious.  For  altitudes  at  sea,  as  no  level, 
plumb-line,  or  artificial  horizon  can  be  used,  the  sea-offing  affords  the  only 
resource ;  and  the  image  of  the  star  observed,  seen  by  reflection,  is  brought 
to  coincide  with  the  boundary  of  the  sea  seen  by  direct  rays.  Thus  the 
altitude  above  the  sea-line  is  found ;  and  this  corrected  for  the  dip  of  the 
Jmizon  (art.  23)  gives  the  true  altitude  of  the  star.    On  land,  an  artifi- 


I 

m 


112 


OUTLINES   OF   ASTRONOMY. 


w 


ciul  horizon  may  bo  used  (art.  17^),  and  tho  consideration  of  dip  is  ren- 
dered unnccessury. 

(190.)  Tlio  adjustments  of  tho  soxtunt  are  »impl'».  Thoy  consist  :u 
fixing  tho  two  reflectors,  tho  ono  on  tho  revolving  idius  C  K,  the  other 
on  the  iixcd  one  C  B,  so  as  to  havo  their  planes  perpendicular  to  tho 
plane  of  tho  circle,  and  parallel  to  each  other,  when  tho  reading  of  the 
instrunient  is  zero.  This  adjustment  in  tho  latter  respect  is  of  little 
moment,  as  its  effect  is  to  produce  a  wmtant  error,  whoso  amount  is 
readily  a.sccrtaincd  by  bringing  tho  two  images  of  ono  and  tho  same  Htnr 
or  other  distant  object  to  coincidence;  when  the  instrument  oiKjht  to  ivj;>c1 
zero,  and  if  it  does  not,  tho  angle  which  it  */«<•.«»  read  is  tho  zero  coi  c^  jtion 
and  must  bo  subtracted  from  all  angles  measured  with  tho  sertant.  '\'-i 
former  adjustments  are  essential  to  bo  maintained,  and  are  p  il  )rmcrl  by 
small  screws,  by  whose  aid  cither  or  both  the  glasses  may  be  tilled  a  little 
one  way  or  another  until  the  direct  and  reflected  imaj^us  of  a  vertical  h'nc  (a 
plumb-line)  can  bo  brought  to  coincidence  over  tkcir  zchohi  (wtcnf,  so  as 
to  form  a  single  unbroken  straight  line,  whatever  be  the  position  of  tho 
movoiiblc  arm,  in  the  middle  of  the  field  of  view  of  the  tohisoope,  whose 
axis  is  carefully  adjusted  by  the  optician  to  parallelism  with  the  plane  of 
the  liuib.  In  practice  it  is  usual  to  leave  only  the  reflector  D  on  the  fixed 
radius  adjustable,  that  on  tie  moveable  being  set  to  great  nicety  by  the 
maker.  In  this  c  isu  the  best  way  of  making  the  adjustment  is  to  view  a 
pair  of  lines  rro-sing  each  other  at  right  angles  (ono  being  horizontal,  the 
other  vertical )  Lhrougli  tho  teles^cope  of  the  instrument,  holding  the  piano 
of  its  limb  vertical,  —  then  having  brought  the  horizonttil  line  and  its 
reflected  image  to  coincidence  by  tho  motion  of  the  radius,  the  two 
images  of  the  vertical  arm  must  be  brought  to  coincidence  by  tilting  one 
way  or  other  tho  fixed  reflector  D  by  means  of  an  adjusting  screw,  with 
which  every  sextant  is  provided  for  that  purpose.  When  both  lines  coin- 
cide in  the  a.nfre  of  thejirld,  the  adjustment  is  correct. 

(197.)  The  reflecting  circle  is  an  in.stTmciifc  destined  for  the  same  uses 
as  tho  sextant,  but  more  complete,  the  cinl.^  being  entire,  and  thi'  'I'vi- 
sions  carried  all  round.  It  is  usually  ;\ii:i'sli»J  vlch  thrc  .ciniers,  so  as 
to  admit  of  three  distinct  readings  oil,  by  tlie  average  of  which  the  error 
of  graduation  and  of  reading  is  reduced.  This  is  altogether  a  very  refined 
and  elegant  instrument. 

(lOS.)  We  must  not  conclude  this  part  of  our  subject  without  mention 
'^f  the  "principle  of  repetition j"  an  invention  of  Borda,  by  which  the 
error  of  fjraduation  may  be  diminished  to  any  degree,  and,  practically 
speaking,  annihilated.  Let  PQ  be  two  objects  which  we  may  suppose 
fixed,  for  purposes  of  mere  explanation,  and  let  K  L  be  a  telescope  move- 


able  on  0, 1 
former,  A IW 
the  graduati 
scope  is  atta 
arm  0  a  A  c 
limb  of  the 
it  can  be  t 
pleasure.     S 
arm  0  A  to 
Then  carry  t 
inner  circle, 
round,  over  i 
angle  POQ. 
inner,  and  re 
angle  POQj 
of  graduatio 
rid  of.     To  t 
the  arm  fron 
clatap  the  an 
scope  to  Q,  b 
second  arc,  E 
will  the  diflFei 
twice  the  ang 
with  the  aami 
peated  as  ofte: 
A  U  C  D  read 
by  the  joint  e 
stant  error  of 
off  alone.      J 
8 


PRINCIPLE   OF  REPETITION. 


118 


.  f.i     1. 


able  OD  0,  the  common  axis  of  two  circles,  A  M  L  and  n  he,  of  which  th«) 
former,  A  M  L,  is  absolutely  fixed  in  the  plane  of  th«  objects,  and  carries 
the  graduations,  and  the  latter  is  freely  moveable  on  thu  mxis.  The  tele- 
scope is  attached  permanently  to  the  latter  circle,  am'  luoves  with  it.  An 
arm  0  a  A  carries  the  index,  or  vernier,  which  rcaus  off  the  graduated 
limb  of  the  fixed  circle.  This  arm  is  provided  with  two  clumps,  by  which 
it  can  be  temporarily  connected  with  either  circle,  and  detached  at 
pleasure.  Suppose,  now,  the  telescope  directed  to  P.  Olamp  the  index 
arm  0  A  to  the  inner  circle,  and  undamp  it  from  the  outer,  and  read  off. 
Then  carry  the  telescope  round  to  the  other  object  Q.  Tu  so  doing,  the 
inner  circle,  and  the  index-arm  which  is  clamped  to  it,  will  also  be  carried 
round,  over  an  arc  A  B,  on  the  graduated  limb  of  the  outer,  equal  to  the 
angle  P  0  Q.  Now  clamp  the  index  to  the  outer  circle,  ai-d  unclamp  the 
inner,  and  read  off :  the  difference  of  readings  will  of  course  measure  the 
angle  P 0 Q;  but  the  result  will  be  liable  to  two  sources  of  error  —  that 
of  graduation  and  that  of  observation,  both  which  it  is  our  object  to  get 
rid  of.  To  this  end  transfer  the  telescope  back  to  P,  without  unclamping 
the  arm  from  the  outer  circle;  then,  having  made  the  bisection  of  P, 
clantp  the  arm  to  b,  and  unclamp  it  from  B,  and  again  transfer  the  tele- 
scope to  Q,  by  which  the  arm  will  now  be  carried  with  it  t«  C,  over  a 
second  arc,  B  C,  equal  to  the  angle  P  0  Q.  Now  again  read  off;  then 
will  the  difference  between  this  reading  and  the  original  one  measure 
twice  the  angle  P  0  Q,  affected  with  both  errors  of  observation,  but  only 
with  (he  same  error  of  graduation  as  before.  Let  this  process  be  re- 
peated OS  often  as  we  please  (suppose  ten  times) ;  then  will  the  final  arc 
A  B  C  D  read  off  on  the  circle  be  ten  times  the  required  angle,  affected 
by  the  joint  errors  of  all  the  ten  observations,  but  only  by  the  same  con- 
stant error  of  graduation,  which  depends  on  the  initial  and  final  readings 
off  alone.  Now  the  errors  of  observation,  when  numerous,  tend  to 
8 


C 

I 

s 

< 


a 
a 


C 


9 


114 


OUTLINES  OF  J^STBONOMT. 


k 


balance  and  destroy  one  anotbcr;  so  that,  if  sufficiently  multi^  lied,  their 
influence  will  disappear  from  the  result.  There  remains,  then,  only  the 
constant  error  of  graduation,  which  comes  to  be  divided  in  the  final  result 
by  the  number  of  observations,  and  is  therefore  diminished  in  its  influence 
to  one  tenth  of  its  possible  amount,  or  to  less  if  need  be.  The  abstract 
beauty  and  advantage  of  this  principle  seem  to  be  counterbalanced  in 
practice  by  some  unknown  cause,  which,  probably,  must  be  sought  for  in 
imperfect  clamping. 

(199.)  Micrometers  are  instruments  (as  the  name  imports')  for  measur- 
ing, with  great  precision,  small  angles,  not  exceeding  a  few  minutes,  or  at 
most  a  whole  degree.  They  are  very  various  in  construction  and  principle, 
nearly  all,  however,  depending  on  the  exceeding  delicacy  with  which  space 
can  be  subdivided  by  the  turns  and  parts  of  a  turn  of  fine  screws.  Thus 
—  -in  the  parallel  wire  micrometer,  two  parallel  threads  (spider's  lines  arc 
generally  used)  stretched  on  sliding  frames,  one  or  both  moveable  by 

'••  -'"  "  ■  ''■'"     '"■■■'      Fig.  28.  -'■  ■'■'   ■ 


K'.vr,^ 


screws  in  a  direction  perpendicular  to  that  of  the  tnreads,  are  placed  in 
the  common  focus  of  the  object  and  eye-glasses  of  a  telescope,  and  brought 
by  the  motion  of  the  screws  exactly  to  cover  the  two  extremities  of  the 
image  of  any  small  object  seen  in.  the  telescope,  as  the  diameter  of  a 
planet,  &c.,  the  angular  distance  between  which  it  is  required  to  measure. 
This  done,  the  threads  are  closed  up  by  turning  one  of  the  screws  till  they 
exactly  cover  each  other,  and  the  number  of  turns  and  parts  of  a  turn 
required  gives  the  interval  of  the  threads,  which  must  be  converted  into 
angular  measure,  either  by  actual  calculation  from  the  linear  measure  of 
the  threads  of  the  screw  and  the  focal  length  of  the  object-glass,  or 
experimentally,  by  measuring  the  image  of  a  known  object  placed  at  a 
known  distance  (as  a  foot-rule  at  a  hundred  yards,  &c.)  and  therefore  sub- 
tending a  known  angle. 

(200.)  The  duplication  of  the  image  of  an  object  by  optical  means 
furnishes  a  valuable  and  fertile  resource  in  micrometry.  Suppose  by  any 
optical  contrivance  the  single  image  A  of  any  object  can  be  converted  into 
two,  exactly  equal  and  similar,  A  B,  at  a  distance  from  one  another, 


dependent 
and  in  any 
be  made  to 
be  brought 
one  side,  as 
cross  and  i 
quantity  of 
to  the  other, 
(201.)  I 
such  duplici 
cations,)  is 
object-glass 
brass  framei 


*  Mtxpof,  small ;  ittrptiv,  to  mesBure. 


Hi^^r^ 


.va!:Kh 


produced  an< 
forms  its  owr 
own  axis;  at 
in  the  focus  ( 
by  the  motio: 
as  above  desc 
(202.)  Doi 

'  This  might 
circular  space  b 


I,  their 
ily  the 
[  result 
fluence 
ibstract 
iced  iu 
b  for  in 

measur- 
38,  or  at 
rinciple, 
jh  space 
.  Thus 
lines  arc 
sable  by 


)laced  in 
brought 
28  of  the 
ter  of  a 
measure, 
till  they 
)f  a  turn 
rted  into 
lasure  of 
iss,  or 
iCed  at  a 
'ore  sub- 

■al  means 
e  by  any 
irted  into 
another, 


MIOROMETERS. 


Fig.  29. 


m 


dependent  (by  some  mechanical  movement)  on  the  will  of  the  observer, 
and  in  any  required  direction  from  one  another.  As  these  can,  therefore, 
be  made  to  approach  to  or  recede  from  each  other  at  pleasure,  they  may 
be  brought  in  the  firsi  place  to  approach  till  they  touch  one  another  on 
one  side,  as  at  A  0,  and  then  being  made  by  continuing  the  motion  to 
cross  and  touch  on  the  opposite  side,  as  A  D,  it  is  evident  that  the 
quantity  of  movement  required  to  produce  the  change  from  one  contact 
to  the  other,  ifumform^  will  measure  the  double  diameter  of  the  object  A. 
(201.)  Innumerable  optical  combinations  may  be  devised  to  operate 
such  duplication.  The  chief  and  most  important  (from  its  recent  appli- 
cations,) is  the  heliometer,  in  which  the  image  is  divided  by  bisecting  the 
object-glass  of  the  telescc^e,  and  making  its  two  halves,  set  in  separate 
brass  frames,  slide  laterally  on  each  other,  as  A  B,  the  motion  being 


Fig.  80. 


produced  and  measured  by  a  screw.  Each  half,  by  the  laws  of  optics, 
forms  its  own  image  (somewhat  blurred,  it  is  true,  by  diffraction,*)  in  its 
own  axis ;  and  thus  two  equal  and  similar  images  are  formed  side  by  side 
in  the  focus  of  the  eye-piece,  which  may  be  made  to  approach  and  recede 
by  the  motion  of  the  screw,  and  thus  afford  the  means  of  measurement 
as  above  described. 
(202.)  Double  refraction  through  crystallized  media  affords  another 

*  This  might  be  cured,  though  at  an  expense  of  light,  by  limiting  each  half  to  a 
circular  space  by  diaphragms,  as  represented  by  the  dotted  lines. 


•A 


I 

n 

t/> 
< 

o 

Vina 

> 
rn 

in* 

pi 

o 
a 

BSMP 


93 


116 


OUTLINES   OF  ASTRONOMY. 


means  of  accomplishing  the  same  end.  Without  going  into  the  intricar 
cies  of  this  difficult  branch  of  optics,  it  will  suffice  to  state  that  objects 
viewed  through  certain  crystals  (as  Iceland  spar,  or  quartz)  appear 
double,  two  images  equally  distinct  being  formed,  whose  angular  distance 
from  each  other  varies  from  nothing  (or  perfect  coincidence,)  up  to  a 
certain  limit,  according  to  the  direction  with  respect  to  a  certain  fixed 
line  in  the  crystal,  called  its  optical  axis.  Suppose,  then,  to  take  the 
simplest  case,  that  the  eye-lens  of  a  telescope,  instead  of  glass,  were 
formed  of  such  a  crystal  (say  of  quartz,  which  may  be  worked  as  well  or 
better  than  glass,)  and  of  a  spherical  form,  so  as  to  offer  no  difference 
when  turned  about  on  its  centre,  other  than  the  inclination  of  its  optical 
ascis  to  the  visual  ray.  Then  when  that  axis  coincides  with  the  line  of 
coUimation  of  the  object-glass,  one  image  only  will  be  seen,  but  when 
made  to  revolve  on  an  axis  perpendicular  to  that  line,  two  will  arise, 
opening  gradually  out  from  each  other,  and  thus  originating  the  desired 
duplication.  In  this  contrivance,  the  angular  amount  of  the  rotation  of 
the  sphere  affords  the  necessary  datum  for  determining  the  separation  of 
the  images. 

(203.)  Of  all  methods  which  have  been  proposed,  however,   the 
simplest  and  most  unobjectionable  would  appear  to  be  the  following.    It 

/  Fig.  31. 


is  well  known  to  every  optical  student,  that  two  prisms  of  glass,  a  flint 
and  a  crown,  may  be  opposed  to  each  other,  so  as  to  produce  a  colourless 
defiection  of  parallel  rays.  An  object  seen  through  such  a  compound  or 
achromatic  prism,  will  be  seen  simply  deviated  in  direction,  but  in  no 
way  otherwise  altered  or  distorted.  Let  such  a  prism  be  constructed 
with  its  surfaces  so  nearly  parallel  that  the  total  deviation  produced  ia 
traversing  them  shall  not  exceed  a  small  amount  (say  5'.)  Let  this  be 
out  in  half,  and  from  each  half  let  a  circular  disc  be  formed,  and  cemented 


on  a  oirculi 

concentric 

cept  but  a 

the  annexe 

one,  and  tl 

be  so  mou 

the  other,  f 

is  evident, 

conspire,  a 

has  passed 

will  emerge 

varying  fro 

one  disc  on 

at  such  a  } 

focus,  that 

Then  will  h 

half   deviat* 

variable  and 

occur.     If  t 

of  its  applic; 

of  the  discs 

mg  for  the  s 

(204.)  Tl 

which  is  carr 

of  the  object 

telescope.     1 

line  in  the  fi 

an  object  see 

seen  at  once 

cover  both  of 

of  junction. 

small  divided 

is  applied  (as 

the  zero  of  its 

longed,  will  i 

"  angles  of  pi 

and  in  one  d: 

position  corre 

sunicd  as  a  ci 

following  ;  1 

the  order  of  c 


? 
.i|; 


MICROMETERS. 


117 


were 


on  a  circular  plate  of  parallel  glass,  or  otherwise  sustained,  close  to  and 
concentric  with  the  other  by  a  framework  of  metal  so  light  as  to  inter* 
cept  but  a  small  portion  of  the  light  which  passes  on  the  outside  (as  in 
the  annexed  figure,)  where  the  dotted  lines  represent  the  radii  sustaining 
one,  and  the  undotted  those  carrying  the  other  disc.  The  whole  must 
be  so  mounted  as  to  allow  one  disc  to  revolve  in  its  own  plane  behind 
the  other,  fixed,  and  to  allow  the  amount  of  rotation  to  be  read  off.  It 
b  evident,  then,  that  when  the  deviations  produced  by  the  two  discs 
conspire,  a  total  deviation  of  10'  will  be  effected  on  all  the  light  which 
has  passed  through  them ;  that  when  they  oppose  each  other,  the  rays 
will  emerge  undeviated,  and  that  in  intermediate  positions  a  deviation 
varying  from  0  to  10',  and  calculable  from  the  angular  rotation  of  the 
one  disc  on  the  other,  will  arise.  Now,  let  this  combination  be  applied 
at  such  a  point  of  the  cone  of  rays,  between  the  object-glass  and  its 
focus,  that  the  discs  shall  occupy  exactly  half  the  area  of  its  section. 
Then  will  half  the  light  of  the  object  lens  pass  undeviated  —  the  other 
half  deviated,  as  above  described;  and  thus  a  duplication  of  image, 
variable  and  measureable  (as  required  for  micrometric  measurement)  will 
occur.  If  the  object-glass  be  not  very  large,  the  most  convenient  point 
of  its  application  will  be  externally  before  it,  in  which  case  the  diameter 
of  the  discs  will  be  to  that  of  the  object-glass  as  707  :  1000 ;  or  (allow- 
mg  for  the  spokes)  about  as  7  to  10. 

(204.)  The  Position  Micrometer  is  simply  a  straight  thread  or  wire 
which  is  carried  round  by  a  smooth  revolving  motion,  in  the  common  focus 
of  the  object  and  eye-glasses,  in  a  plane  perpendicular  to  the  axis  of  the 
telescope.  It  serves  to  determine  the  situation  with  respect  to  some  fixed 
line  in  the  field  of  view,  of  the  line  joining  any  two  objects  or  points  of 
an  object  seen  in  that  field  —  as  two  stars,  for  instance,  near  enough  to  be 
seen  at  once.  For  this  purpose  the  moveable  thread  is  placed  so  as  to 
cover  both  of  them,  or  stand,  as  may  best  be  judged,  parallel  to  their  line 
of  junction.  And  its  angle,  with  the  fixed  one,  is  then  read  off  upon  a 
small  divided  circle  exterior  to  the  instrument.  When  such  a  micrometer 
is  applied  (as  it  most  commonly  is)  to  an  equatorially  mounted  telescope, 
the  zero  of  its  position  corresponds  to  a  direction  of  the  wire,  such  as,  pro- 
longed, will  represent  a  circle  of  declination  in  the  heavens — and  the 
"angles  of  position''  so  read  off  are  reckoned  invariably  from  one  point, 
and  in  one  direction,  viz.,  north,  following,  south,  preceding ;  so  that  0° 
position  corresponds  to  the  situation  of  an  object  exactly  north  of  that  as- 
sumed as  a  centre  of  reference, —  90°  to  a  situation  exactly  eastward  or 
following ;  180°  exactly  south ;  and  270°  exactly  west^  or  preceding  in 
the  order  of  diurnal  moTement. 


I 

IS 

o 


o 
a 

C 

R3 


118 


OUTLINES  OF  ASTRONOMT. 


i  .V   I . '. 


Ml 

L*  ■ 

I 


.1.1 


CHAPTER  IV. 


OF    GEOGRAPHY, 


OP  THE  FiaUEE  OF  THE  EARTH. — ITS  EXACT  DIMENSIONS. — ^ITS  FORM — 
THAT  OP  EQUILIBRIUM  MODIFIED  BY  CENTRIFUGAL  FORCE. — VARIA- 
TION OP  GRAVITY  ON  ITS  SURFACE.  —  STATICAL  AND  DYNAMICAL 
MEASURES  OP  GRAVITY. — THE  PENDULUM.  —  GRAVITY  TO  A  SPHE- 
ROID.— OTHER  EFFtlCTS  OF  THE  EARTH'S  ROTATION. — TRADE  WINDS. 

—  DETERMINATION   OP  GEOGRAPHICAL  POSITIONS. — OF  LATITUDES. 

—  OF  LONGITUDES.  —  CONDUCT  OF  A  TRIGONOMETRICAL  SURVEY. — 
OP  MAPS.  —  PROJECTIONS  OP  THE  SPHERE.  —  MEASUREMENT  OF 
HEIGHTS  BY  THE  BAROMETER. 

(205.)  Geography  is  not  only  the  most  important  of  tho  practical 
branches  of  knowledge  to  which  astronomy  is  applied,  but  it  is  also, 
theoretically  speaking,  an  essential  part  of  the  latter  science.  The  earth 
being  the  general  station  from  which  we  view  the  heavens,  a  knowledge 
of  the  local  situation  of  particular  stations  on  its  surface  is  of  great  con- 
sequence, when  we  come  to  inquire  the  distances  of  the  nearer  heavenly 
bodies  from  us,  as  concluded  from  observations  of  their  parallax  as  well 
as  on  all  other  occasions,  where  a  difference  of  locality  can  be  supposed  to 
influence  astronomical  results.  We  propose,  therefore,  in  this  chapter,  to 
explain  the  principles,  by  which  astronomical  observation  is  applied  to 
geographical  determinations,  and  to  give  at  the  same  time  an  outline  of 
geography  so  far  as  it  is  to  be  considered  a  part  of  astronomy. 

(206.)  Geography,  as  the  word  imports,  is  a  delineation  or  description 
of  the  earth.  In  its  widest  sense,  this  comprehends  not  only  the  delinea- 
tion of  the  form  of  its  continents  and  seas,  its  rivers  and  mountains,  but 
their  physical  condition,  climates,  and  products,  and  their  appropriation 
by  communities  of  men.  With  physical  and  political  geography,  how- 
ever, we  have  no  concern  here.  Astronomical  geography  has  for  its 
objects  the  exact  knowledge  of  the  form  and  dimensions  of  the  earth,  the 
parts  of  its  surface  occupied  by  sea  and  land,  and  the  configuration  of  the 
surface  of  the  latter,  regarded  as  protuberant  above  the  ocean,  and  broken 


into  the  vs 
the  form  o 
face  of  th 
know,  it  ii 
lamented, 
there  are 
.7reatly  ,d^ 
"  (207.) 
already  sh( 
the  reader 
a  loss  to  p( 
tible  of  mi 
at  once,  ca 
be  material 
increasing 
larger  area! 
on  minuter 
in  the  man 
axis  about 
—  this  is  s( 
of  such  pn 
the  nicest  e 
of  diametei 
an  inch.     1 
would  still 
the  differen 
be  termed, 
name  appro 

(208.)  1 
ellipses;  so 
nowhere  (e: 
It  is  easy  t 
form,  arisin, 
quite  impel 
sector;  so  \ 
notice  so  sn 
this  conclus 
the  means  o 
any  part  of 

(209.)  A 
view  it  at  oe 


THE  FIOURE   OF  THE  EARTH. 


119 


into  the  various  forms  of  mouatain,  table  land,  and  valley ;  neither  should 
the  form  of  the  bed  of  the  ocean,  regarded  as  a  oontinuation  of  the  sur* 
face  of  the  land  beneath  the  water,  be  left  out  of  consideration :  we 
know,  it  is  true,  very  little  of  it ;  but  this  is  an  ignorance  rather  to  be 
lamented,  and,  if  possible,  remedied,  than  acquiesced  in,  inasmuch  as 
there  are  many  very  important  branches  of  inquiry  which  would  be 
^rreatly  .dvanced  by  a  better  acquaintance  with  it. 

(207.)  With  regard  to  the  figure  of  the  earth  a«  a  whole,  we  have 
already  shown  that,  speaking  loosely,  it  may  be  regarded  as  spherical ;  but 
the  reader  who  has  duly  appreciated  the  remarks  in  art.  22  will  not  be  at 
a  loss  to  perceive  that  this  result,  concluded  from  observations  not  suscep- 
tible of  much  exactness,  and  embracing  very  small  portions  of  the  surface 
at  once,  can  only  be  regarded  as  a  first  approximation,  and  may  require  to 
be  materially  modified  by  entering  into  minutiae  before  neglected,  or  by 
increasing  the  delicacy  of  our  observations,  or  by  including  in  their  extent 
larger  areas  of  it«  surface.  For  instance,  if  it  should  turn  out  (as  it  will), 
on  minuter  inquiry,  that  the  true  figure  is  somewhat  elliptical,  or  flattened, 
in  the  manner  of  an  orange,  having  the  diameter  which  coincides  with  the 
axis  about  a^^th  part  shorter  than  the  diameter  of  its  equatorial  circle; 
— this  is  so  trifling  a  deviation  from  the  spherical  form  that,  if  a  piodel 
of  such  proportions  were  turned  in  wood,  and  laid  before  us  on  a  table, 
the  nicest  eye  or  hand  would  not  detect  the  flattening,  since  the  difference 
of  diameters,  in  a  globe  of  fifteen  inches,  would  amount  only  to  ^\jth  of 
an  inch.  In  all  common  parlance,  and  for  all  ordinary  purposes,  then,  it 
would  still  be  called  a  globe ;  while,  nevertheless,  by  careful  measurement, 
the  difference  would  not  fail  to  be  noticed;  atid,  speaking  strictly,  it  would 
be  termed,  not  a  globe,  but  an  oblate  ellipsoid,  or  spheroid,  which  is  the 
name  appropriated  by  geometers  to  the  form  above  described. 

(208.)  The  sections  of  such  a  figure  by  a  plane  are  not  circles,  but 
ellipses ;  so  that,  on  such  a  shaped  earth,  the  horizon  of  a  spectator  would 
nowhere  (except  at  the  poles)  be  exactly  circular,  but  somewhat  elliptical. 
It  is  easy  to  demonstrate,  however,  that  its  deviation  from  the  circular 
form,  arising  from  so  slight  an  "  elliptidty  "  as  above  supposed,  would  be 
quite  imperceptible,  not  only  to  our  eye-sight,  but  to  the  test  of  the  dip- 
sector  ;  so  that  by  that  mode  of  observation  we  should  never  be  led  to 
notice  so  small  a  deviation  from  perfect  sphericity.  How  we  are  led  to 
this  conclusion,  as  a  practical  result,  will  appear,  when  we  have  explained 
the  means  of  determining  with  accuracy  the  dimensions  of  the  whole,  or 
any  part  of  the  earth. 

(209.)  As  we  cannot  grasp  the  earth,  nor  recede  from  it  far  enough  to 
view  it  at  once  as  a  whole,  and  compare  it  with  a  known  standard  of  mea- 


G 

I 

m 

mrat 
< 

o 


b 
a 

C 


II  I 


120 


OUTLINES  OF  ASTRONOMY. 


sure  in  any  degree  commensurate  to  its  own  size,  but  can  only  creep  about 
upon  it,  and  apply  our  diminutive  measures  to  comparatively  small  parts 
of  its  vast  surface  in  succession,  it  becomes  necessary  to  supply,  by  geo- 
metrical reasoning,  the  defect  of  our  physical  powers,  and  from  a  delicate 
and  careful  measurement  of  such  small  parts  to  conclude  the  form  and 
dimensions  of  the  whole  mass.  This  would  present  little  difl&culty,  if  we 
were  sure  the  earth  was  strictly  a  sphere,  for  the  proportion  of  the  cir- 
cumference of  a  circle  to  its  diameter  being  known  (viz.  that  of  3  1415926 
to  1  0000000),  we  have  only  to  ascertain  the  length  of  the  entire  circum- 
ference of  any  great  circle,  such  as  a  meridian,  in  miles,  feet,  or  aoy  other 
standard  units,  to  know  the  diameter  in  units  of  the  same  kind.  Now, 
the  circumference  of  the  whole  circle  is  known  as  soon  as  we  know  the 
e::^act  length  of  any  aliquot  part  of  it,  such  as  1'^  or  ^^^th  part ;  and  this, 
being  not  more  than  about  seventy  miles  in  length,  is  not  beyond  the 
limits  of  vary  exact  measurement,  and  could,  in  fact,  be  measured  (if  we 
knew  its  exact  termination  at  each  extremity)  within  a  very  few  feet,  or, 
indeed,  inches,  by  methods  presently  to  be  particularized. 

(210.)  Supposing,  then,  we  were  to  begin  measuring  with  all  due  nicety 
from  any  station,  in  the  exact  direction  of  a  meridian  and  go  measuring 
on,  till  by  some  indication  we  were  informed  that  we  had  accomplished  an 
exact  degree  from  the  point  we  set  out  from,  our  problem  would  then  be 
at  once  resolved.  It  only  remains,  therefore,  to  inquire  by  what  indica- 
tions we  can  be  sure,  1st,  that  we  have  advanced  an  exact  degree ;  and, 
2dly,  that  we  have  been  measuring  in  the  exact  direction  of  a  great  circle. 

(211.)  Now  the  earth  has  no  landmarks  on  it  to  indicate  degrees,  nor 
traces  inscribed  on  its  surface  to  guide  us  in  such  a  course.  The  compass, 
though  it  affords  a  tolerable  guide  to  the  mariner  or  the  traveller,  is  far 
too  uncertain  in  its  indications,  and  too  little  known  in  its  laws,  to  be  of 
any  use  in  such  an  operation.  We  must,  thevefore,  look  outwards,  and 
refer  our  situation  on  the  surface  of  our  globe  to  natural  marks,  external 
to  it,  and  which  are  of  equal  permanence  and  stability  with  the  earth 
itself.  Such  marks  are  afforded  by  the  stars.  By  observations  of  their 
meridian  altitudes,  performed  at  any  station,  and  from  their  known  polar 
distances,  we  conclude  the  height  of  the  pole ;  and  since  the  altitude  of 
the  pole  is  equal  to  the  latitude  of  the  place  (art.  119)  the  same  obser- 
vations give  the  Uti'.,udes  of  any  stations  where  we  may  establish  the 
requisite  instruments.  When  our  latitude  then,  is  found  to  have  dimin- 
ished a  degree,  we  knov*  ibfit,  provided  we  have  kept  to  the  meridian,  we 
have  described  one  three  hundred  and  sixtieth  part  of  the  earth's  circum- 
ference. 

(212.)  The  direction  of  tho  meridian  may  be  secured  at  every  instant 


by  the  obs( 

culties  ma^ 

tion,  yet  if 

very  siniph 

its  meridio 

(213.)  i 

ration,  the 

a  somewhai 

mounted  a 

measure  an 

quence,  pn 

we  have  n 

part,  we  tal 

observing  i 

the  case  va 

dcterminin/ 

between  th( 

(214.)  J 

every  sourc 

a  single  dej 

nearly  115 

error  which 

will  be  esp 

and  fluctuat 

make  it  esp 

we  take  car 

which  passe 

tion,  within 

and  uncertxi 

utterly  inap 

pole  to  be  r 

when  on  a  i 

If  at  one  st 

the  other  to 

the  geograpl 

must  differ  I 

(215.)  G 

ascertained, 

presently  de 

Now,  the  er 

points  cannc 


FIGURE   OF  THE   EARTH. 


121 


by  the  observations  described  in  art.  162,  188 ;  and  although  local  diffi- 
culties may  oblige  us  to  deviate  in  our  measurement  from  this  exact  direc- 
tion, yet  if  we  keep  a  strict  account  of  the  amount  of  this  deviation,  a 
very  simple  calculation  will  enable  us  to  reduce  our  observed  measure  to 
its  wie)*jVZ«o»a?  value.  .  >    ,,  <  ,  ■•      '" 

(213.)  Such  is  the  principle  of  that  most  important  geographical  ope- 
ration, the  measurement  of  an  arc  of  the  meridian.  In  its  detail,  however, 
a  somewhat  modified  course  must  be  followed.  An  observatory  cannot  be 
mounted  and  dismounted  at  every  step ;  so  that  we  cannot  identify  and 
measure  an  exact  degree  neither  more  nor  less.  But  this  is  of  no  conse- 
quence, provided  we  know  with  equal  precision  how  much,  more  or  less, 
we  have  measured.  In  place,  then,  of  measuring  this  precise  aliquot 
part,  we  take  the  more  convenient  method  of  measuring  from  one  good 
observing  station  to  another,  about  a  degree,  or  two  or  three  degrees,  as 
the  case  may  be,  or  indeed  any  determinate  angular  interval  apart,  and 
determining  by  astronomical  observation  the  precise  difference  of  latitudes 
between  the  stations.  ;    .  >  .         i 

(214.)  Again,  it  is  of  great  consequence  to  avoid  in  this  operation 
every  source  of  uncertainty,  because  an  error  committed  in  the  length  of 
a  single  degree  will  be  multiplied  360  times  in  the  circumference,  and 
nearly  115  times  in  the  diameter  of  the  earth  concluded  from  it.  Any 
error  which  may  affect  the  astronomical  determination  of  a  star's  altitude 
will  be  especially  influential.  Now,  there  is  still  too  much  uncertainty 
and  fluctuation  in  the  amount  of  refraction  at  moderate  altitudes,  not  to 
make  it  especially  desirable  to  avoid  this  source  of  error.  To  effect  this, 
we  take  care  to  select  fur  observation,  at  tue  extreme  stations,  some  star 
which  passes  through  or  near  the  zeniths  of  both.  The  amount  of  refrac- 
tion, within  a  few  degrees  of  the  zenith,  is  very  small,  and  its  fluctuations 
and  uncertainty,  in  point  of  quantity,  so  excessively  minute  as  to  bo 
utterly  inappreciable  Now,  it  is  the  same  thing  whether  we  observe  the 
pole  to  be  raised  or  depressed  a  degree,  or  the  zenith  distance  of  a  star 
when  on  a  meridian  to  have  changed  by  the  same  quantity  (fig.  art.  128). 
If  at  one  station  we  observe  any  star  to  pass  through  the  zenith,  and  at 
the  other  to  pass  one  degree  south  or  north  of  the  zenith,  we  are  sure  that 
the  geographical  latitudes,  or  the  altitudes  of  the  pole  at  the  two  stations, 
must  differ  by  the  same  amount. 

(215.)  Granting  that  the  terminal  points  of  one  degree  can  be 
ascertained,  its  lent/th  may  be  measured  by  the  methods  which  will  be 
presently  described,  as  we  have  before  remarked,  to  within  a  very  few  feet. 
Now,  the  error  which  may  be  committed  in  fixing  each  of  these  terminal 
points  cannot  exceed  that  which  may  be  committed  in  the  observation  of 


A 


I 

m 

ttt'M 

< 

"^  ^ 


wJ{ 


o 

o 

c 

09 

i 


122 


OUTLINES  OF  ASTRONOMY. 


the  zenith  distance  of  a  star  properly  situated  for  the  purpose  in  question. 
This  error,  with  proper  care,  can  hardly  exceed  half  a  second.  Supposing 
we  grant  the  possibility  of  ten  feet  of  error  in  the  length  of  each  degree 
in  a  measured  arc  of  five  degrees,  and  of  half  a  second  in  each  of  the 
zenith  distances  of  one  star,  observed  at  the  northern  and  southern  sta- 
tions, and,  lastly,  suppose  all  these  errors  to  conspire,  so  as  to  tend  all  of 
them  to  give  a  result  greater,  or  all  less,  than  the  truth,  it  will  appear, 
by  a  very  easy  proportion,  that  the  whole  amount  of  error  which  would 
be  thus  entailed  on  an  estimate  of  the  earth's  diameter,  as  concluded 
from  such  a  measure,  would  not  exceed  1147  yards,  or  about  two  thirds 
of  a  mile,  and  this  is  ample  allowance. 

(216.)  This,  however,  supposes  that  the  form  of  the  earth  is  that  of  a 
perfect  sphere,  and,  in  consequence,  the  lengths  of  its  degrees  in  all  parts 
precisely  equal.  But,  when  we  come  to  compare  the  measures  of  meri- 
dional arcs  made  in  various  parts  of  the  globe,  the  results  obtained, 
although  they  agree  sufficiently  to  show  that  the  supposition  of  a  spherical 
figure  is  not  very  remote  from  the  truth,  yet  exhibit  discordances  fiir 
greater  than  what  we  have  shown  to  be  attributable  to  error  of  observation, 
and  which  render  it  evident  that  the  hypothesis,  in  strictness  of  its  word- 
ing, is  untenable.  The  following  table  exhibits  the  lengths  of  arcs  of  the 
meridian  (astronomically  determined  as  above  described),  expressed  in 
British  standard  feet,  as  resulting  from  actual  measurement  made  with  all 
possible  care  and  precision,  by  commissioners  of  various  nations,  men  of 
the  first  eminence,  supplied  by  their  respective  governments  with  the  best 
instruments,  and  furnished  with  every  facility  which  could  tend  to  ensure 
a  successful  result  of  their  important  labours.  The  lengths  of  the  degrees 
in  the  last  column  are  derived  from  the  numbers  set  down  in  the  two 
preceding  ones  by  simple  proportion,  a  method  not  quite  exact  when  the 
arcs  are  large,  but  sufficiently  so  for  our  purpose. 


T^.i:■:: 


'fii.: 


flOUAB  OF  THE  BARTH. 


128 


Country. 

Latitude  of 
Middle  of  Are. 

Are 
mtasured. 

Mennured 

Lengtli  in 

Feet. 

Mean 
Length  of 
the  Degree 
at  the  Mid- 
dle Lntl- 
tuilo  in 
I'uet. 

Sweden*  A  B    ■ 

+  00° 

20' 

10"-0 

1° 

37' 

19"-6 

593277 

305744 

Sweden,  A 

+  00 

19 

37 

0 

67 

304 

351832 

307080 

Russia,  A 

+  58 

17 

37 

3 

35 

5-2 

1309742 

305308 

Russia,  B 

+  50 

3 

55-5 

8 

2 

28-9 

2937439 

365291 

Prussia,  B 

+  54 

58 

200 

1 

30 

290 

551073 

365420 

Denmark,  B 

+  54 

8 

13-7 

1 

31 

53-3 

559121 

305087 

Hanover,  A  B 

+  52 

32 

166 

2 

0 

57-4 

730425 

305300 

England,  A 

+  52 

35 

45 

3 

57 

131 

1442953 

304971 

Entjland,  B 

+  52 

2 

19-4 

2 

50 

23-5 

1036409 

304951 

France, A 

+  40 

52 

2 

8 

20 

0.3 

3040005 

304872 

France,  A  B 

+  44 

51 

25 

12 

22 

12-7 

4509832 

304572 

Rome,  A 

+  42 

59 

2 

9 

47 

787919 

304202 

America,  A 

+  39 

12 

« 

1 

28 

45-0 

538100 

303780 

India,  A  B 

+  10 

8 

21-5 

15 

57 

407 

5794598 

303044 

India,  A  B 

+  12 

32 

20-8 

1 

34 

50-4 

574318 

302950 

Peru,  A  B 

—   1 

31 

0-4 

3 

7 

35 

1131050 

363026 

Capo  of  Good  Hope,  A 

—33 

18 

30 

1 

13 

17-5 

445500 

364713 

Cape  of  Good  Hope,  B 

—35 

43 

200 

3 

34 

34-7 

1301993 

364060 

c 
m 


< 

o 


It  is  evident  from  a  mere  inspcotion  of  the  secoDcl  and  fifth  columns  of 
this  table,  that  the  measured  leiu/th  of  a  degree  irn^reascs  %cith  the  lati- 
tude, being  greatest  near  the  poles,  and  least  near  the  equator.  Let  us 
now  consider  what  interpretation  is  to  be  put  upon  this  conclusion,  as 
regards  the  form  of  the  earth. 

(217.)  Suppose  we  held  in  our  hands  a  model  of  the  earth  smoothly 
turned  in  wood,  it  would  be,  as  already  observed,  so  nearly  spherical,  that 
neither  by  the  eye  nor  the  touch,  unassisted  by  instruments,  could  we 
detect  any  deviation  from  that  form.  Suppose,  too,  we  were  debarred 
from  measuring  directly  across  from  surface  to  surface  in  different  direc 
tions  with  any  instrument,  by  which  we  might  at  once  ascertain  whether 

*  Tho  astronomers  by  whom  these  measurements  were  executed  were  as  fol 
lows  :  — 


Sweden,  A  B — Svanberg. 
Sweden,  A — Maupertuis. 
Russia,  A— Struve. 
Russia,  B  —  Struve,  Tenner, 
Prussia  —  Bessel,  Bayer. 
Denmari{  —Schumacher. 
Hanover  —  Gauss. 
England  —  Roy,  Kater. 
France,  A — Lacaille,  Cassini. 


France,  A  B  —  Delambre,  Mechain. 
Rome  —  Boscovich. 
America  —  Mason  and  Dixon. 
India,  1st— -Lambton. 
India,  2d  —  Lambton,  Everest. 
Peru  —  Lacondamine,  Bouguer. 
Cape  of  Good  Hope.  A— Lacaitle. 
Cape  of  Good  HopefB —  Maclear. 
— Jlttr.  Nachr.  574 


5? 

sr 


o 
C 


124 


OUTLINES   OF  ASTRONOMY. 


f    "i 

hi: 


one  diameter  were  longer  than  another ;  how,  then,  we  may  ask,  are  we 
to  ascertain  whether  it  is  a  true  sphere  or  not  ?  It  is  clear  that  we  have 
no  resource,  but  to  endeavour  to  discover,  by  some  nicer  means  than 
simple  inspection  or  feeling,  whether  the  convesity  of  its  surface  is  the 
same  in  every  part;  and  if  not,  where  it  is  greatest,  and  where  least. 
Suppose,  then,  a  thin  plate  of  metal  to  be  cut  into  a  concavity  at  its  edge, 
BO  as  exactly  to  fit  the  surface  at  A :  let  this  now  bo  removed  from  A, 
and  applied  successively  to  several  other  parts  of  the  surface,  taking  care 
to  keep  its  plane  always  on  a  great  circle  of  the  globe,  as  here  represented. 
If,  then,  we  find  any  position,  B,  in  which  the  light  can  enter  in  the 
middle  between  the  globe  and  plate,  or  any  other,  C,  where  the  latter  tilts 
by  pressure,  or  admits  the  light  ui  C.ir  its  edges,  we  are  sure  that  the  cur- 
vature of  the  surface  at  B  is  less,  and  at  C  greater,  than  at  A. 

(218.)  What  we  here  do  by  the  application  of  a  metal  plate  of  deter- 
minate length  and  curvature,  wo  do  on  the  earth  by  the  measurement  of 
a  degree  of  variation  in  the  altitude  of  the  pole.  Curvature  of  a  surface 
is  nothing  but  the  continual  deflection  of  its  tangent  from  one  fixed  direc- 
tion as  we  advance  along  it.  When,  in  the  same  measured  distance  of 
advance  we  find  the  tangent  (which  answers  to  our  horizon)  to  have 
shifted  its  position  with  respect  to  a  fixed  direction  in  space,  (such  as  the 
axis  of  the  heavens,  or  the  line  joining  the  earth's  centre  and  some  given 
star,)  m^re  in  one  part  of  the  earth's  meridian  than  in  another,  we  con- 
clude, of  necessity,  that  the  curvature  of  the  surface  at  the  former  spot  is 
greater  than  at  the  latter ;  and  vice  versd,  when,  in  order  to  produce  the 
same  change  of  horizon  with  respect  to  the  pole  (suppose  1°)  we  require 
to  travel  over  a  longer  measured  space  at  one  point  than  at  another,  we 
assign  to  that  point  a  less  curvature.  Hence  we  conclude  that  the  curva- 
ture of  a  meridional  section  of  the  earth  is  sensibly  greater  at  the  equa* 
tor  than  towards  the  poles ;  or,  in  other  words,  that  the  earth  is  not 
spherical,  but  fattened  at  the  poles,  or,  which  comes  to  the  same,  protu- 
berant at  the  equator. 


(219.) 
its  centre, 
one  degret 
meridian  i 
ling  along 
tive  direcl 
which  we 
will  the  t 
dicular  to 
aA,  2)B  a 
(at  the  poi 
degree,  an 
BD,  GE, 
about  X,  y 
of  curvati 


radii  of  ct 
mined  and 
tend  equal 
of  their  ra 
than  a  E, 
B^  than 
plumb-linet 
centre,  but 
rendered  m 


FiaURE   OF  THE  EARTH. 


136 


(219.)  Let  N  A6DEF  represent  a  meridional  section  of  the  earth,  <1 
its  centre,  and  N  A,  B  D,  G  E,  arcs  of  a  meridian,  each  corresponding  to 
one  degree  of  difference  of  latitude,  or  to  one  degree  of  variation  in  the 
meridian  altitude  of  a  star,  as  referred  to  the  horizon  of  a  spectator  travel- 
ling along  the  meridian.  Let  nN,  a  A,  bB,  dD,  gOt,  eE,  be  the  respec- 
tive directions  of  the  plumb-line  at  the  stations  N,  A,  B,  D,  G,  E,  of 
which  we  will  suppose  N  to  be  at  the  pole  and  E  at  the  equator ;  then 
will  the  tangents  to  the  surface  at  these  points  respectively  be  perpen- 
dicular to  these  directions;  and,  consequently,  if  each  pair,  viz.  nN  and 
aA,  &B  and  c^D,  ^G  and  eE,  be  prolonged  till  they  intersect  each  other 
(at  the  points  x,  y,  z),  the  angles  No;  A,  B^D,  GzE,  will  each  be  one 
degree,  and,  therefore,  all  equal;  so  that  the  small  curvilinear  arcs  NA, 
B  D,  G  E,  may  bo  regarded  as  arcs  of  circles  of  one  degree  each,  described 
about  Xf  y,  z,  as  centres.  These  are  what  in  geometry  are  called  centres 
of  curvature,  and  the  radii  a;N  or  aj  A,  yB  or  yD,  2G  or  »E,  represent 

.    ,   \'.:  ,  „   •'  .  .  -^    <--..-  Fig.  88.      >•■  •'\  I'    !■■'■    ■' 


^     I 


i  -  J; 


I 

n 

IHral 
< 

o 


anvM 

r 


o 


radii  of  curvature,  by  which  the  curvatures  at  those  points  are  deter- 
mined and  measured.  Now,  as  the  arcs  of  different  circles,  which  sub- 
tend equal  angles  at  their  respective  centres,  are  in  the  direct  proportion 
of  their  radii,  and  as  the  arc  N  A  is  greater  than  B  D,  and  that  again 
than  G  E,  it  follows  that  the  radius  Nx  must  be  greater  than  By,  and 
By  than  Ez.  Thus  it  appears  that  the  mutual  intersections  of  the 
plumb-lines  will  not,  as  in  the  sphere,  all  coincide  in  one  point  C,  the 
centre,  but  will  be  arranged  along  a  certain  curve,  xy  z  (which  will  be 
Tendered  more  evident  by  considering  a  number  of  intermediate  stations). 


f.  ' 


Wl 


I-  ' 


126  OUTLINES  OF  ASTRONOMY. 

To  this  curve  geometers  have  given  the  nonte  of  th.  evolute  of  the  cu*ve 
N  A  B  D  G  E,  from  whose  ceutres  of  curvature  it  is  coustruoted. 

(220.)  In  the  flattcDiog  of  a  round  figure  at  two  opposite  points,  and 
its  protuberance  at  points  rectangularly  situated  to  (he  former,  we  recog- 
nize the  distinguishing  feature  of  the  elliptic  form.  Accordingly,  the 
next  and  simplest  supposition  that  we  can  moke  respecting  the  nature  of 
the  meridian,  since  it  is  proved  not  to  be  a  circle,  is,  that  it  is  an  ellipse, 
or  nearly  so,  having  N  S,  the  axis  of  .ae  earth,  for  its  shorter,  and  £  F, 
the  equatorial  diameter,  for  its  longer  axis;  and  that  the  form  of  the 
earth's  surface  is  that  which  would  arise  from  making  such  a  curve  revolve 
about  its  shorter  axis  N  S.  This  agrees  well  with  the  general  course  of 
the  increase  of  the  degree  in  going  from  the  equator  to  the  pole.  In  the 
ellipse,  the  radius  of  curvature  at  £,  the  extremity  of  the  longer  axis  is 
the  least,  and  at  that  of  the  shorter  axis,  the  greatest  it  admits,  and  the 
form  of  its  evolute  agrees  with  that  here  represented.'  Assuming,  then, 
that  it  is  an  ellipse,  the  geometrical  properties  of  that  curve  enable  us  to 
assign  the  proportion  between  the  lengths  of  its  axes  which  shall  corre- 
spond to  any  proposed  rate  of  variation  in  its  curvature,  as  well  as  to  fix 
upon  their  absolute  lengths,  corresponding  to  any  assigned  length  of  the 
dogrec  in  a  given  latitude.  Without  troubling  the  reader  with  the  inves- 
tigation, (which  may  be  found  in  any  work  on  the  conic  sections,)  it  will 
be  sufficient  to  state  results  which  have  been  arrived  at  by  the  most  sys- 
tematic combinations  of  the  measured  arcs  which  have  hitherto  been  made 
by  geometers.  The  most  recent  is  that  of  Bessel',  who  by  a  combination 
of  the  ten  arcs,  marked  B  in  our  table,  has  concluded  the  dimensions  of 
the  terrestrial  spheroid  to  be  as  follows :  — 

Feet  Milea. 

Greater  or  equatorial  diameter  -  •  ■  =  41,847,192  =  79a6604 
Lesser  or  polar  diameter  .  .  .  .  =  41,707,324  =  78991 14 
Difference  of  diameters,  or  polar  compression  =  139,768  =:  '^^6-471 
Proportion  of  diameters  as  29915  to  29815. 

The  other  combination  whose  results  we  shall  Btate,  is  that  of  Mr. 
Airy'',  who  concludes  as  follows:  ,    .;       »  ,-»  ;       :    , 

'    '■■       '   "■■  ■'■■'■     ■  ''    ■  '    '"    ''''  ■         Feet.  MUes. 

Equatorial  diameter ==  41,847,426  =  7925-648 

Polar  diameter =  41,707,620  =  7899170 

Polar  compression =       139,806  s      26*478 

Proportion  of  diameters  as  299-33  to  298-33. 

'  The  dotted  lines  are  the  portions  of  the  evolute  belonginfl^  to  the  other  quadrants. 

*  Schumacher's  Asuronomische  Nachricbten,  Nos.  333,  334,  835,  438. 

*  EncyclopsBdia  Metropolitana,  "Figure  of  the  Earth"  (1831). 


These  c 
which  the 
lueuHurod 
rest,  owin; 
ceoilingly 
employing 
cordaucc  c 
confidence 
Lacuille,  ) 
unsatlsfuot 
erroneous 
Bubstitutio 
second  mc 
final  rcsuli 

(221.) 
hitherto  u 
B'flth  part, 
mind,  that 
degree  of 
ing  looselj 
100  feet; 
than  25,0 
amounts  tc 

(222.)  ' 
and  the  p 
consonant, 
reader's  pr 
that  he  sh( 
ble  concert 
ters,  and  1 
become  ne 
ment.  Ii 
widely  diff 
arrive  at  tl 

(223.)  1 
the  axis  is 
the  numeri 
ment.  W 
observed, 

'  In  those 
from  Besael' 


DIMENSIONS   OF  THB   SAHTH. 


127 


Those  ooDolusions  are  based  on  the  consideration  of  those  18  arcs,  to 
which  tlie  letter  A  is  annexed',  and  of  one  otbor  arc  of  I''  7'  oL"-l, 
uieuHured  in  Piedmont  by  IMuna  and  Carlini,  whoso  disoordanoo  with  the 
rest,  owing  to  local  causes  hereafter  to  be  explained,  arising  from  the  ox- 
ceotiingly  mountainous  nature  of  the  country,  render  the  propriety  of  so 
employing  it  very  doubtful.  Be  that  as  it  may,  the  strikingly  near  ac- 
cordaueo  of  the  two  sets  of  dimenaions  is  such  as  to  inspire  tho  greatest 
oontidcnco  in  both.  The  measurement  at  the  Gape  of  Good  Hope  by 
Lacuille,  also  used  in  this  determination,  has  always  been  regarded  as 
unsttt'sfuctory,  and  has  recently  been  demonstrated  by  Mr.  Maclear  to  be 
erroneous  to  a  cousiderablo  extent.  The  omission  of  the  former,  and  the 
substitution  for  the  latter,  of  tho  far  preferable  result  of  Mr.  Maclear's 
second  measurement  would  induce,  however,  but  a  trifling  change  in  the 
final  result. 

(221.)  Thus  we  see  that  tho  rough  diameter  of  8000  miles  wo  have 
hitherto  used,  is  rather  too  groat,  the  excess  being  about  100  miles,  or 
^ffih  part.  As  convenient  numbers  to  remember,  the  reader  may  bear  in 
mind,  that  in  our  latitude  there  are  just  as  many  thousands  of  feet  in  a 
degree  of  the  meridian  as  there  are  days  in  tho  year  (865) :  that,  speak- 
ing  loosely,  a  degree  is  about  70  British  statute  miles,  and  a  second  about 
100  feet ;  that  the  equatorial  circumference  of  the  earth  is  a  little  less 
than  25,000  miles  (24,899),  and  the  elliptioity  or  polar  flattening 
amounts  to  one  800th  part  of  the  diameter. 

(222.)  The  two  sets  of  results  above  stated  are  placed  in  juxtaposition, 
and  the  particulars  given  more  in  detail  than  may  at  first  sight  appear 
consonant,  cither  with  the  general  plan  of  this  work,  or  tho  state  of  the 
reader's  presumed  acquaintance  with  the  subject.  But  it  is  of  importance 
that  he  should  early  be  made  to  see  how,  in  astronomy,  results  in  admint- 
ble  concordance  emerge  from  data  accumulated  from  totally  different  quar- 
ters,  and  how  local  and  accidental  irregularities  in  the  data  themselves 
become  neutralized  and  obliterated  by  their  impartial  geometrical  treat- 
ment. In  the  cases  before  us,  the  modes  of  calculation  followed  are 
widely  different,  and  in  each  the  mass  of  figures  to  be  gone  through  to 
arrive  at  the  result,  enormous. 

(228.)  Tho  supposition  of  an  elliptic  form  of  the  earth's  section  through 
the  axis  is  recommended  by  its  simplicity,  and  confirmed  by  comparing 
the  numerical  results  we  have  just  set  down  with  those  of  actual  measure- 
ment. When  this  comparison  is  executed,  discordances,  it  is  true,  are 
observed,  which,  although  still  too  great  to  be  referred  to  error  of 

'  In  those  which  have  both  A  and  B,  the  numbers  used  by  Mr.  Airy  difler  slightly 
from  Bessera,  which  are  those  we  have  preferred. 


c 


o 


128 


OUTLINES   OF  ASTRONOMY. 


measurement,  are  yet  80  small,  compared  to  the  errors  which  would  result 
from  the  spherical  hypothesis,  as  completely  to  justify  our  regarding  the 
earth  as  an  ellipsoid,  and  referring  the  ohserved  deviations  to  either  local 
or,  if  general,  to  comparatively  small  causes.  j'  '     ,     ' 

(224.)  Now,  it  is  highly  satisfactory  to  find  that  the  general  elliptical 
figure  thus  •practically  proved  to  exist,  is  precisely  what  ought  theoretically 
to  result  from  the  rotation  of  the  earth  on  its  axis.  For,  let  us  suppose 
the  earth  a  sphere,  at  rest,  of  uniform  materials  throughout,  and  exter- 
nally covered  with  an  ocean  of  equal  depth  in  every  part.  Under  such 
circumstances  it  would  obviously  be  in  a  state  of  equilibrium ;  and  the 
water  on  its  surface  would  have  no  tendency  to  run  one  way  or  the  other. 
Suppose,  now,  a  quantity  of  its  materials  were  taken  from  the  polar 
regions,  and  piled  up  all  around  the  equator,  so  as  to  produce  that  dif- 
ference of  the  polar  and  equatorial  diameters  of  26  miles  which  we  know 
to  exist.  It  is  not  less  evident  that  a  mountain  ridge  or  equatorial  conti- 
nent, only,  would  be  thus  formed,  from  which  the  water  would  run  down 
the  excavated  part  at  the  poles.  However  solid  matter  might  rest  where 
it  was  placed,  the  liquid  part,  at  least,  would  not  remain  there,  any  more 
than  if  it  were  thrown  on  the  side  of  a  hill.  The  consequence  therefore, 
would  be  the  formation  of  two  great  polar  seas,  hemmed  in  all  round  by 
equatorial  land.  Now,  this  is  by  no  means  the  case  in  nature.  The 
ocean  occupies,  indifferently,  all  latitudes,  with  no  more  partiality  to  the 
polar  than  to  the  equatorial.  Since,  then,  as  we  see,  the  water  occupies 
an  elevation  above  the  centre  no  less  than  13  miles  greater  at  the  equator 
than  at  the  poles,  and  yet  manifests  no  tendency  to  leave  the  former  and 
run  towards  the  latter,  it  is  evident  that  it  must  be  retained  in  that 
situation  by  some  adequate  power.  No  such  power,  however,  would  exist 
in  the  case  we  have  supposed,  which  is  therefore  not  conformable  to 
nature.  In  other  words,  the  spherical  form  is  not  the  figure  of  equili- 
brium ;  and  therefore  the  earth  is  either  not  at  rest,  or  is  so  internally 
constituted  as  to  attract  the  water  to  its  equatorial  regions,  and  retain  it 
there.  For  the  latter  supposition  there  is  no  primd  facie  probability,  nor 
any  analogy  to  lead  us  to  such  an  idea.  The  former  is  in  accordance  with 
all  the  phenomena  of  the  apparent  diurnal  motion  of  the  heavens ;  and 
therefore,  if  it  will  furnish  us  with  the  power  in  question,  we  can  have  no 
hesitation  in  adopting  it  as  the  true  one. 

(225.)  Now,  every  body  knows  that  when  a  weight  is  whirled  round, 
it  acquires  thereby  a  tendency  to  recede  from  the  centre  of  its  motion ; 
which  is  culled  the  centrifugal  force.  A  stone  whirled  round  in  a  sling 
is  a  common  illustration ;  but  a  better,  for  our  present  purpose,  will  be  a 
pail  of  water,  suspended  by  a  cord,  and  made  to  spin  round,  while  the 


cord  hangs  ] 
maining  hori 
fugal  force  j 
press  towards 
and  forced  u] 
of  pressure  o 
state  of  eqiii 
instructive  oi 
equilibrium 
ample,  we  all 
shall  see  the 
outward  port 
time  a  perfe 
haustcd,  whe 
(226.)  Su] 
covered  with 
axis,  at  first ' 
once  in  tweni 
whose  genera 
surface  to  rec 
so  swift  as  to 
mop.  But  t 
9 


ViaUBE  OF  THE  EARTH. 


129 


Fig.  83. 


.- 


r 


cord  hangs  perpendicularly.  The  surface  of  the  water,  instead  of  re- 
maining horizontal,  will  become  concave,  as  in  the  figure.  The  centri- 
fugal force  generates  a  tendency  in  all  the  water  to  leave  the  axis,  and 
press  towards  the  circumference ;  it  is,  therefore,  urged  against  the  pail, 
and  forced  up  its  sides,  till  the  excess  of  height,  and  consequent  increase 
of  pressure  downwards,  just  counterbalances  its  centrifugal  force,  and  a 
state  of  equilibrium  is  attained.  The  experiment  is  a  very  easy  and 
instructive  one,  and  is  admirably  calculated  to  show  how  the  form  of 
equilibrium  accommodates  itself  to  varying  circumstances.  If,  for  ex- 
ample, we  allow  the  rotation  to  cease  by  degrees,  as  it  becomes  slower  we 
shall  see  the  concavity  of  the  water  regularly  diminish;  the  elevated 
outward  portion  will  descend,  and  the  depressed  central  rise,  while  all  the 
time  a  perfectly  tmooih  surface  is  maintained,  till  the  rotation  is  ex- 
hausted, when  the  water  resumes  its  horizontal  state. 

(226.)  Suppose,  then,  a  globe,  of  the  size  of  the  earth,  at  rest,  and 
covered  with  a  uniform  ocean,  were  to  be  set  in  rotation  about  a  certain 
axis,  at  first  very,  slowly,  but  by  degrees  more  rapidly,  till  it  turned  round 
once  in  twenty-four  hours;  a  centrifugal  force  would  be  thus  generated, 
whose  general  tendency  would  be  to  urge  the  water  at  every  point  of  the 
surface  to  recede  from  the  axis.  A  rotation  might,  indeed,  be  conceived 
so  swift  as  to  Jlirt  the  whole  ocean  from  the  surface,  like  water  from  a 
mop.  But  this  would  require  a  far  greater  velocity  than  what  we  now 
9 


c 
m 

IM1M 

H 


5» 


o 

Q 


180 


OUTLINES   OF  ASTRONOMY. 


u 


speak  of.  In  the  case  supposed,  the  weight  of  the  water  would  still  keep 
it  on  the  earth ;  and  the  tendency  to  recede  from  the  axis  could  only  be 
satisfied,  therefore,  by  the  water  leaving  the  poles,  and  flowing  towards 
the  equator ;  there  heaping  itself  up  in  a  ridge,  just  as  the  water  in  our 
pail  accumulates  against  the  side ;  and  being  retained  in  opposition  tu  its 
weight,  or  natural  tendency  towards  the  centre,  by  the  pressure  thu" 
caused.  This,  however,  oould  not  take  place  without  laying  dry  the 
polar  portions  of  the  land  in  the  form  of  immensely  protuberant  conti- 
nents ;  and  the  diflFerence  of  our  supposed  cases,  therefore,  is  this :  —  in 
the  former,  a  great  equatorial  continent  and  polar  seas  would  be  formed ; 
in  the  latter,  protuberant  land  would  appear  at  the  poles,  and  a  zone  of 
ocean  be  disposed  around  the  equator.  This  would  be  the  first  or  im- 
mediate efiect.  Let  us  now  see  what  would  afterwards  happen,  in  the 
two  cases,  if  things  were  allowed  to  take  their  natural  course. 

(227.)  The  sea  is  constantly  beating  on  the  land,  grinding  it  down, 
and  scattering  its  worn-off  particles  and  fragments,  in  the  state  of  mud 
and  pebbles,  over  its  bed.  Geological  facts  afford  abundant  proof  that  the 
existing  continents  have  all  of  them  undergone  this  process,  even  more 
than  once,  and  b«pn  entirely  torn  in  fragments,  or  reduced  to  powder,  and 
submerged  and  reconstructed.  Land,  in  this  view  of  the  subject,  loses 
its  attribute  of  fixity.  As  a  mass  it  might  hold  together  in  opposition  to 
forces  which  the  water  freely  obeys;  but  in  its  state  of  successivo  or 
simultaneous  degradation,  when  disseminated  through  the  water,  in  the 
state  of  sand  or  mud,  it  is  subject  to  all  the  impulses  of  that  fluid.  In 
the  lapse  of  time,  then,  the  protuberant  land  in  both  cases  would  be  des- 
troyed, and  spread  over  the  bottom  of  the  ocean,  filling  up  the  lower  parts, 
and  tending  continually  to  remodel  the  surface  of  the  solid  nucleus,  in  cor- 
respondence with  the  form  of  equilibrium  in  both  cases.  Thus,  after  a 
sufficient  lapse  of  time,  in  the  case  of  an  earth  at  rest,  the  equatorial  con- 
tinent, thus  forcibly  constructed,  would  again  be  levelled  and  transferred 
to  the  polar  excavations,  and  the  spherical  figure  be  so  at  length  restored. 
In  that  of  an  earth  in  rotation,  the  polar  protuberances  would  gradually 
be  cut  down  and  disappear,  being  transferred  to  the  equator  (as  being 
tJien  the  deepest  sea),  till  the  earth  would  assume  by  degrees  the  form  we 
observe  it  to  have  —  that  of  a  flattened  or  oblate  ellipsoid. 

(228.)  We  are  far  from  meaning  here  to  trace  the  process  by  which 
the  earth  really  assumed  its  actual  form ;  all  we  intend  is,  to  show  that 
this  is  the  form  to  which,  under  the  conditions  of  a  rotation  on  its  axis, 
it  must  tend ;  and  which  it  would  attain,  even  if  originally  and  (so  to 
speak)  perversely  constituted  otherwise. 

(229.)  But,  further,  the  dimensions  of  the  earth  and  the  time  of  its 


rotation  be 
the  centrif 
the  force  o 
fall  toward 
the  equatoi 
ported  on  : 
poles,  whe 
quence,  th( 
principle  ai 
oped  by  N( 
cians  have 
of  equilibr 
to  believe  1 
revolving  d 
is  found  to 
case.  Fro 
is,  in  fact,  i 
nearly  iden 
accurately  i 
materials  o 

(230.) 

of  the  eart 

deviation  oi 

the  origina 

solely  on  ac 

motion  of  t 

as  a  necess: 

no  other  sa 

connection, 

demonstrate 

actually  cal 

such  a  coi 

the  same  si 

and  import] 

seem  entire 

to  this  thei 

astronomy, 

(231.)  ( 

which  falls 


VARIATION   OF  TERRESTRIAL  GRAVITY. 


181 


rotation  being  known,  it  is  easy  thence  to  calculate  the  exact  amount  of 
the  centrifugal  force,'  which,  at  the  equator,  appears  to  be  ji^^th  part  of 
the  force  or  weight  by  which  all  bodies,  whether  solid  or  liquid,  tend  to 
fall  towards  the  earth.  By  this  fraction  of  its  weight,  then,  the  sea  at 
the  equator  is  lightened,  and  thereby  rendered  susceptible  of  being  sup- 
ported on  a  higher  level,  or  more  remote  from  the  the  centre  than  at  the 
poles,  where  no  such  counteracting  force  exists;  and  where,  in  conse- 
quence, the  water  may  be  considered  as  specifically  heavier.  Taking  this 
principle  as  a  guide,  and  combining  it  with  the  laws  of  gravity  (as  devel- 
oped by  Newton,  and  as  hereafter  to  be  more  fully  explained),  mathemati- 
cians have  been  enabled  to  investigate,  d  priori,  what  would  be  the  figure 
of  equilibrium  of  such  a  body,  constituted  internally  as  we  have  reason 
to  believe  the  earth  to  be ;  covered  wholly  or  partially  with  a  fluid ;  and 
revolving  uniformly  in  twenty-four  hours ;  and  the  result  of  this  inquiry 
is  found  to  agree  very  satisfactorily  with  wha^  experience  shows  to  be  the 
case.  From  their  investigations  it  appears  that  ihe  form  of  equilibrium 
is,  in  fact,  no  other  than  an  oblate  ellipsoid,  of  a  degree  of  ellipticity  very 
nearly  identical  with  what  is  observed,  and  which  would  be  no  doubt 
accurately  so,  did  we  know,  with  precision,  the  internal  constitution  and 
materials  of  the  earth. 

(230.)  The  confirmation  thus  incidentally  furnished,  of  the  hypothesis 
of  the  earth's  rotation  on  its  axis,  cannot  fail  to  strike  the  reader.  A 
deviation  of  its  figure  from  that  of  a  sphere  was  not  contemplated  among 
the  original  reasons  for  adopting  that  hypothesis,  which  was  assumed 
solely  on  account  of  the  easy  explanation  it  offers  of  ihe  apparent  diurnal 
motion  of  the  heavens.  Yet  we  see  that,  once  admitted,  it  draws  with  it, 
as  a  necessary  consequence,  this  other  remarkable  phenomenon,  of  which 
no  other  satisfactory  account  could  be  rendered.  Indeed,  so  direct  is  their 
connection,  that  the  ellipticity  of  the  ebrth's  figure  was  discovered  and 
demonstrated  by  Newton  to  be  a  consequence  of  its  rotation,  and  its  amount 
actually  calculated  by  him,  long  before  any  measurement  had  suggested 
such  a  conclusion.  As  we  advance  with  our  subject,  we  shall  find 
the  same  simple  principle  branching  out  into  a  whole  train  of  singular 
and  important  consequences,  some  obvious  enough,  others  which  at  first 
seem  entirely  unconnected  with  it,  and  which,  until  traced  by  Newton  up 
to  this  their  origin,  had  ranked  among  the  most  inscrutable  arcana  of 
astronomy,  as  well  as  among  its  grandest  phenomena. 

(231.)  Of  its  more  obvious  consequences,  we  may  here  mention  one 
which  falls  naturally  within  our  present  subject.     If  the  earth  really 


m 

tA 


D 


ir  .I* 

o 

o 


Newton's  Principia,  iii.    Prop.  19. 


182 


OUTLINES  OP  ASTRONOMY. 


revolve  on  its  axis,  this  rotation  must  generate  a  centrifugal  force  (see 
art.  225,)  the  effect  of  which  must  of  course  bo  to  counteract  a  certain 
portion  of  the  weight  of  every  body  situated  at  the  equator,  as  compared 
with  its  weight  at  the  poles,  or  in  any  intermediate  latitudes.  Now,  this 
is  fully  confirmed  by  experience.  There  is  actually  observed  to  exist  a 
difference  in  the  gravity,  or  downward  tendency,  of  one  and  the  same 
body,  when  conveyed  successively  to  stations  in  different  latitudes.  Ex- 
periments made  with  the  greatest  care,  and  in  every  accessible  part  of  the 
globe,  have  fully  demonstrated  the  fact  of  a  regular  and  progressive 
increase  in  the  weights  of  bodies  corresponding  to  the  increase  of  lati- 
tude, and  fixed  its  amount  and  the  law  of  its  progression.  From  these  it 
appears,  that  the  extreme  amount  of  this  variation  of  gravity,  or  the 
difference  between  the  equatorial  and  polar  weights  of  one  and  the  same 
mass  of  matter,  is  1  part  in  194  of  its  whole  weight,  the  rate  of  increase 
in  travelling  from  the  equator  to  the  pole  being  as  the  square  of  the  sine 
of  the  latitvde. 

(232.)  The  reader  will  here  naturally  inquire,  what  is  meant  by 
speaking  of  the  same  body  as  having  different  weights  at  different  sta- 
tions; and,  how  such  a  fact,  if  true,  can  be  ascertained.  When  we 
weigh  a  body  by  a  balance  or  a  steelyard,  we  do  but  counteract  its  weight 
by  the  equal  weight  of  another  body  under  the  very  same  circumstances ; 
and  if  both  the  body  weighed  and  its  counterpoise  be  removed  to  another 
station,  their  gravity,  if  changed  at  all,  will  be  changed  equally,  so  that 
they  will  still  contingjiflo  counterbalance  each  other.  A  difference  in  the 
intensify  of  gravitjMMuld,  therefore,  never  be  detected  by  these  means ; 
nor  is  it  in  this  sense  that  we  assert  that  a  body  weighing  194  pounds  at 
the  equator  will  weigh  195  at  the  pole.  If  counterbalanced  in  a  scale 
or  steelyard  at  the  former  station,  an  additional  pound  placed  in  one  or 
other  scale  at  the  latter  would  inevitably  sink  the  beam. 

(283.)  The  meaning  of  the  proposition  may  be  thus  explained:  — 
Conceive  a  weight  x  suspended  at  the  equator  by  a  string  without  weight 


Fig.  85. 


m->ts-^^,  '^■- 


VARIATION   OF  TERRESTRIAL  GRAVITY. 


138 


passing  over  a  pulley,  A,  and  conducted  (supposing  such  a  thing  possi- 
ble) over  other  pulleys,  such  as  B,  round  the  earth's  convexity,  till  the 
other  end  hung  down  at  the  pole,  and  there  sustained  the  weight  y.  If, 
then,  the  weights  x  and  y  were  such  as,  at  any  one  station,  equatorial  or 
polar,  would  exactly  counterpoise  each  other  on  a  balance,  or  when  sus- 
pended side  by  side  over  a  single  pulley,  they  would  not  counterbalance 
each  other  in  this  supposed  situation,  but  the  polar  weight  y  would  pre- 
ponderate \  and  to  restore  the  equipoise  the  weight  x  must  be  increased 
by  -rifth  part  cf  its  quantity. 

(234.)  The  means  by  which  this  variation  of  gravity  may  be  shown 
to  exist,  and  its  amount  measured,  are  twofold  (like  all  estimations  of 
mechanical  power,)  statical  and  dynamical.  The  former  consists  in 
putting  the  gravity  of  a  weight  in  equilibrium,  not  with  that  of  another 
weight,  but  with  a  natural  power  of  a  different  kind  not  liable  to  be 
affected  by  local  situation.  Such  a  power  is  the  elastic  force  of  a  spring. 
Let  A  B  C  be  a  strong  support  of  brass  standing  on  the  foot  A  E  D  cast 
in  one  piece  with  it,  into  which  is  let  a  smooth  plate  of  agate,  D,  which 
can  be  adjusted  to  perfect  horizontality  by  a  level.     At  0  let  a  spiral 


s^-& 


c 

I 

m 


o 

VtM 


o 

o 


spring  G  be  attached,  which  carries  at  its  lower  end  a  weight  F,  polished 
and  convex  below.  The  length  and  strength  of  the  spring  must  be  so 
adjusted  that  the  weight  F  shall  be  sustained  by  it  just  to  swing  clear  of 
contact  with  the  agate  plate  in  the  highest  latitude  at  which 'it  is  intended 
to  use  the  instrument.  Then,  if  small  weights  be  added  cautiously,  it 
may  be  made  to  descend  till  it  ju%t  grazes  the  agate,  a  contact  which  can 
bo  made  with  the  utmost  imaginable  delicacy.     Let  these  weights  be 


134 


OUTLINES  OF  iSTBONOMT. 


;;;V 


noted ;  the  weight  F  detached ;  the  spring  Gt  carefully  lifted  off  its  hook, 
and  secured,  for  travelling,  from  rust,  strain,  or  disturbance,  and  the 
whole  apparatus  conveyed  to  a  station  in  a  lower  latitude.  It  will  then 
be  found,  on  remounting  it,  that,  although  loaded  with  the  same  addi< 
tional  weig.Lts  as  before,  the  weight  F  will  no  longer  have  power  enough 
to  stretch  the  spring  to  the  extent  required  for  producing  a  similar  con- 
tact. More  weights  will  require  to  be  added ;  and  the  additional  quan- 
tity necessary  will,  it  is  evident,  measure  the  difference  of  gravity 
between  the  two  stations,  as  exerted  on  the  whole  quantity  of  pendent 
matter,  i.  e.  the  sum  of  the  weight  F  and  half  that  of  the  spiral  spring 
itself.  Granting  that  a  spiral  spring  can  be  constructed  of  such  strength 
and  dimensions  that  a  weight  of  10,000  grains,  including  its  own,  shall 
produce  an  elongation  of  10  inches  without  permanently  straining  it,* 
one  additional  grain  will  produce  a  further  extension  of  yxj^i^jjtK  of  an 
inch,  a  quantity  which  cannot  possibly  be  mistaken  in  such  a  contact  as 
that  in  question.  Thus  we  should  be  provided  with  the  means  of  mea- 
suring the  power  of  gravity  at  any  station  to  within  79^9 gth  of  its  whole 
quantity.  i  ••  . 

(235.)  The  other,  or  dynamical  process,  by  which  the  force  urging  any 
given  weight  to  the  earth  may  be  determined,  consists  in  ascertaining  the 
velocity  imparted  by  it  to  the  weight  when  suffered  to  fall  freely  in  a  given 
time,  as  one  second.  This  velocity  cannot,  indeed,  be  directly  measured : 
but  indirectly,  the  principles  of  mechanics  furnish  an  easy  and  ceuain 
means  of  deducing  it,  and,  consequently,  the  intensity  of  gravity,  by  ob- 
serving the  oscillations  of  a  pendulum.  It  is  proved  from  mechanical 
principles',  that,  if  one  and  the  same  pendulum  be  made  to  oscillate  at 
different  stations,  or  under  the  influence  of  different  forces,  and  the 
numbers  of  oscillations  made  in  the  same  tine  in  each  case  be  counted, 
the  intensities  of  the  forces  will  be  to  each  other  as  the  squares  of  the 
numbers  of  oscillations  made,  and  thus  their  proportion  becomes  known. 
For  instance,  it  is  found  that,  under  the  equator,  a  pendulum  of  a  certain 
form  and  length  makes  86,400  vibrations  in  a  mean  solar  day ;  and  that, 
when  transported  to  London,  the  same  pendulum  makes  86,535  vibrations 

*  Whether  the  process  above  described  could  ever  be  so  far  perfected  And  refined  as 
to  become  a  substitute  for  the  use  of  the  pendulum  must  depend  on  the  degree  of 
permanence  and  uniformity  of  action  of  springs,  on  the  constancy  or  variability  of  the 
effect  of  temperature  on  their  elastic  force,  on  the  possibility  of  transporting  them, 
absolutely  unaltered,  from  place  to  place,  &c.  The  great  advantages,  however, 
which  such  an  apparatus  and  mode  of  observation  would  possess,  in  point  of  conve- 
nience, cheapness,  portability,  and  expedition,  over  the  present  laborious,  tejUbus,  and 
expensive  process,  render  the  attempt  well  worth  making. 

•Newton's  Principia,  il  Prop.  24,  Cor.  3.  i)  '' '^        ^'  ' -^  '^' 


in  the  saro 
urging  the 
(86,400)'  f 
mass  of  mi 
pressure  on 
it,  that  101 
exert  there. 
(236.)  E 
the  utmost 
sible  latitw 
for  the  fra( 
poles.  Noi 
bably,  occui 
the  fact  by 
tion 


2B^ 


ex 


by  which  th 

in  itself,  bu 

to  be  distin 

if  it  will  no 

(237.)  T 

instructive 

often  exerci 

The  rotatioi 

fugal  force  | 

very  elliptic 

at  its  surfact 

then,  we  ha 

influence.     ' 

latter  with  f 

geometry,  w 

sunt,  and  cai 

(238.)  Tl 

fugal  force) 

as  Newton  1 

any  one  pari 

in  the  univei 

other.     The 

is  not  a  simp 

of  all  its  par 

the  attractio 

whether  at  : 


GRAVITY   OF   A   SPHEROID 


185 


in  tho  same  time.  Hence  ^u  conclude,  that  the  intensity  of  the  force 
urging  the  pendulum  downwards  at  the  equator  is  to  that  at  London  as 
(86,400)'  to  (86,535)^  or  as  1  to  1-00315;  or,  in  other  words,  that  a 
mass  of  matter  weighing  in  London  100,000  pounds,  exerts  tho  same 
pressure  on  the  ground,  or  the  same  effort  to  crush  a  body  placed  below 
it,  that  100,315  of  the  same  pounds  transported  to  the  equator  would 
exert  there.  i    j 

(236.)  Experiments  of  this  kind  have  been  made,  as  above  stated,  with 
the  utmost  care  and  minutest  precaution  to  ensure  exactness  in  all  acces- 
sible latitudes ;  and  their  general  and  final  result  has  been,  to  give  j-^^ 
for  the  fraction  expressing  the  difference  of  gravity  at  the  equator  and 
poles.  Now,  it  will  not  fail  to  be  noticed  by  the  reader,  and  will,  pro- 
bably, occur  to  him  as  an  objection  against  the  explanation  here  given  of 
the  fact  by  the  earth's  rotation,  that  this  differs  materially  from  the  frac- 
tion -n^-g  expressing  the  centrifugal  force  at  the  equator.  The  difference 
by  which  the  former  fraction  exceeds  the  latter  is  3^^,  a  small  quantity 
in  itself,  but  still  far  too  large,  compared  with  the  others  in  question,  not 
to  be  distinctly  accounted  for,  and  not  to  prove  fatal  to  this  explanation 
if  it  will  not  render  a  strict  account  of  it. 

(237.)  The  mode  in  which  this  difference  arises  affords  a  curious  and 
instructive  example  of  the  indirect  influence  which  mechanical  causes 
often  exercise,  and  of  which  astronomy  furnishes  innumerable  instances. 
The  rotation  of  the  earth  gives  rise  to  the  centrifugal  force ;  the  centri- 
fugal force  produces  an  ellipticity  in  the  form  of  the  earth  itself;  and  this 
very  ellipticity  of  form  modifies  its  power  of  attraction  on  bodies  placed 
at  its  surface,  and  thus  gives  rise  to  the  difference  in  question.  Here, 
then,  we  have  the  same  cause  exercising  at  once  a  direct  and  an  indirect 
influence.  The  amount  of  the  former  is  easily  calculated,  that  of  the 
latter  with  far  more  difficulty,  by  an  intricate  and  profound  application  of 
geometry,  whose  steps  we  cannot  pretend  to  trace  in  a  work  like  the  pre- 
t'jnt,  and  can  only  state  its  nature  and  result. 

(238.)  The  weight  of  a  body  (considered  as  undiminished  by  a  centri- 
fugal force)  is  the  effect  of  the  earth's  attraction  on  it.  This  attraction, 
as  Newton  has  demonstrated,  consists,  not  in  a  tendency  of  all  matter  to 
any  one  particular  centre,  but  in  a  disposition  of  every  particle  of  matter 
in  the  universe  to  press  towards,  and  if  not  opposed  to  approach  to,  every 
other.  The  attraction  of  the  earth,  then,  on  a  body  placed  on  its  surface, 
is  not  a  simple  but  a  complex  force,  resulting  from  the  separate  attractions 
of  all  its  parts.  Now,  it  is  evident,  that  if  the  earth  were  a  perfect  sphere, 
the  attraction  exerted  by  it  on  a  body  any  where  placed  on  its  surface, 
whether  at  its  equator  or  pole,  must  be  exactly  alike, — for  the  simple 


e 
m 

'"si 


rn 


o 


186 


OUTLINES  OF  ASTRONOMY. 


reason  of  the  exact  symmetry  of  the  sphere  in  every  direction.  It  ia  not 
less  evident  that,  the  earth  being  elliptical,  and  this  symmetry  or  simili- 
tude of  all  its  parts  not  existing,  the  same  result  cannot  be  expected.  A 
body  placed  at  the  equator,  and  a  similar  one  at  the  pole  of  a  flattened 
ellipsoid,  stand  in  a  different  geometrical  relation  to  the  mass  as  a  whole. 
This  difference,  without  entering  further  into  particulars,  may  be  expected 
to  draw  with  it  a  difference  in  its  forces  of  attraction  on  the  two  bodies. 
Calculation  confirms  this  idea.  It  is  a  question  of  purely  mathematical 
investigation,  and  has  been  treated  with  perfect  clearness  and  precision 
by  Newton,  Maclaurin,  Glairaut,  and  many  other  eminent  geometers ;  and 
the  result  of  their  investigations  is  to  show  that,  owing  to  the  elliptic  form 
of  the  earth  alone,  and  independent  of  the  centrifugal  force,  its  attraction 
ought  to  increase  the  weight  of  a  body  in  going  from  the  equator  to  tbe 
pole  by  almost  exactly  ^^^th  part;  which,  together  with  ^l^th  due  to 
the  centrifugal  force,  make  up  the  whole  quantity,  j^^ th,  observed. 

(239.)  Another  great  geographical  phenomenon,  which  owes  its  exis- 
tence to  the  earth's  rotation,  is  that  of  the  trade-winds.  These  mighty 
currents  in  our  atmosphere,  on  which  so  important  a  part  of  navigation 
depends,  arise  from,  1st,  the  unequal  exposure  of  the  earth's  surface  to 
the  sun's  rays,  by  which  it  is  unequally  heated  in  different  latitudes; 
and,  2dly,  from  that  general  law  in  the  constit  ion  of  all  fluids,  in  virt.ue 
of  which  they  occupy  a  larger  bulk,  and  become  specifically  lighter  when 
hot  than  when  cold.  These  causes,  combined  with  the  earth's  rotation 
from  west  to  east,  afford  an  easy  and  satisfactory  explanation  of  the  mag- 
nificent phenomena  in  question. 

(240.)  It  is  a  matter  of  observed  fact,  of  which  we  shall  give  the 
explanation  farther  on,  that  the  sun  is  constantly  vertical  over  some  one 
or  other  part  of  the  earth  between  two  parallels  of  latitude,  called  the 
tropics,  respectively  23^*^  north,  and  as  much  south  of  the  equator;  and 
that  the  whole  of  that  zone  or  belt  of  the  earth's  surface  included  between 
the  tropics,  and  equally  divided  by  tbe  equator,  is,  in  consequence  of  the 
great  altitude  attained  by  the  sun  in  its  diurnal  course,  maintained  at  a 
much  higher  temperature  than  those  regions  to  the  n'^rfh  and  south 
which  lie  nearer  th?  poles.  Now,  the  heat  thus  acquired  by  the  earth's 
surface  is  oommunicated  to  the  incumbent  air,  which  is  thereby  expanded, 
and  rendered  specifically  lighter  than  the  air  incumbent  on  the  rest  of  tbe 
globe.  It  is  therefore,  in  obedience  to  the  general  laws  of  hydrostatics, 
displaced  and  buoyed  up  from  the  surface,  and  its  place  occupied  by 
colder,  and  therefore  heavier  air,  which  glides  in,  on  both  sides,  along  tbe 
surface^  from  the  regions  beyond  the  tropics;  while  the  displaced  air,  thus 


raised  abo 
over,  as  it 
towards  tl 
down  to  SI 
a  coDtinua 
(241.) 
poles,  the 
rotation,  t 
circles  of  1 
tively  and 
because  in 
part,  it  fol 
the  region 
circle,  in  e 
found  dcfic 
the  speed  < 
rents  of  ai: 
must,  as  tl 
and  drag  i 
from  east  t 
be  simply  ] 
tive  directi 
north-easte 
(242.)  ^ 
frcv  ijeyoD 
cities  prop 
merely  a  w 
is  not  the 
gradual,  an 
friction  of 
progress  tc 
almost  imi 
after  which 
rest.     We 
ing  which 
mense  mag 
least  100,( 
any  extens 
incumbent 
(243.) 


TRADE  WINDS. 


137 


raised  above  its  due  level,  and  unsustained  by  any  lateral  pressure,  flows 
over,  as  it  wore,  and.  forms  au  upper  current  in  tbe  contrary  direction,  or 
towards  the  poles,  which,  being  cooled  in  its  course,  and  also  sucked 
down  to  supply  the  deficiency  in  the  extra-tropical  regions,  keeps  up  thus 
a  continual  circulation. 

(241.)  Since  the  earth  revolves  about  an  axis  passing  through  the 
poles,  the  equatorial  portion  of  its  surface  has  the  greatest  velocity  of 
rotation,  and  all  other  parts  less  in  the  proportion  of  the  radii  of  the 
circles  of  latitude  to  which  they  correspond.  But  as  the  air,  when  rela- 
tively and  apparel  ly  at  rest  on  any  part  of  the  earth's  surface,  is  only  so 
because  in  reality  1 1  participates  in  the  motion  of  rotation  proper  to  that 
part,  it  follows  that  when  a  mass  of  air  near  the  poles  is  transferred  to 
the  region  near  the  equator  by  any  impulse  urging  it  directly  towards  that 
circle,  in  every  point  of  its  progress  towards  its  new  situation  it  must  be 
found  deficient  in  rotatory  velocity,  and  therefore  unable  to  keep  up  with 
the  speed  of  the  new  surface  over  which  it  is  brought.  Hence,  the  cur- 
rents of  air  which  set  in  towards  the  equator  from  the  north  and  south 
must,  as  they  glide  along  the  surface,  at  the  same  time  lag,  or  hang  back, 
and  draff  upon  it  in  the  direction  opposite  to  the  earth's  rotation,  i.  e. 
from  east  to  west.  Thus  these  currents,  which  but  for  the  rotation  would 
be  simply  northerly  and  southerly  winds,  acquire,  from  this  cause,  a  rela- 
tive direction  towards  the  west,  and  assume  the  character  of  permanent 
north-easterly  and  south-easterly  winds. 

(242.)  Were  any  considerable  mass  of  air  to  be  suddenly  transferred 
fro^v  ueyond  the  topics  to  the  equator,  the  difference  of  the  rotatory  velo- 
cities proper  to  tbe  two  situations  would  be  so  great  as  to  produce  not 
merely  a  wind,  but  a  tempest  of  the  most  destructive  violence.  But  this 
is  not  the  case:  the  advance  of  the  air  from  the  north  and  south  is 
gradual,  and  all  the  while  the  earth  is  continually  acting  cu,  and  by  the 
friction  of  \ta  surface  acceleradng  its  rotatory  velocity.  Supposing  its 
progress  towards  the  equator  to  cease  at  any  point,  this  cause  would 
almost  immediately  communicate  to  it  the  deficient  motion  of  rotation, 
after  which  it  would  revolve  quietly  with  the  earth,  and  be  at  relative 
rest.  We  have  only  to  call  to  mind  the  comparative  thinness  of  the  coat- 
ing which  the  atmosphere  forms  around  the  globe  (art.  35),  and  the  im- 
mense mass  of  the  latter,  compared  with  the  former  (which  it  exceeds  at 
least  100,000,000  times),  to  appreciate  fully  the  absolute  command  of 
any  extensive  territory  of  the  earth  over  the  atmosphere  immediately 
incumbent  on  it,  in  point  of  motion. 

(243.)  It  follows  from  this,  then,  that  as  the  winds  on  both  sides  ap- 


c 

z 

m 

riM*| 


o 

Q 

S 


138 


OUTLINES   OP  ASTRONOMY. 


proach  the  equator,  their  easterly  tendency  must  diminish.'  The  lengths 
of  the  diurnal  circles  increase  very  slowly  in  the  immediate  vicinity 
of  the  equator,  and  for  several  degrees  on  either  Hide  of  it  hardly  change 
at  all.  Thus  the  friction  of  the  surface  has  more  time  to  act  in  accelera- 
ti.:g  the  velocity  of  the  air,  bringing  it  towards  a  state  of  relative  rest, 
and  diminishing  thereby  the  relative  set  of  the  currents  from  east  to  west, 
which,  on  the  other  hand,  is  feebly,  and,  at  length,  not  at  all  reinforced 
by  the  cause  which  originally  produced  it.  Arrived,  then,  at  the  equator, 
the  trades  must  be  expected  to  lose  their  easterly  character  altogether. 
But  not  only  this  but  the  northern  and  southern  currents  here  meeting 
and  opposing,  will  mutually  destroy  each  other,  leaving  only  such  pre- 
ponderancy  as  may  be  due  to  a  difference  of  local  causes  acting  in  the  two 
hemispheres,  —  which  in  some  regions  around  the  equator  may  lie  one 
way,  in  some  another. 

(244.)  The  result,  then,  must  be  the  production  of  two  great  tropical 
belts,  in  the  northern  of  which  a  constant  north-easterly,  and  in  the 
southern  a  south-easterly,  wind  must  prevail,  while  the  winds  in  the 
equatorial  belt,  which  separates  the  two  former,  should  be  comparatively 
calm  and  free  from  any  steady  prevalence  of  easterly  character.  All 
these  consequences  are  agreeable  to  observed  fact,  and  the  system  of  aerial 
currents  above  described  constitutes  in  reality  what  is  understood  by  the 
regular  trade  winds. 

(245.)  The  constant  friction  thus  produced  between  the  earth  and  at- 
mosphere in  the  regions  near  the  equator  must  (it  may  be  objected)  by 
degrees  reduce  and  at  length  destroy  the  rotation  of  the  whole  mass. 
The  laws  of  dynamics,  however,  render  such  a  consequence,  generally, 
impossible ;  and  it  is  easy  to  see,  in  the  present  case,  where  and  how  the 
compensation  takes  place.  The  heated  equatorial  air,  while  it  rises  and 
flows  over  towards  the  poles,  carries  with  it  the  rotatory  velocity  due  to 
its  equatorial  situation  into  a  higher  latitude,  where  the  earth's  surface 
has  less  motion.  Hence,  as  it  travels  northward  or  southward,  it  will 
gain  continually  more  and  more  on  the  surface  of  the  earth  in  its  diurnal 
motion,  and  assume  constantly  more  and  more  a  ivesterly  relative  direc- 
tion; and  when  at  length  it  returns  to  the  surface,  in  its  circulation, 
which  it  must  do  more  or  less  in  all  the  interval  betwe^'n  the  tropics  and 
ihQ  poles,  it  will  act  on  it  by  its  friction  as  a  powerful  south-west  wind  in 
tb  northern  hemisphere,  and  a  north-west  iu  the  southern,  and  restore  to 
it  the  impulse  taken  up  from  it  at  the  equator.     We  have  here  the  origin 

*  See  Captain  Hall's  "  Fragments  of  Voyages  and  Travels,"  2d  series,  vol.  i.  p. 
162,  where  this  is  very  distinctly,  and,  so  far  as  I  am  aware,  for  the  first  time,  reasoned 


0  le  soul 
the  almost 
fact,  nothii 
trades,  and 
tion  is  mai 

(246.)  ] 
a  knowledj 
of  the  outl 
mountain  c 
of  those  pc 
or  from  otl 
correctly  tl 
two  elemen 
assigning  i( 
dian  on  wh 
should  be  a 
this  had  be 

(247.)  1 
length  of  a 
nearest  poir 
as  the  eartfa 
cable,  and  ^ 
generalizati 
means  of  d 
being  inde] 
exactly  an  i 
station,  the 
nomically  c 

*  As  it  is  0 
the  atmospho 
such  as  mom 

It  seems  h 
portions  of  tl 
velocity  has 
lower  strata ; 
them  their  d 
been  given, 
general,  a  n 
temporary  ca 
lurfaee,  wou 
should  strike 
ter  in  mid  air 
their  combini 


ll 


DETERMINATION   OF  LATITUDES. 


189 


0^  10  south-west  and  westerly  gales  so  prevalent  in  our  latitudes,  and  of 
the  almost  universal  westerly  winds  in  the  North  Atlantic,  which  are,  in 
fact,  nothing  else  than  a  part  of  the  general  system  of  the  re-action  of  the 
trades,  and  of  the  process  by  which  the  equilibrium  of  the  earth's  mo- 
tion is  maintained  under  their  action.' 

(246.)  In  order  to  construct  a  map  or  model  of  the  earth,  and  obtain 
a  knowledge  of  the  distribution  of  sea  and  land  over  its  surface,  the  forms 
of  the  outlines  of  its  continents  and  islands,  the  courses  of  its  rivers  and 
mountain  chains,  and  the  relative  situations,  with  respect  to  tach  other, 
of  those  points  which  chiefly  interest  us,  as  centres  of  human  habitation, 
or  from  other  causes,  it  is  necessary  to  possess  the  means  of  determining 
correctly  the  situation  of  any  proposed  station  on  its  surface.  For  this 
two  elements  require  to  be  known,  the  latitude  and  longitude,  the  former 
assigning  its  distance  from  the  poles  or  the  equator,  the  latter,  the  meri- 
dian on  which  that  distance  is  to  be  reckoned.  To  these,  in  strictness, 
should  be  added,  its  height  above  the  sea  level ;  but  the  consideration  of 
this  had  better  be  deferred,  to  avoid  complicating  the  subject. 

(247.)  The  latitude  of  a  station  on  a  sphere  would  be  merely  the 
length  of  an  arc  of  the  meridian,  intercepted  between  the  station  and  the 
nearest  point  of  the  equator,  reduced  into  degrees.  (See  art.  88.)  Hut 
as  the  earth  is  elliptic,  this  mode  of  conceiving  latitudes  becomes  inappli- 
cable, and  we  are  compelled  to  resort  for  our  definition  of  latitude  to  a 
generalization  of  that  property  (art.  119,)  which  affords  the  readiest 
means  of  determining  it  by  observation,  and  which  has  the  advantage  of 
being  independent  of  the  figure  of  the  earth,  which,  after  all,  is  not 
exactly  an  ellipsoid,  or  any  known  geometrical  solid.  The  latitude  of  a 
station,  then,  is  the  altitude  of  the  elevated  pole,  and  is,  therefore,  astro- 
nomically determined  by  those  methods  already  explained  for  ascertaining 


c 

2 

m 


m 

mm 

o 

o 


'  As  it  is  our  object  merely  to  illustrate  the  mode  in  which  the  earth's  rotation  afiecta 
the  atmosphere  on  the  great  scale,  we  omit  all  consideration  of  local  periodical  winds, 
such  as  monsoons,  &c. 

It  seems  worth  inquiry,  whether  hurricanes  in  tropical  climates  may  not  arise  from 
portions  of  the  upper  currents  prematurely  diverted  downwards  before  their  relative 
velocity  has  been  sufficiently  reduced  by  friction  on,  and  gradual  mixing  with,  the 
lower  strata ;  and  so  dashing  upon  the  earth  with  that  tremendous  velocity  which  gives 
them  their  destructive  character,  and  of  which  hardly  any  rational  account  has  yet 
been  given.  But  it  by  no  means  follows  that  this  must  always  be  the  case.  In 
general,  a  rapid  transfer,  either  way,  in  latitude,  of  any  mass  of  air  which  local  or 
temporary  causes  might  carry  ahove  the  immediate  reach  of  the  friction  of  the  earth's 
iurfaee,  would  give  a  fearful  exaggeration  to  its  velocity.  Wherever  such  a  mass 
should  strike  the  earth,  a  hurricane  might  arise  ;  and  should  two  such  masses  encoun- 
ter in  mid  air,  a  tornado  of  any  degree  of  intensity  on  record  might  easily  result  from 
their  combination. 


140 


OUTLINES  OF  ASTRONOMY. 


that  important  clement.  In  consequence,  it  will  be  remembered  that,  to 
make  a  perfectly  correct  map  of  the  whole,  or  any  part  of  the  earth's 
Burfaco,  equal  differences  of  latitude  are  not  represented  by  exactly  equal 
intervals  of  surface. 

(248.)  For  the  purposes  of  gcodcsical '  measurements  and  trigonome- 
trical surveys,  an  exceedingly  correct  determination  of  the  latitudes  of  the 
most  important  stations  is  required.  For  this  purpose,  therefore,  the 
zenith  sector  (an  instrument  capable  of  great  precision)  is  most  commonly 
used  to  observe  stars  passing  the  meridian  near  the  zenith,  whose  declina- 
tions have  become  known  by  previous  long  series  of  observations  at  fixed 
observatories,  and  which  are  therefore  called  standard  or  fundamental 
stars,     llecently  a  method'  has  been  employed  with  great  success,  which 


y.:  •-r      in 


consiats  in  the  use  of  an  instrument  similar  in  every  respect  to  the  transit 
instrument,  but  having  the  plane  of  motion  of  the  telescope  not  coinci- 
dent with  the  meridian,  but  with  the  prime  vertical,  so  that  its  axis  of 
rotation  prolonged  passes  through  the  north  and  south  points  of  the 
horizon.  Let  A  B  C  D  be  the  celestial  hemisphere  projected  on  the 
horizon,  P  the  pole,  Z  the  zenith,  A  B  the  meridian,  C  D  the  prime 
vertical,  Q  R  S  part  of  the  diurnal  circle  of  a  star  passing  near  the 
zenith,  whose  polar  distance  P  B  is  but  little  greater  than  the  co-latitude 
of  the  place,  or  the  arc  P  Z,  between  the  zenith  and  pole  (art.  112.) 
Then  the  moments  of  this  star's  arrival  on  the  prime  vertical  at  Q  and  S 

'  Trt,  the  earth  ;  ltai%  (from  itia,  to  bind,)  a  joining  or  connection  (of  parts.) 
»  Devised  originally  by  Romer.    Revived  or  re-invented  by  Bessel.— il«(r.  "Naehr. 
No.  40. 


will,  if  the 
middle  wire 
quotitly  the 
passing  fror 
corresponds 
comes  know 
is  not  even  : 
the  star  pass 
even  the  ra 
be  uoglectec 
polar  distan( 
pole  can  be 
triangle  P  2 
the  place  of 
mode  of  obs( 
so  that  errc 
arc  Q  11  S  ii 
difference  K 
the  star  is  ^ 
than  itself,  c 
consequence, 
of  even  a  co 
vation  all  th 
the  transit  i 
reverniug  th< 
(249,)  1\ 
otherwisii  wi 
difficulty.     : 
the  earth,  an 
OS  in  the  cas 
to  the  heavei 
difference  iu 
mendian  (i. 
at  all  mome 
plete  diurnal 
both  describe 
divided  by  t 
observers  siti 
the  heavens 
same ;  and  t 
divided  by  t 


DETERMINATION   OF  LATITUDES. 


141 


will,  if  the  instrument  be  correctly  adjuated,  be  tiioso  of  its  crossing  the 
middle  wire  in  the  iiuld  of  view  of  the  telescope  (art.  160.)  Gonso- 
quuntly  the  interval  between  these  moments  will  be  the  time  of  the  star 
puM»ing  from  Q  to  S,  or  the  measure  of  the  diurnal  are  Q  R  S,  which 
corresponds  to  the  angle  Q  P  S  at  the  pole.  This  angle,  therefore,  be- 
comes known  hy  tfie  mere  observation  of  an  interval  of  time,  in  which  it 
is  not  even  necessary  to  know  the  error  of  the  clock,  and  in  which,  when 
the  star  passes  near  the  zenith,  so  that  the  interval  in  question  is  small, 
even  the  rate  of  the  clock,  or  its  gain  or  loss  on  true  sidereal  time,  may 
be  neglected.  Now  the  angle  Q  P  S,  or  its  half  Q  P  R,  and  P  Q  the 
polar  distance  of  the  star,  being  known,  P  Z  the  zenith  distance  of  the 
pole  can  be  calculated  by  the  resolution  of  the  right-angled  spherical 
triangle  P  Z  Q,  and  thus  the  co-latitude  (and  of  course  the  latitude)  of 
the  place  of  observation  becomes  known.  The  advantages  gained  by  this 
mode  of  observation  are,  1st,  that  no  readings  of  a  divided  arc  are  needed, 
so  that  errors  of  graduation  and  reading  are  avoided:  2dly,  that  the 
arc  Q  11  S  is  very  much  greater  than  its  versed  sine  R  Z,  so  that  the 
difference  R  Z  between  the  latitude  of  the  place  and  the  declination  of 
the  star  is  given  by  the  observation  of  a  magnitude  very  much  greater 
than  itself,  or  is,  as  it  were,  observed  on  a  greatly  enlarged  scale.  In 
consequence,  a  very  minute  error  is  entailed  on  R  Z  by  the  commission 
of  even  a  considerable  ono  in  Q  R  S :  Sdly,  that  in  this  mode  of  obser- 
vation  all  the  merely  instrumental  errors  which  alfoct  the  ordinary  use  of 
the  transit  instrument  ore  either  uninfluontial  or  eliminated  by  simply 
reversing  the  axis. 

(249.)  To  determine  the  latitude  of  a  station,  then,  is  easy.  It  is 
otherwi^  with  its  longitude,  whose  exact  determination  is  a  matter  of  more 
difficulty.  The  reason  is  this :  —  as  there  are  no  meridians  marked  upon 
the  earth,  any  more  than  parallels  of  latitude,  we  are  obliged  in  this  case, 
as  in  the  case  of  the  latitude,  to  r^ort  to  marks  external  to  the  earth,  i.  e. 
to  the  heavenly  bodies,  for  the  objects  of  our  measurement ;  but  with  this 
difference  in  the  two  cases  —  to  observers  situated  at  stations  on  the  same 
meridian  (i.  e.  differing  in  latitude)  tlie  heavens  present  different  aspects 
at  all  moments.  The  portions  of  them  which  become  visible  in  a  com- 
plete diurnal  rotation  are  not  the  same,  and  stars  which  are  common  to 
both  describe  circles  differently  inclined  to  their  horizons,  and  differently 
divided  by  them,  and  attain  different  altitudes.  On  the  other  hand,  to 
observers  situated  on  the  same  parallel  (i.  e.  differing  only  in  longitude) 
the  heavens  present  the  same  aspects.  Their  visible  portions  are  the 
same ;  and  the  same  stars  describe  circles  equally  inclined,  and  similarly 
divided  by  their  horizons,  and  attain  the  same  altitudes.    In  the  former 


m 

KMn 

■< 


O 


o 
o 

C 


142 


OUTLINES   OP  ASTRONOMY. 


i   [ 


case  there  ts,  in  the  latter  there  is  not,  any  thing  in  the  appearance  of  the 
heavens,  watched  through  a  whole  diurnal  rotation,  which  indicates  a  dif- 
ference of  locality  in  the  observer. 

(250.)  But  not  two  observers,  at  different  points  of  the  earth's  surface, 
can  have  at  the  same  instant  the  same  celestial  hemisphere  visible.  Sup- 
pose, to  fix  our  ideas,  an  observer  stationed  at  a  given  point  of  the  equator, 
and  that  at  the  moment  when  he  noticed  some  bright  star  to  be  in  his 
zenith,  and  therefore  on  his  meridian,  he  should  be  suddenly  transported, 
in  an  instant  of  time,  round  one  quarter  of  the  globe  in  a  westerly  direction, 
it  is  evident  that  he  will  no  longer  have  the  same  star  vertically  above 
him :  it  will  now  appear  to  him  to  be  just  rising,  and  he  will  have  to  wait 
six  hours  before  it  again  comes  to  his  zenith,  i.  e.  before  the  earth's  rota- 
tion from  west  to  east  carries  Mm  back  again  to  the  line  joining  the  star 
and  the  earth's  centre  from  which  he  set  out. 

(251.)  The  difference  of  the  cases,  then,  may  be  thus  stated,  so  as  to 
afford  a  key  to  the  astronomical  solution  of  the  problem  of  the  longitude. 
In  the  case  of  stations  differing  only  in  latitude,  the  same  star  comes  to 
the  meridian  at  the  same  time,  but  at  different  altitvdes.  In  that  of 
stations  differing  only  in  longitude,  it  comes  to  the  meridian  at  the  same 
alfitmfe,  but  at  different  times.  Supposing,  then,  that  an  observer  is  in 
possession  of  any  means  by  which  he  can  certainly  ascertain  the  time  of  a 
known  star's  transit  across  his  meridian,  he  knows  his  longitude ;  or  if  he 
knows  the  difference  between  its  time  of  transit  across  his  meridian  and 
across  that  of  any  other  station,  he  knows  their  difference  of  longitudes. 
For  instance,  if  the  same  star  pass  the  meridian  of  a  place  A  at  a  certain 
moment,  and  that  of  B  exactly  one  hour  of  sidereal  time,  or  one  twenty- 
fourth  part  of  the  earth's  diurnal  period,  later,  then  the  difference  of  lon- 
gitude between  A  and  B  is  one  hour  of  time  or  15°  of  arc,  and  B  is  so 
much  west  of  A. 

(252.)  In  order  to  a  perfectly  clear  understanding  of  the  principle  on 
which  the  problem  of  finding  the  longitude  by  astronomical  observations 
is  resolved,  the  reader  must  learn  to  distinguish  between  time,  in  the 
abstract,  as  common  to  the  whole  universe,  and  therefore  reckoned  from 
an  epoch  independent  of  local  situation,  and  local  time,  which  reckons,  at 
each  particular  place,  from  an  epoch,  or  initial  instant,  determined  by  local 
convenience.  Of  time  reckoned  in  the  former,  or  abstract  manner,  wc 
have  an  example  in  what  we  have  before  defined  as  equinoctial  time,  which 
dates  from  an  epoch  determined  by  the  sun's  motion  among  the  stars. 
Of  the  latter,  or  local  reckoning,  we  have  instances  in  every  sidereal  clock  in 
an  observatory,  and  in  every  town  clock  for  common  use.  Every  astrono- 
mer regulates,  or  aims  at  regulating,  his  sidereal  clock,  so  that  it  shall 


indicate  0 
is  on  the  i 
which  is, 
say  that  a 
unless  we 
tains.     Ji 
reckoning, 
times  thro 
ticular  j[>/( 
we  date  ai 
particulari: 
by  equinoc 
(253.)  ' 
ing  the  me 
Each  of  thi 
with  respec 
times  of  th( 
nox  passed, 
and  if  it  dit 
or  disagree 
whether  hij 
diurnal  pei 
although  hi 
go  truly, 
termed),  h( 
times  eorref 
ble  operatic 
tion,  howev 
comes  to  t 
consulted, 
(254.) 
each,  indep 
sidereal  ti 
could  be  ta 
of  the  othc 
difference 
nox,  or  by 
other  wordf 
minutes,  ai 

(255.) 
from  place 


DETERMINATION   OF   LONGITUDES. 


143 


indicate  O""  O"  0',when  a  certain  point  in  the  heavens,  called  the  equinox, 
is  on  the  meridian  of  his  station.  This  ia  the  cjpoch  of  his  sidereal  time ; 
which  is,  therefore,  entirely  a  local  reckoning.  It  gives  no  information  to 
say  that  an  event  happened  at  such  i>nd  such  an  hour  of  sidereal  time, 
unless  we  particularize  the  station  to  which  the  sidereal  time  meant  apper- 
tains. Just  so  it  is~with  mean  or  common  time.  This  is  also  a  local 
reckoning,  having  for  its  epoch  mean  noon,  or  the  average  of  all  the 
times  throughout  the  3'ear,  when  the  sun  is  on  the  meridian  of  that  par- 
ticular place  to  which  it  belongs;  and,  therefore,  in  like  manner,  when 
we  date  any  event  by  mean  time,  it  is  necessary  to  name  the  place,  or 
particularize  what  mean  time  we  intend.  On  the  other  hand,  a  date 
by  equinoctial  time  is  absolute,  and  requires  no  such  explanatory  addition. 

(253.)  The  astronomer  sets  and  regulates  his  sidereal  clock  by  observ- 
ing the  meridian  passages  of  the  more  conspicuous  and  well-known  stars. 
Each  of  these  holds  in  the  heavens  a  certain  determinate  and  known  place 
with  respect  to  that  imaginary  point  called  the  equinox,  and  by  noting  the 
times  of  their  passage  in  succession  by  his  clock  he  knows  when  the  equi- 
nox passed.  At  that  moment  his  clock  ought  to  have  marked  0"  0""  0' ; 
and  if  it  did  not,  he  knows  and  can  correct  its  error,  and  by  the  agreement 
or  disagreement  of  the  errors  assigned  by  each  star  he  can  ascertain 
whether  his  clock  is  correctly  regulated  to  go  twenty-fofir  hours  in  one 
diurnal  period,  and  if  not,  can  ascertain  and  allow  for  its  rate.  Thus, 
although  his  clock  may  not,  and  indeed  cannot,  either  be  set  correctly,  or 
go  truly,  yet  by  applying  its  error  and  rate  (as  they  are  technically 
termed),  he  can  correct  its  indications,  and  ascertain  the  exact  sidereal 
times  corresponding  to  them,  and  proper  to  his  locality.  This  indispensa- 
ble operation  is  called  getting  his  local  time.  For  simplicity  of  explana- 
tion, however,  we  shall  suppose  the  clock  a  perfect  instrument ;  or,  which 
comes  to  the  same  thiiii^,  its  error  and  rate  applied  at  every  moment  it  is 
consulted,  and  included  in  its  indications. 

(254.)  Suppose,  now,  of  two  observers,  at  distant  stations,  A  and  B, 
each,  independently  of  the  other,  to  set  and  regulate  his  clock  to  the  true 
sidereal  time  of  his  station.  It  is  evident  that  if  one  of  these  clocks 
could  be  taken  up  without  deranging  its  going,  and  set  down  by  the  side 
of  the  other,  they  would  be  found,  on  comparison,  to  diflPer  by  the  exact 
difference  of  their  local  epochs ;  that  is,  by  the  time  occupied  by  the  equi- 
nox, or  by  any  star,  in  passing  from  the  meridian  of  A  to  that  of  B ;  in 
other  words,  by  their  difference  of  longitude,  expressed  in  sidereal  hours, 
minutes,  and  seconds. 

(255.)  A  pendulum  clock  cannot  be  thus  taken  up  and  transported 
from  place  to  place  without  derangement,  but  a  chronometer  may.     Sup- 


'\. 


5^ 
fll  I 

-< 


n 


m 

c 

(9 


144 


OUTLINES  OF  ASTRONOMY. 


t  ^ 


'fi:: 


pose,  then,  the  observer  at  B  to  use  a  chronometer  instead  of  a  clock,  he 
may,  by  bodily  transfer  of  the  instrument  to  the  other  station,  procure  a 
direct  comparison  of  sidereal  times,  and  thus  obtain  his  longitude  from  \. 
And  even  if  he  employ  a  clock,  yet  by  comparing  it  first  with  a  good 
chronometer,  and  then  transferring  the  latter  instrument  for  comparison 
with  the  other  clock,  the  same  end  will  be  accomplished,  provided  the 
going  of  the  chronometer  can  be  depended  on. 

(256.)  Were  chronometers  perfect,  nothing  more  complete  and  conve- 
nient than  this  mode  of  ascertaining  differences  of  longitude  could  be 
desired.  An  observer,  provided  with  such  an  instrument,  and  with  a  por- 
table transit,  or  some  equivalent  method  of  determining  the  local  time  at 
any  given  station,  might,  by  journeying  from  place  to  place,  and  observing 
the  meridian  passages  of  stars  at  each,  (taking  care  not  to  alter  his  chro- 
nometer, or  let  it  run  down,)  ascertain  their  differences  of  longitude  with 
any  required  precision.  In  this  case,  the  same  time-keeper  being  used  at 
every  station,  if,  at  one  of  them.  A,  it  mark  true  sidereal  time,  at  any 
other,  B,  it  will  be  just  so  much  sidereal  time  in  error  as  the  difference  of 
longitudes  of  A  and  B  is  equivalent  to :  in  other  words,  the  longitude  of 
B  from  A  will  appear  as  the  error  of  the  time-keeper  on  the  local  time  of 
B.  If  he  travel  westward,  then  his  chronometer  will  appear  continually 
to  gain,  although  it  really  goes  correctly.  Suppose,  for  instance,  he  set 
out  from  A,  when  the  equinox  was  on  the  meridian,  or  his  chronometer  at 
0",  and  in  twenty-four  hours  (sid.  time)  had  travelled  15**  westward  to  B. 
At  the  moment  of  arrival  there,  his  chronometer  will  again  point  to  0" ; 
but  the  equinox  will  be,  not  on  his  new  meridian,  but  on  that  of  A,  and 
he  must  wait  one  hour  more  for  its  arrival  at  that  of  B.  When  it  does  ar- 
rive there,  then  his  watch  will  point  not  to  0"  but  to  l"",  and  will  therefore 
be  1^  fast  on  the  local  time  of  B.  If  he  travel  eastward,  the  reverse  will 
happen. 

(257.)  Suppose  an  observer  now  to  set  out  from  any  station  as  above 
described,  and  constantly  travelling  westward  to  make  a  tour  of  the  globe, 
and  return  to  the  point  he  set  out  from.  A  singular  consequence  will 
happen :  he  will  have  lost  a  day  in  his  reckoning  of  time.  He  will  enter 
the  day  of  his  arrival  in  his  diary,  as  Monday,  for  instance,  when,  in  fact, 
it  is  Tuesday.  The  reason  is  obvious.  Days  and  nights  are  caused  by  the 
alternate  appearance  of  the  sun  and  stars,  as  the  rotation  of  the  earth  car- 
ries the  spectator  round  to  view  them  in  succession.  So  many  turns  as 
he  makes  absolutely  round  the  centre,  so  often  will  he  pass  through  the 
earth's  shadow,  and  emerge  into  light,  and  so  many  nights  and  days  will 
he  experience.  But  if  he  travel  once  round  the  globe  in  the  direction  of 
its  motion,  he  will,  on  his  arrival,  have  really  made  one  turn  more  round 


its  centre; 
remained  u 
have  witnes 
less,  than  ij 
round.    As 
direction  of 
him  to  lose 
it,  to  gain 
latter,  short 
actually  haf 
happen  thai 
in  their  usui 
settlers  arri^ 
which  may 
with  each  ot 
the  disputes 
recourse  to  t 
(258.)  IT 
though  grea 
artists,  is  yei 
However  su 
few  hours,  oi 
error  and  ace 
ance  on  oven 
by  carrying 
besides  the 
the  great  anc 
tioh  of  longi 
fore,  to  resor 
a  knowledge 
tiun,  as  a  ce 
local  time  at 
thus  the  long 
tral  point. 

(259.)  Th 
can  be  accom 
telegraphic  si 
provided  with 
and  let  us  firs 
regulated,  ant 
be  made  at  A 
10 


DETERMINATION  OF   LON'^ITUDES. 


145 


its  centre ;  and  if  in  the  opposite  direction,  one  turn  less  than  if  he  had 
remained  upon  one  point  of  its  surface :  in  the  former  case,  then,  he  will 
have  witnessed  one  alternation  of  day  and  night  more,  in  the  latter  one 
less,  than  if  he  had  trusted  to  the  rotation  of  the  earth  alone  to  carry  him 
round.  As  the  earth  revolves  from  west  to  east,  it  follows  that  a  wcstwutd 
direction  of  his  journey,  by  which  he  counteracts  its  rotation,  will  cause 
him  to  lose  a  day,  and  an  eastward  direction,  by  which  he  conspires  with 
it,  to  gain  one.  In  the  former  case,  all  his  days  will  be  longer ;  in  the 
latter,  shorter  than  those  of  a  stationary  observer.  This  contingency  has 
actually  happened  to  circumnavigators.  Hence,  also,  it  must  necessarily 
happen  that  distant  settlements,  on  the  same  meridian,  will  differ  a  day 
in  their  usual  reckoning  of  time,  according  as  they  have  been  colonized  by 
settlers  arriving  in  an  eastward  or  in  a  westward  direction, — a  circumstance 
which  may  produce  strange  confusion  when  they  come  to  communicate 
with  each  other.  The  only  mode  of  correcting  th^  ambiguity,  and  settling 
the  disputes  which  such  a  difference  may  give  rise  to,  consists  in  having 
recourse  to  the  equinoctial  date,  which  can  never  be  ambiguous. 

(258.)  Unfortunately  for  geography  and  navigation,  the  chronometer, 
though  greatly  and  indeed  wonderfully  improved  by  the  skill  of  modern 
artists,  is  yet  far  too  imperfect  an  instrument  to  be  relied  on  implicitly. 
However  such  an  instrument  may  preserve  its  uniformity  of  rate  for  a 
few  hours,  or  even  days,  yet  in  long  absences  from  home  the  chances  of 
error  and  accident  become  so  multiplied,  as  to  destroy  all  security  of  reli- 
ance on  oven  the  best.  To  a  certain  extent  this  may,  indeed,  be  remedied 
by  carrying  out  several,  and  using  them  as  checks  on  each  other ;  but, 
besides  the  expense  and  trouble,  this  is  only  a  palliation  of  the  evil  — 
the  great  and  fundamental, —  as  it  is  the  only  one  to  which  the  dctcrmina- 
iiou  of  longitudes  hy  time-heepers  is  liable.  It  becomes  necessary,  there- 
fore, to  resort  to  other  means  of  communicating  from  one  station  to  another 
a  knowledge  of  its  local  time,  or  of  propagating  from  some  principal  sta- 
tion, as  a  centre,  its  local  time  as  a  universal  stiindard  with  which  the 
local  time  at  any  other,  however  sHuated,  may  be  at  once  compared,  and 
thus  the  longitudes  of  all  places  be  referred  to  the  meridian  of  such  cen- 
tral point. 

(259.)  The  simplest  and  mos^  accurate  method  by  which  this  object 
can  be  accomplished,  when  circumstances  admit  of  its  adoption,  is  that  by 
telegraphic  signal.  Let  A  and  B  be  two  observatories,  or  other  stations, 
provided  with  accurate  means  of  determining  their  respective  local  times, 
and  let  us  first  suppose  them  visible  from  each  other.  Their  clocks  being 
regulated,  and  their  errors  and  rates  nscertained  and  applied,  let  a  signal 
be  made  at  A,  of  some  sudden  and  definite  kind,  such  as  the  flash  of  gun- 
10 


I 

m 

rat*) 


o 


146 


OUTLINES   OF  ASTRONOMY. 


I- 

I; 

h 


h:i 


powder,  the  txplosion  of  a  rocket,  the  sudden  extinction  of  a  bright  light, 
or  any  other  which  admits  of  no  mistake,  and  can  be  seen  at  great  dis- 
tances. The  moment  of  the  signal  being  made  must  be  noted  by  each 
observer  at  his  respective  clock  or  watch,  as  if  it  were  the  transit  of  a  star, 
or  other  astronomical  phenomenon,  and  the  error  and  rate  of  the  clock  at 
each  station  being  applied,  the  local  time  of  the  signal  at  each  is  deter- 
mined. Consequently,  when  the  observers  communicate  their  observations 
of  the  signal  to  each  other,  since  (owing  to  the  almost  instantaneous 
transmission  of  light)  it  must  have  been  seen  at  the  same  absolute  instant 
by  both,  the  difference  of  their  local  times,  and  t^erefore  of  their  longitudes, 
becomes  known.  For  example,  at  A  the  signal  is  observed  to  Nappen  at 
b^  0»  0*  sill,  time  at  A,  as  obtained  by  applying  the  error  and  rf»^^  to  the 
time  shown  by  the  clock  at  A,  when  the  signal  was  seen  there.  At  B  the 
same  signal  was  seen  at  5^  4"  0",  sid.  time  at  B,  similarly  deduced  from 
the  time  noted  by  the  clock  at  B,  by  applying  its  er  :r  and  rate.  Conse- 
quently, the  difference  c^  their  local  epochs  is  4"  0*,  which  is  also  their 
difference  of  longitudes  in  time,  or  1°  0'  0"  in  hour  angle. 

(260.)  The  accuracy  of  the  final  determination  may  be  increased  by 
making  and  observing  c^^^veral  signals  at  stated  intervals,  each  of  which 
affords  a  comparison  of  times,  and  the  mean  of  all  which  is,  of  course, 
more  to  be  depended  on  than  the  result  of  any  single  comparison.  By 
this  means,  the  error  introduced  by  the  comparison  of  clocks  may  be  re- 
garded as  altogether  destroyed. 

(261.)  The  distances  at  which  signals  can  be  rendered  visible  must  of 
course  depend  on  the  nature  of  the  interposed  country.  Over  sea  the 
explosioa  of  rockets  may  easily  be  seen  at  fifty  or  sixty  miles ;  and  in 
mountainous  countries  the  flash  of  gunpowder  in  an  open  spoon  may  be 
seen,  if  a  proper  station  be  chosen  for  its  exhibition,  at  much  greater 
distances. 

(262.)  When  the  direct  light  of  the  flash  can  no  longer  be  perceived, 
either  owing  to  the  convexity  of  the  interposed  segment  of  the  earth,  or 
to  intervening  obstacles,  the  sudden  illumination  cast  on  the  under  surface 
of  the  clouds  by  the  explosion  of  considerable  quantities  of  powder  may 
often  be  observed  with  success ;  and  in  this  way  signals  have  been  made 
at  very  much  greater  distances.  Whatever  means  can  be  devised  of  exci- 
ting in  two  distant  observers  the  same  sensation,  whether  of  sound,  light, 
or  visible  mction,  at  precisely  the  same  instant  of  lime,  may  be  employed 
as  a  longitude  signal.  Wherever,  for  instance,  an  unbroken  line  of  elec- 
tro-telegraphic connection  has  been,  or  hereafter  may  be,  established,  the 
means  exist  of  making  as  complete  a  comparison  of  clocks  or  watches  as 
if  they  stood  side  b^  side,  so  that  no  method  more  complete  for  the  deter- 


mination 
longitud( 
delphia, 
nomers  a 

(263.; 
interval 
.signals  t( 
provided 
they  are 
would  b( 
for  the 
any  dista 

(264.) 
stations, 
the  local 
destined 
stations, 
are  fired 
with  a  ch 
and  chroD 
that  the  s 
£ ;  and  8( 

'  '  i 


the  oxocks 
be  made  ai 
difference  1 
a  short  int 
observed  b 
chronomet 
the  clock  { 
A  and  ohr 
the  interm 
known  rat 
purposely  i 


DETERMINATION   OF  LONGITUDES. 


14T 


it  light, 
•eat  dis- 
by  each 
if  a  star, 
clock  at 
is  deter- 

• 

jrvations 
Dta.neous 
';  instant 
QgitudeB, 
appen  at 
>V  to  the 
At  B  the 
ced  from 
Consc- 
ilso  their 

'eased  by 
of  which 
)f  course, 
on.  By 
ay  be  re- 

I  must  of 
sea  the 
and  in 
may  be 

pi  greater 


)erceived, 
earth,  or 
3r  surface 
fder  may 
een  made 
i  of  exci- 
nd,  light, 
employed 
e  of  elec- 
shed,  the 
atcbes  as 
the  deter- 


mination of  differences  of  longitude  can  be  desired.  The  differences  of 
longitude  between  the  observatories  of  New  York,  Washington,  and  Phila- 
delphia, have  been  very  recently  determined  in  this  manner  by  the  astro- 
nomers at  those  observfltories. 

(263.)  Where  no  such  electric  communication  exists,  however,  the 
interval  between  observing  stations  may  be  increased  by  causing  the 
signals  to  be  made  not  at  one  of  them,  but  at  an  intermediate  point;  for, 
provided  they  are  seen  by  both  parties,  it  is  a  matter  of  indifference  where 
they  are  exhibited.  Still  the  interval  which  could  be  thus  embraced 
would  be  very  limited,  and  the  method  in  consequence  of  little  use,  but 
for  the  following  ingenious  contrivance,  by  which  it  can  be  extended  to 
any  distance,  and  carried  over  any  tract  of  country,  however  difficult. 

(264.)  This  contrivance  consists  in  establishing,  between  the  extreme 
stations,  whose  difference  of  longitude  is  to  be  ascertained,  and  at  which 
the  local  times  are  observed,  a  chain  of  intermediate  stations,  alternately 
destined  for  signals  and  for  observers.  Thus,  let  A  and  Z  be  the  extreme 
stations.  At  B  let  a  signal  station  be  established,  at  which  rockets,  &c. 
are  fired  at  stated  intervals.  At  C  let  an  observer  be  placed,  provided 
with  a  chronometer ;  at  D,  another  signal  station ;  at  E,  another  observer 
and  chronometer ;  till  the  whole  line  is  occupied  by  stations  so  arranged, 
that  the  signal  at  B  can  be  seen  from  A  and  C;  thoF  at  D,  from  C  and 
£ ;  and  so  on.     Matters  being  thus  arranged,  and  the  errors  and  rates  of 


Fig.  38. 


P 


« 


I 
I 


B 


D       E      IP 


the  CiOcks  at  A  and  Z  ascertained  by  astronomical  observation,  let  a  signal 
be  made  at  B,  and  observed  at  A  and  C,  &nd  the  times  noted.  Thus  the 
difference  between  A's  clock  and  C's  chronometer  becomes  known.  After 
a  short  interval  (five  minutes  for  instance)  let  a  signal  be  made  at  D,  and 
observed  by  C  and  E.  Then  will  the  difference  between  their  respective 
chronometers  be  determined ;  and  the  difference  between  the  former  and 
the  clock  at  A  being  already  ascertained,  the  difference  between  the  clock 
A  and  chronometer  E  is  therefore  known.  This,  however,  supposes  that 
the  intermediate  chronometer  C  has  kept  true  sidereal  time,  or  at  least  a 
known  rate,  in  the  interval  between  the  signals.  Now  this  interval  is 
purposely  made  so  very  short,  that  no  instrument  of  any  pretensions  to 


c 
m 

•CMp} 
-< 


o 

Cm? 


148 


OUTLINES  OP  ASTRONOMY. 


character  can  possibly  produce  an  appreciable  amount  of  error  in  its  lapse 
by  deviations  from  its  usual  rate.  Thus  the  time  propagated  from  A  to 
C  may  be  considered  as  handed  over,  without  gain  or  loss  (save  from  error 
of  observation),  to  E.  Similarly,  by  the  signal  made  at  F,  and  observed 
at  E  and  Z,  the  time  so  transmitted  to  E  is  forwarded  on  to  Z ;  and  thus 
at  length  the  clocks  at  A  and  Z  are  compared.  The  process  may  bo 
repeated  as  often  as  is  necessary  to  destroy  error  by  a  mean  of  results ; 
and  when  the  line  of  stations  is  numerous,  by  keeping  up  a  succes- 
sion of  signals,  so  as  to  allow  each  observer  to  note  alternately  those  on 
either  side,  which  is  easily  pre-arranged,  many  comparisons  may  ':8  kept 
running  along  the  line  at  once,  by  which  time  is  saved,  and  other  advan- 
tages obtained.'  In  important  cases  the  process  is  usually  repeated  on 
several  nights  in  succession. 

(265.)  In  place  of  artificial  signals,  natural  ones,  vthttn  they  occur 
iufficiently  definite  for  observation,  may  be  equally  employed.  In  a  clear 
night  the  number  of  those  singular  meteors,  called  shooting  stars,  which 
may  be  observed,  is  often  very  great,  especially  on  the  9th  and  10th  of 
August,  and  some  other  days,  as  November  12  and  18;  and  as  they  arc 
sudden  in  their  appearance  and  disappearance,  and  from  the  great  height 
at  which  they  have  been  ascertained  to  take  place  are  visible  over  exten- 
sive regions  of  the  earth's  surface,  there  is  no  doubt  that  they  may  be 
resorted  to  with  advantage,  by  previous  concert  and  agreement  between 
distant  observers  to  watch  and  note  them.'  Thosfi  sudden  disturbances 
of  the  magnetic  needle,  to  which  the  name  of  magnetic  shocks  has  been 
given,  have  been  satisfactorily  ascertained  to  be,  very  often  at  least, 
simultaneous  over  whole  continents,  and  in  some,  perhaps,  over  the  whole 
globe.  These,  if  observed  at  magnetic  observatories  with  precise  atten- 
tion to  astronomical  time,  may  become  the  means  of  determining  their 
difierences  of  longitude  with  more  precision,  possibly,  than  by  any  other 
method,  if  a  sufficient  number  of  remarkable  shocks  be  observed  to 
ascertain  their  identity,  about  which  the  intervals  of  time  between  their 
occurrence  (esLactly  alike  at  both  stations)  will  leave  no  doubt. 


*  For  a  complete  account  of  this  method,  and  the  mode  of  deducing  the  most  advan- 
tageous result  from  a  combination  of  all  the  observations,  see  a  paper  on  the  difTerence 
of  longitudes  of  Greenwich  and  Paris,  Phil.  Trans.  1826 ;  by  the  Author  of  this 
volume. 

*  This  idea  was  first  suggested  by  the  'ate  Dr.  Maskelyne,  to  whom,  however,  the 
practically  useful  fact  of  their  periodic  recurrence  was  unknown.  Mr.  Cooper  has  thus 
employed  the  meteors  of  the  10th  and  12th  August,  1847,  to  determine  the  difference 
uf  longitudes  of  Markree  and  Mount  Eagle,  in  Ireland.  Those  of  the  same  epoch  have 
also  been  used  in  Germany  for  ascertaining  the  longitudes  of  several  stations,  and  with 
very  satisfactory  results. 


LUNAR   METHOD. 


149 


(266.)  Another  species  of  natural  signal,  visible  at  once  over  a  whole 
terrestrial  hemisphere,  is  aifordcd  by  the  eclipses  of  Jupiter's  satellites,  of 
which  we  shall  speak  more  at  large  when  we  come  to  treat  of  those  bodies. 
Every  such  eclipse  is  an  event  which  possesses  one  great  advantage  in  its 
applicability  to  the  purpose  in  question,  viz.  that  the  time  of  its  happen- 
ing, at  any  fixed  station,  such  as  Greenwich,  can  he  predicted  from  a  long 
course  of  previous  recorded  observation  and  calculation  thereon  founded, 
and  that  this  prediction  is  sufficiently  precise  and  certain,  to  stand  in  the 
place  of  a  corresponding  observation.  So  that  an  observer  at  any  other 
station  wherever,  who  shall  have  observed  one  or  more  of  these  eclipses, 
and  ascertained  his  local  time,  instead  of  waiting  for  a  communication 
with  Greenwich,  to  inform  him  at  what  moment  the  ecUpse  took  place 
there,  may  use  the  predicted  Greenwich  time  instend,  and  thence,  at 
once,  and  on  the  spot,  determine  his  longitude.  This  mode  of  ascertain- 
ing longitudes  is,  however,  as  will  hereafter  appear,  not  susceptible  of 
great  exactness,  and  should  only  be  resorted  to  when  others  cannot  bo 
had.  The  nature  of  the  ^^^scrvution  also  is  such  that  it  cannot  be  made 
at  sea';  so  that,  however  u,.^i\il  lo  the  geographer,  it  is  of  no  advantage 
to  navigation. 

(267.)  But  such  phenomena  as  these  are  o^'  only  occasional  occurrence; 
and  in  their  intervals,  and  when  cut  off  from  all  communication  with  any 
fixed  station,  it  is  indispensable  to  possess  some  means  of  determining 
longitudes,  on  which  not  only  the  geographer  may  rely  for  a  knowledge 
of  the  exact  position  of  important  stations  on  land  in  remote  regions,  but 
on  which  the  navigator  can  securely  stake,  at  every  instant  of  his  adven- 
turous course,  the  lives  of  himself  and  comrades,  the  interests  of  his 
country,  and  the  fortunes  of  his  employers.  Such  a  method  is  afiforded 
by  Lunar  Observations.  Jhough  we  have  not  yet  introduced  the 
reader  to  the  phenomena  of  the  moon's  motion,  this  will  not  prevent  us 
from  giving  here  the  exposition  of  the  principle  of  the  lunar  method ;  on 
the  contrary,  it  will  be  highly  advantageous  to  do  so,  since  by  this  course 
we  shall  have  to  deal  with  the  naked  principle,  apart  from  all  the  peculiar 
sources  of  difficulty  with  which  the  lunar  theory  is  encumbered,  but 

'  To  accomplish  this  is  still  a  desideratum.  Observing  chairs,  suspended  with  stu- 
dious precaution  for  ensuring  freedom  of  motion,  have  been  resorted  to,  under  the  vain 
hope  of  mitigating  the  eflTect  of  the  ship's  oscillation.  The  opposite  course  seems  more 
promising,  viz.  to  merely  deaden  the  motion  by  a  somewhat  stiff  suspension  (as  by  a 
coarse  and  rough  cable),  and  by  friction  strings  attached  to  weights  running  through 
loops  (not  pulleys)  fixed  in  the  wood-work  of  the  vessel.  At  least,  such  means  have 
been  found  by  the  author  of  singular  efiicacy  in  increasing  personal  comfort  in  the  sus- 
pension of  a  cot.        -       -I  


a 

I 

P 


o 


150 


OUTLINES  OF  ASTRONOMT. 


I  '■ 


which  are,  in  fact,  completely  extraneous  to  the  principle  of  its  applica- 
tion to  the  problem  of  the  longitudes,  which  is  quite  elementary. 

(268.)  If  there  were  in  the  heavens  a  clock  furnished  with  a  dial-plate 
and  hands,  which  always  marked  Greenwich  time,  the  longitude  of  any 
ctation  would  be  at  once  determined,  so  soon  as  the  local  time  was  known, 
by  comparing  it  with  this  clock.  Now,  the  offices  of  the  dial-plate  and 
hands  of  a  clock  are  these :  —  the  foruer  carries  a  set  of  marks  upon  it, 
whose  position  is  known;  the  latter,  by  passing  over  and  among  these 
marks,  inform  us,  by  the  place  it  holds  with  respect  to  them,  what  it  is 
o'clock,  or  what  time  has  elapsed  since  a  certain  moment  when  it  stood  at 
one  particular  spot. 

(269.)  In  a  clock  the  marks  on  the  dial-plate  are  unlfonuly  distributed 
all  around  the  circumference  of  a  circle,  whose  centre  is  that  on  which  the 
hands  revolve  with  a  uniform  motion.  But  it  is  clear  that  we  should,  with 
equal  certainty,  though  with  much  more  trouble,  tell  what  o'clock  it  were, 
if  the  marks  on  the  dial-plate  were  ttnequally  distributed, —  if  the  hands 
were  cj;centric,  and  their  motion  not  uniform, —  provided  we  knew,  1st, 
the  exact  intervals  round  the  circle  at  which  the  hour  and  minute  marks 
were  placed ;  which  would  be  the  case  if  we  had  them  all  registered  in  a 
table,  from  the  results  of  previous  careful  measurement:  —  2dly,  if  we 
knew  the  exact  amount  and  direction  of  excentricity  of  the  centre  of  mo- 
tion of  the  hands;  —  and  3dly,  if  we  were  fully  acquainted  with  all  the 
mechanism  which  put  the  hands  in  motion,  so  as  to  be  able  to  say  at  every 
instant  what  were  their  velocity  of  movement,  and  so  as  to  be  able  to  cal- 
culate, without  fear  of  error,  how  much  time  should  correspond  to  so 
MUCH  angular  movement. 

(270.)  The  visible  surface  of  the  starry  heavens  is  the  dial-plate  of  our 
clock,  the  stars  are  the  fixed  marks  distributed  around  its  circuit,  the  moon 
is  the  moveable  hand,  which,  with  a  motion  that,  superficially  considered, 
seems  uniform,  but  which,  when  carefully  examined,  is  found  to  be  far 
otherwise,  and  which,  regulated  by  mechanical  laws  of  astonishing  com- 
plexity and  intricacy  in  result,  though  beautifully  simple  in  principle  and 
design^,  performs  a  monthly  circuit  among  them,  passing  visibly  over  and 
hiding,  or,  as  it  is  called,  occulting  some,  and  gliding  beside  and  between 
others ;  and  whose  position  among  them  can,  at  any  moment  when  it  is 
visible,  be  exactly  measured  by  the  help  of  a  sextant,  just  as  we  might 
measure  the  place  of  our  clock-haud  among  the  marks  on  its  dial-phtte 
with  a  pair  of  compasses,  and  thence,  from  the  known  and  calculated  la>rs 
of  its  motion,  deduce  the  time.  That  the  moon  does  so  move  among  the 
stars,  while  the  latter  hold  constantly,  with  respect  to  each  other,  the  same 


relative } 

oommenc 

(271.) 

complete. 

to  the  dii 

of  it.     U 

their  cem 

their  proj 

cause  of 

taking  it 

time,  by  r 

its  distanc 

*  in  every  c 

tion  of  th( 

for  the  pi 

this  is  jus 

the  stars. 

—  the  lati 

ing  the  ce 

constantly 

moon  appai 

tell  the  tru 

(272.)  S 

sidered  a  v 

interests  w( 

regard  it  as 

the  laws  oi 

correctly. 

whose  obje( 

irregular-gc 

absolute  ce 

and  second; 

moon  xcoulc 

accessible  j 

tudes.     Th( 

and  conspic 

centre,  are  < 

almanacks  \ 

in  any  part 

from  any  oc 

been  ascerta 


t 


LUNAR   METHOD. 


151 


relative  position,  the  notico  of  a  few  nights,  or  even  hours,  will  satisfy  the 
commencing  student,  and  this  is  all  that  at  present  we  require. 

(271.)  There  is  only  one  circumstance  wanting  to  make  our  analogy 
complete.  Suppose  the  bands  of  our  clock,  instead  of  moving  quite  close 
to  the  dial-plate,  were  considerably  elevated  above,  or  distant  in  front  of 
of  it.  Unless,  then,  in  viewing  it,  we  kept  our  eye  just  in  the  line  of 
their  centre,  we  should  not  see  them  exactly  thrown  or  projected  upon 
their  proper  places  on  the  dial.  And  if  we  were  either  unaware  of  this 
cause  of  optical  change  of  place,  this  parallax  —  or  negligent  in  not 
taking  it  into  account  —  we  might  make  great  mistakes  in  reading  the 
time,  by  referring  the  hand  to  the  wrong  mark,  or  incorrectly  appreciating 
its  distance  from  the  right.  On  the  other  hand,  if  we  took  care  to  note, 
'  in  every  case  when  we  had  occasion  to  observe  the  time,  the  exact  posi- 
tion of  the  eye,  there  would  be  no  difficulty  in  ascertaining  and  allowing 
for  the  precise  influence  of  this  cause  of  apparent  displacement.  Now, 
this  is  just  what  obtains  with  the  apparent  motion  of  the  moon  among 
the  stars.  The  former  (as  will  appear)  is  comparatively  near  to  the  earth 
—  the  latter  immensely  distant  j  and  in  consequence  of  our  not  occupy- 
ing the  centre  of  the  earth,  but  being  carried  about  on  its  surface,  and 
constantly  changing  place,  there  arises  a  parallax,  which  displaces  the 
moon  apparently  among  the  stars,  and  must  be  allowed  for  before  we  can 
tell  the  true  place  she  would  occuj  y  if  seen  from  the  centre. 

(272.)  Such  a  clock  as  we  have  described  might,  no  doubt,  be  con- 
sidered a  very  bad  one ;  but  if  it  were  our  only  oub^  and  if  incalculable 
interests  were  at  stake  on  a  perfect  knowledge  of  time,  we  should  justly 
regard  it  as  most  precious,  and  think  no  pains  ill  bestowed  in  studying 
the  laws  of  its  movements,  or  in  facilitating  the  means  of  readimj  it 
correctly.  Such,  in  the  parallel  we  are  drawing,  is  the  lunar  theory, 
whose  object  is  to  reduce  to  regularity,  the  indications  of  this  strangely 
irregular-going  clock,  to  enable  us  to  predict,  long  beforehand,  and  with 
absolute  certainty,  whereabouts  among  the  stars,  at  every  hour,  minute, 
and  second,  in  every  day  of  every  year,  in  Greenwich  local  time,  the 
moon  tpould  be  seen  from  the  earth's  centre,  and  will  be  seen  from  every 
accessible  point  of  its  surface ;  and  such  is  the  lunar  metliod  of  longi- 
tudes. The  moon's  apparent  angular  distance  from  all  those  principal 
and  conspicuous  stars  which  lie  in  its  course,  as  seen  from  the  earth's 
centre,  are  computed  and  tabulated  with  the  utmost  care  and  precision  in 
almanacks  published  under  national  control.  No  sooner  does  an  observer, 
in  any  part  of  the  globe,  at  sea  or  on  land,  measure  its  actur'  distance 
from  any  one  of  those  standard  stars  (whose  places  in  the  heavens  have 
been  ascertained  for  the  purpose  with  the  most  nnxious  solicitude,)  than 


e 
m 

O 


Wirt 


153 


OUTLINES  OP  ASTRONOMY. 


V 


he  has,  in  fact,  performed  that  comparison  of  his  local  time  with  the 
local  times  of  every  observatory  in  the  world,  which  enables  him  to  as- 
certain his  difference  of  longitude  from  one  or  all  of  thom. 

(273.)  The  latitudes  and  longitudes  of  any  number  of  points  on  the 
earth's  surface  may  be  ascertained  by  the  methods  above  described ;  and 
by  thus  laying  down  a  sufficient  number  of  principal  points,  and  filling  in 
the  intermediate  spaces  by  local  .surveys,  might  maps  of  countries  be 
constructed.  In  practice,  however,  it  is  found  simpler  and  easier  to 
divide  each  particular  nation  into  a  scries  of  great  triangles,  the  angles 
of  which  are  stations  conspicuously  visible  from  each  other.  Of  these 
triangles,  the  awjles  only  are  measured  by  means  of  the  theodolite,  with 
the  exception  of  one  side  only  of  one  triangle^  which  is  called  a  base, 
and  which  is  measured  with  every  refinement  which  ingenuity  can  devise 
or  expense  command.  This  base  is  of  moderate  extent,  rarely  surpassing 
six  or  seven  miles,  and  purposely  selected  in  a  perfectly  horizontal  plane, 
otherwise  conveniently  adapted  to  the  purposes  of  measurement.  Its 
length  between  its  two  extreme  points  (which  are  dots  on  plates  of  gold 
or  platina  let  into  massive  blocks  of  stone,  and  which  are,  or  at  least 
ought  to  be,  in  all  cases  preserved  with  almost  religious  care,  as  monu- 
mental records  of  the  highest  importance,)  is  then  measured,  with  every 
precaution  to  ensure  precision,'  and  its  position  with  respect  to  the 
meridian,  as  well  as  the  geographical  positions  of  its  extremities;  carefully 
ascertained.  •    .  v 

(274.)  The  annexed  figure  represents  such  a  chain  of  triangles.    A  B 


Fig.  88. 


;>   .-■' 


is  the  base,  O,  C,  stations  visible  from  both  its  extremities  (one  of  which, 
0,  we  wUl  suppose  to  be  a  national  observatory,  with  which  it  is  a  prin- 
cipal object  that  the  base  should  be  as  closely  and  immediately  connected 
as  possible  y)  and  D,  E,  F,  Gr,  H,  K,  other  stations,  remarkable  points  in 

'  The  greatest  poitible  error  in  the  Irish  base  of  between  seven  and  eight  miles, 
near  Londonderry,  is  supposed  not  to  exceed  two  inches. 


the  cou 
were,  w 
the  triu 
sured,  t 
trigonon 
turn  a  b 
For  inst 
by  obsei 
lengths 
and  the 
may  all 
process 
may  be  t 

(275.) 
made.     ' 
stations, 
their  ung 
one  to  del 
the  angle 
a  great  oi 
triangles, 
accuracy 
short  of  1 
practicabli 
centre,  it  \ 
larger  trii 
step  of  th 
and  embn 
the  above 
becomes  ei 
from  30  t( 
which,  bei 
of  subordi 
into  others 
the  limits 
structed,  v 

(276.) 
question  a 
the  surface 
very  smal 
neglected, 


CONSTRUCTION  OP  MAPS. 


158 


which, 
ia  prin> 
mected 
lints  in 

miles, 


tbo  country,  by  whose  connection  its  whole  surface  may  be  covered,  as  it 
were,  with  a  network  of  triangles.  Now,  it  is  evident  that  the  angles  of 
the  triangle  A,  li,  C  being  observed,  and  one  of  its  sides,  A,  B,  mea* 
sured,  the  other  two  sides,  A  C,  B  0,  may  bo  calculated  by  the  rules  of 
trigonometry;  and  thus  each  of  the  sides  A  C  and  B  C  becomes  in  its 
turn  a  base  capable  of  being  employed  as  known  sides  of  other  triangles. 
For  instance,  the  angles  of  the  triangles  A  C  G  and  B  C  F  being  known 
by  observation,  and  their  sides  A  G  and  B  C,  we  can  thence  calculate  the 
lengths  A  G,  C  G,  and  B  F,  C  F.  Again,  C  G  and  C  F  being  known 
and  the  included  angle  G  G  F,  G  F  nmy  bo  calculated,  and  so  on.  Thus 
may  all  the  stations  be  accurately  determined  and  laid  down,  and  as  this 
process  may  be  carried  on  to  any  extent,  a  map  of  the  whole  country 
may  be  thus  constructed,  and  filled  in  to  any  degree  of  detail  we  please. 

(275.)  Now,  on  this  process  there  are  two  important  remarks  to  be 
made.  The  first  is,  that  it  is  necessary  to  be  careful  in  the  selection  of 
stations,  so  as  to  form  triangles  free  from  any  vrry  great  inequality  in 
their  angles.  For  instance,  the  triangle  K  B  F  would  be  a  very  improper 
one  to  determine  the  situation  of  F  from  observations  at  B  and  K,  because 
the  angle  F  being  very  acute,  a  small  error  in  the  angle  K  would  produce 
a  great  one  in  the  place  of  F  upon  the  line  B  F.  Such  ill-conditioned 
triangles,  therefore,  must  be  avoided.  But  if  this  be  attended  to,  the 
accuracy  of  the  determination  of  the  calculated  sides  will  not  be  much 
short  of  that  which  would  be  obtained  by  actual  measurement  (were  it 
practicable) ;  and,  therefore,  as  we  recede  from  the  base  on  all  sides  as  a 
centre,  it  will  speedily  become  practicable  to  use  as  bases,  the  sides  of  much 
larger  triangles,  such  as  G  F,  G  H,  H  K,  &c. ;  by  which  means  the  next 
step  of  the  operation  will  come  to  be  carried  on  on  a  much  larger  scale, 
and  embrace  far  greater  intervals,  than  it  would  have  been  safe  to  do  (for 
the  above  reason)  in  the  immediate  neighbourhood  of  the  base.  Thus  it 
becomes  easy  to  divide  the  whole  face  of  a  country  into  great  triangles  of 
from  80  to  100  miles  in  their  sides  (according  to  the  nature  of  the  ground), 
which,  being  once  well  determined,  may  be  afterwards,  by  a  second  series 
of  subordinate  operations,  broken  up  into  smaller  ones,  and  these  again 
into  others  of  a  still  minuter  order,  till  the  final  filling  in  is  brought  within 
the  limits  of  personal  survey  and  draftsmanship,  and  till  a  map  b  con- 
structed, with  any  required  degree  of  detail. 

(276.)  The  next  remark  we  have  to  make  is,  that  all  the  triangles  in 
question  are  not,  rigorously  speaking,  jj^ane,  but  splierical — existing  on 
the  surface  of  a  sphere,  or  rather,  to  speak  correctly,  of  an  ellipsoid.  lb 
very  small  triangles,  of  six  or  seven  miles  in  the  side,  this  may  be 
neglected,  as  the  difference  is  imperceptible;  but  in  the  larger  ones  it 


c 
z 

m 

C/) 

o 


o 


bSMM 


154 


OUTLINES   OF  ASTRONOMY. 


must  be  taken  into  consideration.  It  is  evident  that,  as  every  object  used 
for  pointing  the  telescope  of  a  theodolite  has  some  certain  elevation,  not 
only  above  the  soilf  but  above  the  level  of  the  sea,  and  as,  moreover, 
these  elevations  differ  in  every  instance,  a  reduction  to  the  horizon  of  all 
the  measured  angles  would  appear  to  bo  required.  But,  in  fact,  by  the 
construction  of  the  theodolite  (art.  192),  which  is  nothing  more  than  an 
altitude  and  azimuth  instrument,  this  reduction  is  made  in  the  very  act 


of  reading  off  the  horizontal  angles.  Let  E  be  the  centre  of  the  earth; 
A,  B,  C,  the  places  on  its  spherical  surface,  to  which  three  stations.  A, 
F,  Q,  in  a  country  are  referred  by  radii  E  A,  £  B  P,  E  C  Q.  If  a  theo- 
dolite be  stationed  at  A,  the  axis  of  its  horizontal  circle  will  point  to  E 
when  truly  adjusted,  and  its  plane  will  be  a  tangent  to  the  sphere  at  A, 
intersecting  the  radii  E  B  P,  E  C  Q,  at  M  and  N,  above  the  spherical 
surface.  The  telescope  of  the  theodolite,  it  is  true,  is  pointed  in  succes- 
sion to  F,  and  Q ;  but  the  readings  off  of  its  azimuth  circle  give  —  not 
the  angle  P  A  Q,  between  the  directions  of  the  telescope,  or  between  the 
objects  P,  Q,  as  seen  from  A  j  hut  the  azimuthal  angle  MAN,  which  is 
the  measure  of  the  angle  A  of  the  spherical  triangle  BAG.  Hence 
arises  this  remarkable  circumstance, — that  the  sum  of  the  three  observed 
angles  of  any  of  the  great  triangles  in  geodesioal  operations  is  always 
fuund  to  be  rather  more  than  180''.  Were  the  earth's  surface  a  plane,  it 
ought  to  be  exacMy  180° ;  and  this  excess,  which  is  called  the  spherical 
excess,  is  so  far  from  being  a  proof  of  incorrectness  in  the  work,  that  it  is 
essential  to  its  accuracy,  and  offers  at  the  same  time  another  palpable 
proof  of  the  earth's  sphericity. 

(277.)  The  true  way,  then,  of  conceiving  the  subject  of  a  triognomet- 
rical  survey,  when  the  spherical  form  of  the  earth  is  taken  into  considera- 


tion, is 
covered, 
centre  of 
aii(/lfs  ii 
imaginar 
of  spheri 
stations  ( 
tain  and 
this  cons 
survey,  a 
called  the 
on  trigon 
earth,  it 
however, 
(278.) 
reduction 
determina 
observed, 
to  Jay  dow 
thd  places 
and  the  pi 
ihoy  belon, 
raphy,  we 
sary  respec 
raphy. 

(279.)  . 

some  portic 

lars  intend 

points.     N 

or  projecte( 

some  parts 

tending  or  ' 

tively  contri 

portions  of 

represcntati( 

(280.)  T 

stereof/raphi 

point  of  th< 

'  Wo  here  i 
tnakiiig,  is  too 


CONSTRUCTION  OP  MAPS. 


165 


succes* 
e  —  not 
een  the 
vhich  is 
Hence 
bserved 
always 
lane,  it 
iherical 
at  it  ia 
alpable 

i;nomet- 
isidera- 


tion,  is  to  regard  the  network  of  triangloa  with  which  the  country  is 
covered,  as  the  bases  of  an  assemblage  of  pyramids  converging  to  the 
centre  of  the  earth.  The  theodolite  gives  us  the  true  mcamrv.H  of  the 
awjln  inrludfd  hy  the  plmica  of  these  pi/ramiih }  and  the  surface  of  an 
imaginary  sphere  on  the  level  of  the  sea  intersects  thea<  in  an  assemblage 
of  spherical  triangles,  above  whose  angles,  in  the  radii  prolonged,  the  real 
stations  of  observation  are  raiHcd,  by  the  superficial  incqup.'*  'oa  of  mouiw 
tain  and  valley.  The  opcrose  calculations  of  spherical  trigC'i<  >nctry  which 
this  consideration  would  seem  to  render  necessary  for  the  reductiona  of  a 
survey,  are  diapenscd  with  in  practice  by  a  very  simple  and  easy  rule, 
called  the  rule  for  the  spherknl  excesK,  vhich  is  to  be  found  in  most  works 
on  trigonometry.  If  wo  would  take  into  account  the  ellipticity  of  the 
earth,  it  may  also  be  done  by  appropriate  processes  of  calculation,  which, 
however,  are  too  abstruse  to  dwell  upon  ii;  a  worL  like  the  <  .cscnt. 

(278.)  Whatever  process  of  calculation  we  adopt,  the  t  ».ult  will  be  a 
reduction  to  the  level  of  the  sea,  of  all  the  triangles,  aU'l  the  conso'jucnt 
determination  of  the  geographical  latitude  and  '  li.-'ftude  of  every  r  ation 
observed.  Thus  we  are  at  length  enabled  to  construct  maps  of  countries; 
to  lay  down  the  outlines  of  continents  and  ialands ;  the  courses  of  rivers ; 
the  places  of  cities,  towns  and  villages ;  the  direction  of  mountain  ridges, 
and  the  places  of  their  principal  summits;  and  all  those  details  which,  as 
r.hoy  belong  to  physical  and  statistical,  rather  than  to  astronomical  geog- 
raphy, we  need  not  here  dilate  on.  A  few  words,  however,  will  be  neces- 
sary respecting  maps,  which  are  used  as  well  in  astronomy  as  in  geog- 
raphy. 

(279.)  A  map  is  nothing  more  than  a  representation,  upon  a  plane,  of 
some  portion  of  the  surface  of  a  sphere,  on  which  are  traced  the  particu- 
lara  intended  to  be  expressed,  wh«  '^;"  they  be  continuous  outlines  or 
points.  Now,  as  a  spherical  surface'  can  by  no  contrivance  be  extended 
or  projected  into  a  plane,  without  undue  enlargement  or  contraction  uf 
some  parts  in  proportion  to  others;  and  as  the  system  adopted  in  so  ex- 
tending or  projecting  it  will  decide  what  parts  shall  be  enlarged  or  rela- 
tively contracted,  and  in  what  proportions ;  it  follows,  that  when  large 
portions  of  the  sphere  are  to  be  mapped  down,  a  great  difference  in  their 
representations  may  subsist,  according  to  the  system  of  projection  adopted. 
(280.)  The  projections  chiefly  used  in  maps,  are  the  orthographic, 
stereograph iCf  and  Mercator's.  In  the  orthographic  projection,  every 
point  of  the  hemisphere  is  referred  to  its  diametral  plane  or  base,  by  a 

'  Wc  here  neglect  the  ellipticity  of  the  earth,  which,  for  sach  a  purpose  as  map- 
making,  is  too  trifling  to  have  any  material  influence. 


I 

a 


156 


OUTLINES   OF  ASTRONOMY. 
Fig.  41. 


perpendicular  let  fall  on  it,  so  that  the  representation  of  the  hemisphere 
thus  mapped  on  its  base,  is  such  as  would  actually  appear  to  an  eye  placed 
at  an  infinite  distance  from  it.  It  is  obvious,  from  the  annexed  figure, 
that  in  this  projection  only  the  central  portions  are  represented  of  their 
true  forms,  while  all  the  exterior  is  more  and  more  distorted  and  crowded 
together  as  wc  approach  the  edges  of  the  map.  Owing  to  this  cause,  the 
orthographic  projection,  though  very  good  for  small  portions  of  the  globe, 
is  of  little  service  for  large  ones. 

(281.)  The  stereographic  projection  is  in  great  measure  free  from  this 
defect.  To  understand  this  projection,  wc  must  conceive  an  eye  to  be 
placed  at  E,  one  extremity  of  a  diameter,  E  C  B,  of  the  sphere,  and  to 
view  the  concave  surface  of  the  sphere,  every  poi.it  of  which,  as  P,  is 
referred  to  the  diametral  plane  A  D  F,  perpendicular  to  E  B  by  the 
visual  line  P  M  E.     The  stereographic  projection  of  a  sphere,  then,  is  a 


true  perspective  representation  of  its  concavity  on  a  diametral  plane; 
and,  as  such,  it  possesses  some  singularly  elegant  geometrical  properties, 
of  which  we  shall  state  one  or  two  of  the  principal. 

(282.)  And  first,  then,  all  circles  on  the  sphere  are  represented  by 


circles  ii 
great  cii 
traversir 

2dly. 
by  a  sin 
property 
the  reali 
in  a  sin 
the  surfa 
borders 
graphic, 
in  recedi 

(283.) 
much  as 
plane.  1 
it  cannot 
carried  su 
and  those 


equator  is 
dians  are  i 
the  genera 
what  woul 
scribing  c] 
cylinder  ii 
representa 
greatly  in 
particular 
single  hen 
(284.) 
details;  b 


PROJECTIONS   OF  THE   SPHERE. 


15T 


circles  in  the  projection.  Thus  the  circle  X  is  projected  into  x.  Only 
great  circles  passing  through  the  vertex  B  are  projected  into  straight  lines 
traversing  the  centre  C :  thus,  B  P  A  is  projected  into  C  A. 

'2dly.  Every  very  small  triangle,  G-  H  K,  on  the  sphere,  is  represented 
by  a  similar  triangle,  g  hk,iix  the  projection.  This  is  a  very  valuable 
property,  as  it  insures  a  general  similarity  of  appearance  in  the  map  to 
the  reality  in  all  its  parts,  and  enables  us  to  project  at  least  a  hemisphere 
in  a  single  map,  without  any  violent  distortion  of  the  configurations  on 
the  surface  from  their  real  forms.  As  in  the  orthographic  projection,  the 
borders  of  the  hemisphere  are  unduly  crowded  together ;  in  the  stereo- 
graphic,  their  projected  dimensions  are,  on  the  contrary,  somewhat  enlarged 
in  receding  from  the  centre. 

(283.)  Both  these  projections  may  be  considered  natural  ones,  inas- 
much as  they  are  really  perspective  representations  of  the  surface  on  a 
plane.  Mcrcator's  is  entirely  an  artificial  one,  representing  the  sphere  as 
it  cannot  be  seen  from  any  one  point,  but  as  it  might  be  seen  by  an  eye 
carried  successively  over  every  part  of  it.  In  it,  the  degrees  of  hmgihide, 
and  those  of  latitude,  bear  always  to  each  other  their  due  proportion :  the 


equator  is  conceived  to  be  extended  out  into  a  straight  line,  and  the  meri- 
dians are  straight  lines  at  right  angles  to  it,  as  in  the  figure  Altogether, 
the  general  character  of  maps  on  this  projection  is  not  very  dissimilar  to 
what  would  be  produced  by  referring  every  point  in  the  globe  to  a  circum- 
scribing cylinder,  by  lines  drawn  from  the  centre,  and  then  unrolling  the 
cylinder  into  a  plane.  Like  the  stereographic  projection,  it  gives  a  true 
representation,  as  to  form,  of  every  particular  small  part,  but  varies 
greatly  in  point  of  &cale  in  its  di£fercnt  regions;  the  polar  portions  in 
particular  being  extravagantly  enlarged ;  and  the  whole  map,  even  of  a 
single  hemisphere,  not  being  comprisable  within  any  finite  limits. 

(284.)  We  shall  not,  of  course,  enter  here  into  any  geographical 
details ;  but  one  result  of  maritime  discovery  on  the  great  scale  is,  so  to 


i 

m 


m 

hem 


o 


158 


OUTLINES  OF  ASTRONOMY. 


speak,  massive  enough  to  call  for  mention  as  an  astroaomical  feature. 
When  the  continents  and  seas  are  laid  down  on  a  globe  (and  since  the 
discovery  of  Australia  and  the  recent  addition  to  our  antarctic  knowledge 
of  Victoria  Land  by  Sir  J.  C.  Ross,  we  are  sure  that  no  very  extensive 
tracts  of  land  remain  unknown),  we  find  that  it  is  possible  so  to  divide 
the  globe  into  two  hemispheres,  that  one  shall  contain  neurit/  all  the  land; 
the  other  being  almost  entirely  sea.  It  is  a  fact,  not  a  little  interesting 
to  Englishmen,  and,  combined  with  our  insular  station  in  that  great  high- 
way of  nations,  the  Atlantic,  not  a  little  explanatory  of  our  commercial 
eminence,  that  London'  occupies  nearly  the  centre  of  the  terrestrial  hemi- 
sphere. Astronomically  speaking,  the  fact  of  this  divisibility  of  the 
globe  into  an  oceanic  and  a  terrestrial  hemisphere  is  important,  as  demon- 
strative of  a  want  of  absolute  equality  in  the  density  of  the  solid  mate- 
rial of  the  two  hemispheres.  Considering  the  whole  mass  of  land  and 
water  as  in  a  state  of  equilihriumy  it  is  evident  that  the  half  which  pro- 
trudes must  of  necessity  be  buoyant;  not,  of  course,  that  we  mean  to 
assert  it  to  be  lighter  than  water,  but,  as  compared  with  the  whole  globe, 
in  a  less  degree  heavier  than  that  fluid.  We  leave  to  geologists  to  draw 
from  these  premises  their  own  conclusions  (and  we  think  them  obvious 
enough)  as  to  the  internal  constitution  of  the  globe,  and  the  immediate 
nature  of  the  forces  which  sustain  its  continents  at  their  actual  elevation ; 
but  in  any  future  investigations  which  may  have  for  their  object  to  explain 
the  local  deviations  of  the  intensity  of  gravity,  from  what  the  hypothesis 
of  an  exact  elliptic  figure  would  require,  this,  as  a  general  fact,  ought  not 
to  be  lost  sight  of. 

(285.)  Our  knowledge  of  the  surface  of  our  globe  is  incomplete,  un- 
less it  include  the  heights  above  the  sea  level  of  every  part  of  the  land, 
and  the  depression  of  the  bed  of  the  ocean  below  the  surface  over  all  its 
extent.  The  latter  object  is  attainable  (with  whatever  difficulty,  and 
howsoever  slowly)  by  direct  sounding;  the  former  by  two  distinct  methods : 
the  one  consisting  in  trignometrical  measurement  of  the  differences 
of  level  of  all  the  stations  of  a  survey;  the  other,  by  the  use  of  the 
barometer,  the  principle  of  which  is,  in  fact,  identical  with  that  of  the 
sounding  line.  In  both  cases  we  measure  the  distance  of  the  point  whoso 
level  we  would  know  from  the  surface'  of  an  equilibrated  ocean :  only  in 
the  one  case  it  is  an  ocean  of  water;  in  the  other,  of  air.     In  the  one 

'  More  exactly,  Falmouth.  The  central  point  of  the  hemisphere  which  contains  the 
maximum  of  land  falls  very  nearly  indeed  upon  this  port.  The  land  in  the  opposite 
hemisphere,  with  exception  of  the  tapering  extremity  of  South  America  and  the 
slender  peninsula  of  Malacca,  is  wholly  insular,  and  were  it  not  for  New  Holland 
A'ould  be  quite  insignificant  in  amount. 


case  01 
measur 
air  is  qi 
(286 
with  oi 
Let  A 


above  th 
depth  01 
point  D 
we  woul< 
send  up 
same  at 
gives  the 
(287.) 
positive  s 
any  float 
fluid  real] 
over  the 
in  a  state 
what  wau 
and  there 
surface  tc 
Now,  the 
is  support 
bent  on  E 
(indicated 
conclude, 
that  degre 
Such  is  th 
ment  of  h 

'  Newton' 

» Biot,  As 

those  of  01 

Annjaire;  i 


BAROMETRIC   MEASUREMENT  OF  HEIGHTS. 


159 


feature, 
ince  the 
owledge 
ictensive 
)  divide 
le  land; 
Cresting 
>at  high- 
Qidercial 
al  hemi- 
r  of  the 
3  demon- 
id  mate- 
land  and 
lich  pro- 
mean  to 
)le  globe, 
B  to  draw 
1  obvious 
mmediate 
ilevation ; 
o  explain 
ypothesis 
)ught  not 

)lete,  un- 
the  land, 
er  all  its 
ilty,  and 
lethods : 
lifferences 
of  the 
,t  of  tbc 
nt  whoso 
only  in 
the  one 

Lntains  the 
|e  opposite 
and  the 
Holland 


case  our  sounding  is  real  and  tangible ;  in  the  other,  an  imaginary  one, 
measured  by  the  length  of  the  column  of  quicksilver  the  superincumbent 
air  is  capable  of  counterbalancing.  " 

(286.)  Suppose  that  instead  of  air,  the  earth  and  ocean  were  covered 
with  oil,  and  that  human  life  could  subsist  under  such  circumstances. 
Let  A  B  C  D  £  be  a  continent,  of  which  the  portion  ABC  projects 

Fig.  44. 


above  the  water,  but  is  covered  by  the  oil,  which  also  floats  at  an  uniform 
depth  on  the  whole  ocean.  Then  if  we  would  know  the  depth  of  any 
point  D  below  the  sea-level,  we  let  down  a  plummet  from  F.  But,  if 
we  would  know  the  height  of  B  above  the  same  level,  we  have  only  to 
send  up  a  float  from  B  to  the  surface  of  the  oil ;  and  having  done  the 
same  at  C,  a  point  at  the  sea  level,  the  difference  of  the  two  float  lines 
gives  the  height  in  question. 

(287.)  Now,  though  the  atmosphere  diflers  from  oil  in  not  having  a 
positive  surface  equally  definite,  and  in  not  being  capable  of  carrying  up 
any  float  adequate  to  such  an  use,  yet  it  possesses  all  the  properties  of  a 
fluid  really  essential  to  the  purpose  in  view,  and  this  in  particular,-—  that, 
over  the  whole  surfcce  of  the  globe,  its  strata  of  equal  density  supposed 
in  a  state  of  equilibrium,  are  parallel  to  the  surface  of  equilibrium,  or  to 
what  would  he  the  surface  of  the  sea,  if  prolonged  under  the  continents, 
and  therefore  each  or  any  of  them  has  all  the  characters  of  a  definite 
surface  to  measure  from,  provided  it  can  be  ascertained  and  identified. 
Now,  the  height  at  which,  at  any  station  B,  the  mercury  in  a  barometer 
is  supported,  informs  us  at  once  how  much  of  the  atmosphere  is  incum- 
bent on  B,  or,  in  other  words,  in  what  stratum  of  the  general  atmosphere 
(indicated  by  its  density)  B  is  situated :  whence  we  are  enabled  finally  to 
conclude,  by  mechanical  reasoning,'  at  what  height  above  the  sea-level 
that  degree  of  density  is  to  be  found  over  the  whole  surface  of  the  globe. 
Such  is  the  principle  of  the  application  of  the  barometer  to  the  measure- 
ment of  heights.     For  details,  the  reader  is  referred  to  other  works.' 

'  Newton's  Princip.  il.  Prop.  22. 

*  Biot,  Astronomie  Physique,  vol.  iii.  For  tables,  see  the  work  of  Biot  cited.  Also 
those  of  Oltmann,  annually  published  by  the  French  board  oi  longitudes  in  their 
Ann uaire ;  and  Mr.  Baily's  collection  of  Astronomical  Tables  and  Formuls. 


n 

m 

rMKJ 


P0 


160 


OUTLINES  OF  ASTRONOMY. 


(288.)  We  will  content  ourselves  here  with  a  general  caution  against 
an  implicit  dependence  on  barometric  measurements,  except  as  a  differ- 
ential process,  at  stations  not  too  remote  from  each  other.  They  rely  in 
their  application  on  the  assumption  of  a  state  of  equilibrium  in  the  atmo- 
spheric -trata  over  the  whole  globe  —  which  is  very  far  from  being  their 
actual  state  (art.  37.)  Winds,  especially  steady  and  general  currents 
sweev'sag  f^ver  extensive  contine-^.ts,  undoubtedly  tend  to  produc3  some 
dcgi'G'  of  conformity  in  the  curvatut'  of  these  strata  to  the  generaJ  form 
of  the  land-surface,  and  therefore  to  give  an  undue  elevation  to  the  mer- 
curial column  at  soaie  poini^.  On  the  other  hand,  the  existence  of 
localities  on  the  earth's  surface  where  a  permanent  depression  of  the 
barometer  prevails  to  the  astonishing  extent  of  nearly  an  inch,  has  been 
clearly  proved  by  the  observations  of  Ermann  in  Siberia  and  of  Ross  in 
the  Antarctic  Seas,  and  is  probably  a  result  of  the  same  cause,  and  may 
be  conceived  as  complementary  to  an  undue  habitual  elevation  in  other 
regions. 

(289.)  Possessed  of  a  knowledge  of  the  height  of  stations  above  the 
sea,  we  may  connect  all  stations  at  the  seme  altitude  by  level  lines,  the 
lowest  of  which  will  be  the  outline  of  the  sea-coast;  and  the  rest  will 
mark  out  the  successive  coast-lines  which  would  take  place  were  the  sea 
to  rise  by  regular  and  equal  accessions  of  level  over  the  whole  world,  till 
the  highest  mountains  were  submerged.  The  bottoms  of  valleys,  and  the 
ridgc-lincs  of  hills  are  determined  by  theur  property  of  intersecting  all 
these  level  lines  at  right  angles,  and  being,  subject  to  that  condition,  the 
shortest  and  longest,  that  is  to  say,  the  steepest,  and  the  most  gently 
sloping  courscb  r<'spectively  which  can  be  pursued  from  the  summit  to 
the  sea.  The  form  >•  constitute  the  "water  courses"  of  a  country;  the 
latter  its  lines  of  "  water-shed"  by  which  it  is  divided  into  distinct  basins 
of  drainage.  Thus  originate  natural  districts  ^of  the  most  inefiiiceable 
character,  on  which  the  distribution,  limits,  and  peculiarities  of  human 
communities  are  in  a  great  measure  dependent.  The  mean  height  of  the 
continent  of  Europe,  or  that  height  which  its  surface  would  have  were  all 
inequalities  levelled  aud  the  mountains  spread  equally  over  the  plains,  is 
according  to  Humboldt  671  English  feet;  that  of  Asia,  1137;  of  North 
America,  748;  and  of  South  America,  1151. 


;n 


At 


■.  v*l? 


CONSTRUC 
OP  RIGH 
TINGUIS 
—  NATU 
ZODIAC. 
TUDE8.  - 
TION. — 1 
GRAPHIC 

(290.)  a 
heavens,  an 
present  the: 
preserve  a  ii 
at  once  simj 
e^vth  is  ma 
which  appet 
tion ;  and  a 
measuring  i 
other,  which 
laying  down 
and  this  wit 
rise  above  oi 

(291.)  G 
and  excellen 
easier,  and  a 
us  if  we  tak( 
ing  each  celc 
independent! 
surface  of  an 
it,  and  on  wl 

(292.)  Tl 
11 


CONSTRUCTION  OF   CELESTIAL  MAPS. 


161 


some 


aiDS,  13 

If  Nortli 


CHAPTER  V. 
OFURANOGRAPHT. 

CONSTRUCTION  OP  CELESTIAL  MAPS  AND  GLOBES  BY  0B8EP  VATIO^"  ^ 
OP  RIGHT  ASCENSION  AND  DECLINATION.  —  CELESTIAL  OBJECTS  DIS- 
TINGUISHED INTO  FIXED  AND  ERRATIC. —  OP  THE  CONSTELLATIONS. 
—  NATURAL  REGIONS  IN  THE  HEAVENS. — THE  MILKY  WAY.  —  THE 
ZODIAC.  —  OP  THE  ECLIPTIC.  —  CELESTIAL  LATITUDES  AND  LONGI- 
TUDES.—  PRECESSION  OP  THE  EQUINOXES. — NUTATION.  —  ABERRA- 
TION.— REPRACTION.— PARALLAX. — SUMMARY  VIEW  OP  THE  URANO- 
ORAPHICAL  CORRECTIONS. 

(290.)  The  determination  of  the  relative  situations  of  objects  in  the 
heavens,  and  the  construction  of  maps  and  globes  v/hich  shall  truly  re- 
present their  mutual  configurations  as  well  as  of  catalogues  which  shall 
preserve  a  more  precise  numerical  record  of  the  position  of  each,  is  a  task 
at  once  simpler  und  less  laborious  than  that  by  which  the  surface  of  the 
ea;th  is  mapped  and  measured.  Every  star  in  the  great  constellation 
which  appears  to  revolve  above  us,  constitutes,  so  to  speak,  a  celestial  sta- 
tion ;  and  among  these  stations  we  may,  as  upon  the  earth,  triangulate,  by 
measuring  with  proper  instrument  their  angular  distances  from  each 
other,  which,  clenred  of  th§  effect  of  refraction,  are  then  in  a  state  for 
laying  down  on  charts,  as  we  would  the  towns  and  villages  of  a  country : 
and  this  without  moving  from  our  place,  at  least  for  all  the  stars  which 
rise  above  our  horizon. 

(291.)  Great  exactness  might,  no  doubt,  be  attained  by  this  means, 
and  excellent  celestial  charts  constructed ',  but  there  is  a  far  simpler  and 
easier,  and  at  the  same  time,  infinitely  more  accurate  course  laid  open  to 
us  if  we  take  advantage  of  the  earth's  rotation  on  its  &xis,  and  by  observ- 
ing each  celestial  object  as  it  passes  our  meridian,  refer  it  separately  and 
independently  tj  the  celestial  equator,  and  thus  ascertain  its  place  on  the 
surface  of  an  imaginary  sphere,  which  may  be  conceived  to  revolve  with 
it,  and  on  which  it  may  be  considered  as  projected. 

(292.)  The  right  ascension  and  declination  of  a  point  in  the  heavens 
11 


z 


n 


Si* 

o 
o 


162 


OUTLINES   OF  ASTRONOMY. 


correspond  to  the  longitude  and  latitude  of  a  station  on  the  earth ;  and 
the  place  of  a  star  on  the  celestial  sphere  is  determined,  when  the  former 
elements  are  known,  just  as  that  of  a  Umv  on  a  map,  by  knowing  the 
latter.  The  great  advantages  which  the  miethcd  nt'  mevilian  observation 
possessf'S  over  that  of  triangulation  iVom  v-mi:  to  star,  arc,  then,  1st,  That 
in  it  every  star  is  observed  in  that  point  of  its  diurnal  c<  '''se,  when  it  is 
best  seen  and  least  dissplaced  by  refnictiou.  -dly,  Thai  fi;  instruments 
required  (the  transit  nnd  meridian  circle)  are  the  simplest  and  least  liable 
to  error  ox-  dcrangeintr>t  of  any  used  by  astronomers  3dly,  That  all  the 
observations  can  be  nta  ie  systematically,  in  regular  succession,  and  with 
equal  advantages;  there  bein^  here  no  question  iibcit  ad yantageous  or 
disadvantageou'v  triangl:>3,  &ii.  And,  lastly,  Thjif:,  by  adopting  this 
course,  the  very  quantities  which  we  should  ot  rwiso  have  to  calculate 
by  long  and  tedious  operations  of  sphericrJ  trigonometry,  and  which  are 
essential  to  the  formation  of  a  catalogue,  are  made  the  objects  of  imme- 
diate measurement.  It  is  almost  needless  to  state,  then,  that  this  is  the 
course  adopted  by  astronomers. 

(293.)  To  determine  the  right  ascension  of  a  celestial  object,  all  that 
is  necessary  is  to  observe  the  moment  of  its  meridian  passage  with  a 
transit  instrument,  by  a  clock  regulated  to  exact  sidereal  time,  or  reduced 
to  such  by  applying  its  known  error  and  rate.  The  rate  may  be  obtained 
by  repeated  observations  of  the  same  .star  at  its  successive  meridian  pas- 
sages. The  error f  however,  requires  a  knowledge  of  the  equinox,  or 
initial  point  from  which  all  right  ascensions  in  the  heavens  reckon,  as 
longitudes  do  on  the  earth  from  a  first  meridian. 

(294.)  The  nature  of  this  point  will  be  explained  presently ;  but  for 
the  purposes  of  uranography,  in  so  far  as  they  concern  only  the  actual 
configurations  of  the  stars  inter  se,  a  knowledge  of  the  equinox  is  not  neces- 
sary. The  choice  of  the  equinox,  as  a  zero  point  of  right  ascensions,  is 
purely  artificial,  and  a  matter  of  convenience ;  but  as  on  the  earth,  any 
station  (as  a  national  observatory)  may  be  chosen  for  an  origin  of  longi- 
tides ;  so  in  uranography,  any  conspicuous  star  might  be  selected  as  an 
initial  point  from  which  hour  angles  might  be  reckoned,  and  from  which, 
by  merely  observing  differences  or  intervals  of  time,  the  situation  of  all 
others' might  be  deduced.  In  practice,  these  intervals  are  affected  by 
certain  minute  causes  of  inequality,  which  must  be  allowed  for,  and 
which  will  be  explained  in  their  proper  places. 

(295.)  The  declinations  of  celestial  objects  are  obtained,  1st,  By  ob- 
servation of  their  meridian  altitudes,  with  the  mural  or  meridian  circle, 
or  other  proper  instruments.  This  requires  a  knowledge  of  the  geogra- 
phical latitude  of  the  station  of  observation,  which  itself  is  only  to  be 

.  ..  '  .    If  -      " 


obtained 

tion  of  t 

which  is 

of  the  E 

directly  ; 

quire  to 

causes  of 

ascension 

(296.) 

all  celest 

Now  her 

permanen 

serve  for 

if  they  fo 

great  nat 

distances 

idea  we  cc 

rest  in  tb 

and  carryi 

we  must 

tinct  histc 

peculiar  n 

between  tl 

(297.) 

even  of  thi 

of  the  cele 

continual  ( 

indeed,  the 

tion  vdth  r 

noticed  an' 

nights,  can: 

too,  the  chi 

from  the  in 

readily  reco 

instruments 

struck  with 

greater  mer 

stars  which 

an  hemisph 

luminary  foi 

a  great  chan 


FIXED  AND   ERRATIC  SIARS. 


168 


imox,  or 


obtained  by  celestial  observation.  2dly,  And  more  directly,  by  observa- 
tion of  their  polar  distances  on  the  mural  circle,  as  explained  in  art.  170, 
which  is  independent  of  any  previous  determination  of  the  latitude 
of  the  station;  neither,  however,  in  this  case,  does  observation  give 
directly  and  immediately  the  exact  declinations.  The  observations  re- 
quire to  be  corrected,  first  for  refraction,  and  moreover  for  those  minute 
causes  of  inequality  which  have  been  just  alluded  to  in  the  case  of  right 
ascensions. 

(296.)  In  this  manner,  then,  may  the  places,  one  among  the  other,  of 
all  celestial  objects  be  ascertained,  and  maps  and  globes  constructed. 
Now  here  arises  a  very  important  question.  How  far  are  these  places 
permanent  ?  Do  these  stars  and  the  greater  luminaries  of  heaven  pre- 
serve for  ever  one  invariable  connection  and  relation  of  place  inter  se,  as 
if  they  formed  part  of  a  solid  though  invisible  firmament;  and,  l'*-^  the 
great  natural  land-marks  on  the  earth,  preserve  immutably  tlu  s;ime 
distances  and  bearings  each  from  the  other?  If  so,  the  most  rational 
idea  we  could  form  of  the  universe  would  be  that  of  an  earth  at  absolute 
rest  in  the  centre,  and  a  hollow  crystalline  sphere  circulating  round  it, 
and  carrying  sun,  moon,  and  stars  along  in  its  diurnal  motion.  If  not, 
we  must  dismiss  all  such  notions,  and  inquire  individually  into  the  dis- 
tinct history  of  each  object,  with  a  view  to  discovering  the  laws  of  its 
peculiar  motions,  and  whether  any  and  what  other  connection  subsists 
between  them. 

(297.)  So  far  is  this,  however,  from  being  the  case,  that  observations, 
even  of  the  most  cursory  nature,  are  sufficient  to  show  that  some,  at  least, 
of  the  celestial  bodies,  and  those  the  most  conspicuous,  are  in  a  state  of 
continual  change  of  place  among  the  rest.  In  the  case  of  the  moon, 
indeed,  the  change  is  so  rapid  and  remarkable,  that  its  alteration  of  situa- 
tion with  respect  to  such  bright  stars  as  may  happen  to  be  near  it  may  be 
noticed  any  fine  night  in  a  few  hours ;  and  if  noticed  on  two  successive 
nights,  cannot  fail  to  strike  the  most  careless  observer.  With  the  sun, 
too,  the  change  of  place  among  the  stars  is  constant  and  rapid ;  though, 
from  the  invisibility  of  stars  to  the  naked  eye  in  the  day-time,  it  is  not  so 
readily  recognized,  and  requires  either  the  use  of  telescopes  and  angular 
instruments  to  measure  it,  or  a  longer  continuance  of  observation  to  be 
struck  with  it.  Nevertheless,  it  is  only  necessary  to  call  to  mind  its 
greater  meridian  altitude  in  summer  than  in  winter,  and  the  fact  that  the 
stars  which  come  into  view  at  night  (and  which  are  therefore  situated  in 
an  hemisphere  opposite  to  that  occupied  by  the  sun,  and  having  that 
luminary  for  its  centre)  vary  with  the  season  of  the  year,  to  perceive  that 
a  great  change  must  have  taken  place  in  that  interval  in  its  relative  situa- 


i 


fcvt*» 


164 


OUTLINES   OP  ASTRONOMY. 


I) 


tion  with  respect  to  all  the  stars.  Besides  the  sun  and  moon,  too,  there 
are  several  other  bodies,  called  planets,  which,  for  the  most  part,  appear 
to  the  naked  eye  only  as  the  largest  and  most  brilliant  stars,  and  which 
offer  the  same  phenomenon  of  a  constant  change  of  place  among  the 
stars ;  now  approaching,  and  now  receding  from,  such  of  them  as  we  may 
refer  them  to  as  marks;  and,  some  in  longer,  some  in  shorter  periods, 
making,  like  the  sun  and  mo^n,  the  complete  tour  of  the  heavens. 

(298.)  These,  however,  are  exceptions  to  the  general  rule.  The  innu- 
merable multitude  of  the  stars  which  are  distributed  over  the  vault  of  the 
heavens  form  a  constellation,  which  preserves,  not  only  to  the  eye  of  the 
casual  observer,  but  to  the  nice  examination  of  the  astronomer,  a  uni- 
formity of  aspect  which,  when  contrasted  with  the  perpetual  change  in 
the  configurations  of  the  sun,  moon,  and  planets,  may  well  be  termed 
invariable.  It  is  true,  indeed,  that,  by  the  refinement  of  exact  measure- 
ments prosecuted  from  u^.e  to  age,  some  small  changes  of  apparent  place, 
attributable  to  no  illusion  and  to  no  terrestrial  cause,  have  been  detected 
in  many  of  them.  Such  are  called,  in  astronomy,  the  proper  motions  of 
the  stars.  But  these  are  so  excessively  slow,  that  their  accumulated 
amount  (even  in  those  stars  for  which  they  are  greatest)  has  been  insuffi- 
cient, in  the  whole  duration  of  astronomical  history,  to  produce  any 
obvious  or  material  alteration  in  the  appearance  of  the  starry  hoavens. 

(299.)  This  circumstance,  then,  establishes  a  broad  distinction  of  the 
heavenly  bodies  into  two  great  classes ;  —  the  fixed,  among  which  (unless 
in  a  course  of  observations  continued  for  many  years)  no  change  of  mutual 
situation  can  be  detected;  and  the  erratic,  or  wandering  —  ^whieh  is 
implied  in  the  word  planet ')  —  including  the  sun,  moon,  and  planets,  as 
well  as  the  singular  class  of  bodies  termed  comets,  in  whose  apparent 
places  among  the  stars,  and  among  each  other,  the  observation  of  a  few 
days,  or  even  hours,  is  sufficient  to  exhibit  an  indisputable  alteration. 

(300.)  Uranography,  then,  as  it  concerns  the  fixed  celestial  bodies  (or, 
as  they  are  usually  called,  the  Jixed  stars'),  is  reduced  to  a  simple  marking 
down  of  their  relative  places  oi  a  globe  or  on  maps ;  to  the  insertion  on 
that  globe,  in  its  due  place  in  the  great  constellation  of  the  stars,  of  the 
pole  of  the  heavens,  or  the  vanishing  point  of  parallels  to  the  earth's 
axis ;  and  of  the  equator  and  place  of  the  equinox :  points  and  circles 
these,  which,  though  artificial,  and  having  reference  entirely  to  our  earth, 
and  therefore  subject  to  all  changes  (if  any)  to  which  the  earth's  axis  may 
be  liable,  are  yet  so  convenient  in  practice,  that  they  have  obtained  an 
admission  (with  some  other  circles  and  lines),  sanctioned  by  usage,  in  all 
globes  and  planispheres.    The  reader,  however,  will  take  care  to  keep 

*  UXavtirmt  a  wanderer. 


them  sei 
of  tico 
one  of  w 
imaginar 
their  owi 
conceive 
any  man 
demonstr 
by  a  slov 
they  are 
ferent  sts 
confusion 
(801.) 
outlines  o 
globes  an( 
talk  of  g 
though  ab 
which  it  w 
some  have 
by  a  view 
venience ; 
natural  svil 
or  altogethi 
a  Leonis,  )a 
them.    Th 
compare  th 
(302.)  1 
which  offci 
such  is  the 
evening,  a] 
traced  with 
pletely  enci 
an  hour  cii 
mata.     It 
branch,  wb 
for  about  h 

•  This  disrc 
have  been  al 
iticonvenienci 
areas  of  the  I 
large  and  smi 
tern  of  conate 


OP  THE   CONSTELLATIONS. 


165 


them  separate  in  his  mind,  and  to  familiarize  himself  with  the  idea  rather 
of  tico  or  more  celestial  globes,  superposed  and  fitting  on  each  other,  on 
one  of  which  —  a  real  one  —  are  inscribed  the  stars;  on  the  others  those 
imaginary  points,  lines,  and  circles,  which  astronomers  have  devised  for 
their  own  uses,  and  to  aid  their  calculations ;  and  to  accustom  himself  to 
conceive  in  the  latter  or  rirtl'\  ial  spheres  a  capability  of  beirg  shifted  in 
any  manner  upon  tlw>  uitace  of  the'  other;  so  that,  should  experience 
demonstrate  (as  it  dm  >)  that  these  artificial  points  and  lines  are  brought, 
by  a  slow  motion  of  the  earth's  axis,  or  by  other  secular  variations  (as 
they  are  called),  to  coincide,  at  very  distant  intervals  of  times,  with  dif- 
ferent stars,  he  may  not  bo  unprepared  for  ihe  change,  and  may  have  no 
confusion  to  correct  in  his  notions. 

(801.)  Of  course  we  do  not  here  speak  of  those  uncouth  figures  and 
outlines  of  men  and  monsters,  which  are  usually  scribbled  over  celestial 
globes  and  maps,  and  serve,  in  a  rude  and  barbarous  way,  to  enable  us  to 
talk  of  groups  of  stars,  or  districts  io  the  heavens,  by  names  which, 
though  absurd  or  puerile  in  their  origin,  have  obtained  a  currency  from 
which  it  wobld  be  difficult  to  dislodge  them.  In  so  far  as  they  have  really  (as 
some  have)  any  slight  resemblance  to  the  figures  called  up  in  imagination 
by  a  view  of  the  more  splendid  "constellations,"  they  have  a  certain  con- 
venience ;  but  as  they  are  otherwise  entirely  arbitrary,  and  correspond  to  no 
na/»ra^  subdivisions  or  groupings  of  the  stars,  astronomers  treat  them  lightly, 
or  altogether  disregard  them,'  except  for  briefly  naming  remarkable  stars,  as 
a  Leonis,  j3  Scorpii,  &c.  &c.,  by  letters  of  the  Greek  alphabet  attached  to 
them.  The  reader  will  find  them  on  any  celestial  charts  or  globes,  and  may 
compare  them  with  the  heavens,  and  there  learn  for  himself  their  position. 

(302.)  There  are  not  wanting,  however,  natural  districts  in  the  heavens, 
which  offer  great  peculiarities  of  character,  and  strike  every  observer: 
such  is  the  milk^  way,  that  great  luminous  band,  which  stretches,  every 
evening,  all  across  the  sky,  from  horizon  to  horizon,  and  which,  when 
traced  with  diligence,  and  mapped  down,  is  found  to  form  a  zone  com- 
pletely encircling  the  whole  spliere,  almost  in  a  great  circle,  which  is  neither 
an  hour  circle,  nor  coincident  with  any  other  of  our  astronomical  gram- 
mata.  It  is  divided  in  one  part  of  its  course,  sending  off  a  kind  of 
branch,  which  unites  again  with  the  main  body,  after  remaining  distinct 
for  about  150  degrees,  within  which  it  suffers  an  interruption  in  its  con- 

'  This  disregard  is  neither  supercilious  nor  causeless.  The  constellations  seem  to 
have  been  almost  purposely  named  and  delineated  to  cause  as  much  confusion  and 
inconvenience  aa  possible.  Innumerable  snakes  twine  through  long  and  contorted 
areas  of  the  heavens,  where  no  memory  can  follow  them  ;  bears,  lions,  and  fishes, 
large  and  small,  northern  and  southern,  confuse  all  nomenclature,  &c.  A  better  sys 
tern  of  constellations  might  have  been  a  material  help  as  an  artificial  memory.' 


f 

O 


o 


S3D 


166 


OUTLINES  OF  ASTRONOMY. 


tinuity.  This  remarkable  belt  has  maintained,  from  the  earliest  ages,  the 
same  relative  situation  among  the  stars;  and,  when  examined  through 
powerful  telescope,  is  found  (wonderful  to  relate  !)  to  consist  entirely  of 
stars  scattered  by  millions^  like  glittering  dust,  on  the  black  ground  of  the 
general  heavens.  It  will  be  described  mure  particularly  in  the  subsequent 
portion  of  this  work. 

(303.)  Another  remarkable  region  in  the  heavens  is  the  zodiac,  not 
from  any  thing  peculiar  in  its  own  constitution,  but  from  its  being  the 
area  within  which  the  apparent  motions  of  the  sun,  moon,  and  all  the 
greater  planets  are  confined.  To  trace  the  path  of  any  one  of  these,  it  is 
only  necessary  to  ascertain,  by  continued  observation,  its  places  at  succes- 
sive epochs,  and  entering  these  upon  our  map  or  sphere  in  sufficient  num- 
ber to  form  a  scries,  not  too  far  disjoined,  to  connect  them  by  lines  from 
point  to  point,  as  we  mark  out  the  course  of  a  vessel  at  sea  by  mapping 
down  its  place  from  day  to  day.  Now  when  this  is  done,  it  is  found,  first, 
that  the  apparent  path,  or  track,  of  the  sun  on  the  surface  of  the  heavens, 
is  no  other  than  an  exact  great  circle  of  the  sphere  which  is  called  the 
ecliptic,  and  which  is  inclined  to  the  equinoctial  at  an  angle  of  about  23° 
28',  intersecting  it  at  two  opposite  points,  called  the  equinoctial  points,  or 
equinoxes,  and  which  are  distinguished  from  each  other  by  the  epithets 
vernal  and  autumnal ;  the  vernal  being  that  at  which  the  sun  crosses  the 
equinoctial  from  south  to  north ;  the  autumnal,  when  it  quits  the  northern 
and  enters  the  southern  heroinphere.  Secondly,  that  the  mooi\  and  all 
the  planets  pursue  paths  which,  in  like  manner,  encircle  the  whole 
heavens,  but  are  not,  like  that  of  the  sun,  great  circles  exactly  returning 
into  themselves  and  bisecting  the  sphere,  but  rather  spiral  curves  of  much 
complexity,  and  described  with  very  unequal  velocities  in  their  dififerent 
parts.  They  have  all,  however,  this  in  common,  that  the  goieral  direc- 
tion of  their  motions  is  the  same  with  that  of  the  sun,  viz.  from  west  to 
east,  that  is  to  say,  the  contrary  to  that  in  which  both  they  and  the  stars 
appear  to  be  carried  by  the  diurnal  motion  of  the  heavens;  and,  more- 
over, that  they  never  deviate  far  from  the  ecliptic  on  either  side,  crossing 
and  recrossing  it  at  regular  and  equal  intervals  of  time,  and  confining 
themselves  within  a  zone,  or  belt  (the  zodiac  already  spoken  of),  extend- 
ing (with  certain  exceptions  among  the  smaller  planets)  not  further  than 
8°  or  9°  on  either  side  of  the  ecliptic. 

(304.)  It  would  manifestly  be  useless  to  map  down  on  globes  or  charts 
the  apparent  paths  of  any  of  those  bodies  which  never  retrace  the  same 
course,  and  which,  therefore,  demonstrably,  must  occupy  at  some  one  mo- 
ment or  other  of  their  history,  every  point  in  the  area  of  that  zone  of  the 
Deaveps  within  which  they  are  circumscribed.    The  apparent  complication 


of  their  i 
them  froi 
we  shift  0 
hand  the 
involved  i 


us  in  oth 

in  the  firs 

other  bodi 

(305.) 

/ersed   bj/ 

865"  6"  9' 

oned  in  sic 

constitutes 

is,  that  as 

in  a  contra 

stars,  it  co; 

so  much  i 

them  in  its 

sun  will  h 

heavens  — 

diurnal  rev 

time  which 

365  days, 

the  proper 

which,  red  I 

measuremc 

that  of  spa 

proportions 

a  source  of 

(306.) 
sent  purpos 
the  case;  t 
which  it  he 
we  find  evic 
nature  will 
that  for  a  f 
circle  may  ' 
position  in  t 

(307.) 
of  the  £phe 


OF  THE  ECLIPTIC  AND  ZODIAC. 


167 


;o8,  the 
h  rough 
rely  of 
I  of  the 
sequent 

iaCf  not 
ing  the 
all  the 
3se,  it  is 
k  Bucces- 
nt  Dum- 
les  from 
napping 
nd,  first, 
heavens, 
lUed  the 
bout  23° 
)oints,  or 
I  epithets 
osses  the 
northern 
and  all 
le  whole 
■eturning 
of  much 
different 
al  direo 
a  west  to 
the  stars 
id,  more- 
crossing 
confining 
,  extend- 
)her  than 

or  charts 

"he  same 

one  mo- 

ine  of  the 

UlicatioQ 


of  their  movements  arise  (that  of  the  moon  excepted)  from  our  viewing 
them  from  a  station  which  is  itaolf  in  motion,  and  would  disappear,  could 
we  shift  our  point  of  view  and  observe  them  from  the  sun.  On  the  other 
hand  the  apparent  motion  of  the  sun  is  presented  to  us  under  its  least 
involved  form,  and  is  studied,  from  the  station  we  occupy,  to  the  greatest 
advantage.  So  that,  independent  of  the  importance  of  that  kminary  to 
us  in  other  respects,  it  is  by  the  investigation  of  the  laws  of  it)  motions 
in  the  first  instance  that  we  must  rise  to  a  knowledge  of  those  of  all  the 
other  bodies  of  our  system. 

(305.)  Tlip  ocliptic,  which  is  its  apparent  path  among  the  stars,  is  tra- 
/ersed  by  it  in  the  period  called  the  sidereal  yenvj  which  consists  of 
865*  6"  9"  9-6*,  reckoned  in  mean  solar  time  or  366*  6"  9«  9-6»  reck- 
oned  in  sidereal  time.  The  reason  of  this  difference  (and  it  is  this  whii'h 
constitutes  the  origin  of  the  difference  between  solar  and  sidereal  time) 
is,  that  as  the  sun's  apparent  annual  motion  amony  the  stars  is  performed 
in  a  contrary  direction  to  the  apparent  diurnal  motion  of  both  sun  and 
stars,  it  comes  to  the  same  thing  as  if  the  diurnal  motion  of  the  sun  were 
so  much  slower  than  that  of  the  stars,  or  as  if  the  sun  lagged  behind 
them  in  its  daily  course.  When  this  has  gone  on  for  a  whole  year,  the 
sun  will  have  fallen  behind  the  stars  by  a  whole  circumference  of  the 
heavens  —  or,  in  other  words  —  in  a  year  the  sun  will  have  made  fewer 
diurnal  revolutions,  by  one,  than  the  stars.  So  that  the  same  interval  of 
time  which  is  measured  by  366*  6'',  &o.  of  sidereal  time,  will  be  called 
365  days,  6  hours,  &o.,  if  reckoned  in  mean  solar  time.  Thus,  then,  is 
the  proportion  between  the  mean  solar  and  sidereal  time  established, 
which,  reduced  into  a  decimal  fraction,  is  that  of  1  00273791  to  1.  The 
measurement  of  time  by  these  different  standards  may  be  compared  to 
that  of  space  by  the  standard  feet,  or  ells  of  two  different  nations ;  the 
proportions  of  which,  once  settled  and  borre  in  mind,  can  never  become 
a  source  of  error. 

(306.)  The  position  of  the  ecliptic  am(>ng  ihe  stars  may,  for  our  pre- 
sent purpose,  bo  regarded  as  invariable.  It  is  true  that  this  is  not  strictly 
the  case;  and  on  comparing  together  its  position  at  present  with  that 
which  it  held  at  the  most  distant  epoch  at  which  we  possess  observations, 
we  find  evidences  of  a  small  change,  which  theory  accounts  for,  and  whose 
nature  will  be  hereafter  explained ;  but  that  change  is  so  excessively  slow, 
that  for  a  great  many  successive  years,  or  even  for  whole  centuries,  this 
circle  may  be  regarded,  for  most  ordinary  purposes,  as  holding  the  same 
position  in  the  sidereal  heavens. 

(307.)  The  poles  of  the  ecliptic^  like  those  of  any  other  great  circle 
of  ihe  sphere,  are  opposite  points  on  its  surface,  equidistant  from  the 


•MM 

o 


'•■■'■  \.  I 

o 
o 


^ 


168 


OUTLINES  OF  AC'VftONOnrY. 


I 


eoliptio  in  every  direction.  They  are  of  course  not  coincident  with  those 
of  the  equinoctial,  but  removed  from  it  by  an  angular  interval  equal  to 
the  inclination  of  the  ecliptic  to  the  equinoctial  (28°  28'),  which  is  called 
the  ohliquiti/  of  thv  ecliptic  In  the  next  figure,  if  P  jj  represent  the 
north  and  south  poles  (by  which  when  used  without  qualification  we  aU 
ways  mean  the  poles  of  the  equinoctial),  and  E  A  Q  V  the  equinoctial, 

V  S  A  W  the  ecliptic,  and  K  k,  its  poles  —  the  spherical  angle  Q  V  S  is 
the  obliquity  of  the  ecliptic,  and  is  equal  in  angular  measure  to  P  K  or 
S  Q.     If  wo  suppose  the  sun's  apparent  motion  to  be  in  the  direction 

V  S  A  W,  V  will  be  the  vcmnl  and  A  the  autumnal  equinox.  S  and  W, 
the  two  points  at  wliich  the  ecliptic  is  most  distant  from  the  equinoctial, 
are  termed  solstices,  because,  when  arrived  there,  the  sun  ceases  to  recede 
from  the  equator,  and  (in  that  sense,  so  far  as  its  motion  in  declination  is 
concerned)  to  stand  still  in  the  heavens.  S,  the  point  where  the  sun  has 
the  greatest  northern  declination,  is  called  the  summer,  and  W,  that  where 
it  is  farthest  south,  the  winter  solstice.  These  epithets  obviously  have 
their  origin  in  the  dependence  of  the  seasons  on  the  sun's  declination, 
which  will  be  explained  in  the  next  chapter.  The  circle  E  K  P  Q  hp, 
which  passes  through  the  poles  of  the  ecliptic  and  equinoctial,  is  called 
the  solstitial  colure ;  and  a  meridian  drawn  through  the  equinoxes,  P  V 
p  A,  the  equinoctial  colure. 

(308.)  Since  the  ecliptic  holds  a  determinate  situation  in  the  starry 
heavens,  it  may  be  employed,  like  the  equinoctial,  to  refer  the  positions 

-    .'"  -.  ,."-'\.  Fig.  45.  'u        '    ■    'r^..    ;  ,  ,':, 


i 


of  the  stars  to,  by  circles  drawn  through  them  from  its  poles,  and  there- 
fore perpendicular  to  it.  Such  circles  are  termed,  in  astronomy,  circles 
of  latitude-  the  distance  of  a  star  from  the  ecliptic,  reckoned  on  the  circle 
of  lati  ude  passing  through  it,  is  called  the  latitude  of  the  stars — and  the 


arc  of  tl 
its  loiif/i 
drawn  tli 
circle  of 
ascension 
TX  its 
sense,  rc( 
kind  of 
the  earth 
stars,  as 
The  force 
(309.) 
may  find 
of  great  \ 
our  last  fi 
V,  the  ve 
ascension^ 
spherical 
KPX,  th 
of  the  pol 
the  eclipti 
of  the  dec 
fore,  by  sf 
the  remain 
tude  X  T, 
angle  (bee 
this  is  no 
The  invers 
■  exactly  sin 
(310.)  ] 
heavens  at j 
the  altitude 
point  of  tl 
itself  from 
data  and  qi 
the  zenith 
equinoctial 
given,  and 
always  the 
known.     T 
the  polar  d 


'*»• 


NONAOESIMAL.      ANOLE  OF  SITUATION. 


169 


there- 
,  circles 
e  circle 
and  the 


arc  of  the  ecliptic  intercepted  between  the  vernal  equinox  and  this  circle, 
its  lomjltiuh;  In  the  figure,  X  is  a  star,  P  X  R  a  circle  of  declination 
drawn  through  it,  by  which  it  is  referred  to  the  equinoctial,  and  K  X  T  a 
circle  of  latitude  referring  it  to  the  ecliptic  —  then,  as  V  R  is  the  right 
ascension,  and  R  X  the  declination,  of  X,  so  also  is  V  T  its  longitude,  and 
T  X  its  latitude.  The  use  of  the  terms  longitude  and  latitude,  in  this 
sense,  seems  to  have  originated  in  considering  the  ecliptic  as  forming  a 
kind  of  natural  equator  to  the  heavens,  as  the  terrestrial  equator  does  to 
the  earth — the  former  holding  an  invariable  position  with  respect  to  the 
stars,  as  the  latter  does  with  respect  to  stations  on  the  earth's  surfuoo. 
The  force  of  this  observation  will  presently  become  apparent. 

(309.)  Knowing  the  right  ascension  and  declination  of  an  object,  we 
may  find  its  longitude  and  latitude,  and  vice  versd.  This  is  a  problem 
of  great  use  in  physical  astronomy  —  the  following  is  its  solution :  —  In 
our  last  figure,  £  K  P  Q,  the  solstitial  colure  is  of  course  OO*'  distant  from 
V,  the  vernal  equinox,  which  is  one  of  its  poles  —  so  that  V  R  (the  right 
ascension)  being  given,  and  also  Y  E,  the  arc  K  R,  and  its  measure,  the 
spherical  angle  EPR,  or  KPX,  is  known.  In  the  spherical  triangle 
K  P  X,  then,  we  have  given,  1st,  The  side  P  K,  which,  being  the  distance 
of  the  poles  of  the  ecliptic  and  equinoctial,  is  equal  to  the  obliquity  of 
the  ecliptic ;  2d>  The  side  P  X,  the  polar  dintancef  or  the  complement 
of  the  declination  R  X ;  and,  3d,  the  included  angle  KPX;  and  there- 
fore, by  spherical  trigonometry,  it  is  easy  to  find  the  other  side  K  X,  and 
the  remaining  angles.  Now  K  X  is  the  complement  of  the  required  lati- 
tude X  T,  and  the  angle  P  K  X  being  known,  and  P  K  V  being  a  right 
angle  (because  S  V  is  90°),  the  angle  X  K  V  becomes  known.  Now 
this  is  no  other  than  the  measure  of  the  longitude  V  T  of  the  object. 
The  inverse  problem  is  resolved  by  the  same  triangle,  and  by  a  process 
■  exactly  similar. 

(310.)  It  is  often  of  use  to  know  the  situation  of  the  ecliptic  in  the  visible 
heavens  at  any  instant;  that  is  to  say,  the  points  where  it  cuts  the  horizon,  and 
the  altitude  of  its  highest  point,  or,  as  it  is  sometimes  called,  the  nonagesimal 
point  of  the  eoliptio,  as  well  as  the  longitude  of  this  point  on  the  ecliptio 
itself  from  the  equinox.  These,  and  all  questions  referable  to  the  same 
data  and  qusesita,  are  resolved  by  the  spherical  triangle  Z  P  E,  formed  by 
the  zenith  Z  (considered  as  the  pole  of  the  horizon),  the  pole  of  the 
equinoctial  P,  and  the  pole  of  the  ecliptio  E.  The  sidereal  time  being 
given,  and  also  the  right  ascension  of  the  pole  of  the  ecliptio  (which  is 
always  the  same,  viz.  \^^  0"  0*),  the  hour  angle  Z  P  E  of  that  point  is 
known.  Then,  in  this  triangle  we  have  given  P  Z,  the  oolatitude ;  P  E, 
the  polar  distance  of  the  pole  of  the  eoliptio,  23°  28',  and  the  angle  Z  P  E 


5 

m 

rMK] 


3? 


170 


OUTLINES   OP  ASTRONOMY. 


i.^ 


from  which  we  may  fiud,  1st,  the  side  Z  E,  which  is  easily  seen  to  be 
equal  to  the  altitude  of  the  nonagesimal  point  sought ;  and  2dly,  the  angle 
P  Z  E,  which  is  the  azimuth  of  the  pole  of  the  ecliptic,  and  which,  there- 
fore, being  added  to  and  subtracted  from  90°,  gives  the  azimuth  of  the 
eastern  and  western  intersections  of  the  ecliptic  with  the  horizon.  Lastly, 
the  longitude  of  the  nonagesimal  point  may  be  had,  by  calculating  in  the 
same  triangle  the  angle  FEZ,  which  is  its  complement. 

(311.)  The  angle  of  situation  of  a  star  is  the  angle  included  between 
circles  of  latitude  and  of  declination  passing  through  it.  To  determine  it 
in  any  proposed  case,  we  must  resolve  the  triangle  P  S  E,  in  which  are 
given  P  S,  P  E,  and  the  angle  S  P  E,  which  is  the  difiFerence  between  the 
star's  right  ascension  and  18  hours ;  from  which  it  is  easy  to  find  the 
angle  P  S  E  required.  This  angle  is  of  use  in  many  inquiries  in  physical 
astronomy.  It  is  called  in  most  books  on  astronomy,  tha  angle  of  posi- 
tion, but  this  expression  has  become  otherwise  and  more  conveniently 
appropriated.     (See  Art.  204.) 

(312.)  The  same  course  of  observations  by  which  the  path  of  the  sun 
among  the  fixed  stars  is  traced,  and  the  ecliptic  marked  out  among  them, 
determines,  of  course,  the  place  of  the  equinox  V  (Fig.  art.  308)  upon 
the  starry  sphere,  at  that  time — a  poin^  of  great  importance  in  practical 
astronomy,  as  it  is  the  origin  or  zero  point  of  right  ascension.  Now, 
when  this  process  is  repeated  at  considerably  distant  intervals  of  time,  a 
very  remarkable  phenomenon  is  observed ;  viz.  that  the  equinox  does  not 
preserve  a  constant  place  among  the  stars,  but  shifts  its  position,  travel- 
ling continually  and  regularly,  although  with  extreme  slowness,  hach- 
wards,  along  the  ecliptic,  in  the  direction  V  W  from  east  to  west,  or  the 
contrary  to  that  in  which  the  sun  appears  to  move  in  that  circle.  As 
the  ecliptic  and  equinoctial  arc  not  very  much  inclined,  this  motion  of  the 


equinox  fi 
with  the 
continual! 
of  the  pri 
the  stars, 
diurnal  m 
this  motio 
is  called), 
minute  qi 
year,  at  la 
venient  to 
number  o 
it  necessai 
logue  on  I 
30°.  Thi 
25,868  ye 

(313.) 
equinoxes 
bodies,  wh 
point  of  1( 
on  the  ecli 
motion,  an 
motion  in 
rotation  ro 
similar  to 
noctial.     1 
bear  in  m 
ment  of  th 
shifting  of 
fixed  star  1 
invariable. 

(314.)  ' 
however,  \ 
as  tending 
stability  oi 
80G)  only 
equinoctial 
tuatioo,  w 
phical  call! 


PRECESSION   OF  THE  EQUINOXES. 


171 


equinox  from  east  to  west  along  the  former,  conspires  (speaking  generally) 
with  the  diurnal  motion,  and  carries  it,  with  reference ,  to  that  motion, 
continually  in  advance  upon  the  stars :  hence  it  has  acquired  the  name 
of  the  precession  of  the  equinoxes,  because  the  place  of  the  equinox  among 
the  stars,  at  every  subsequent  moment,  precedes  (with  reference  to  the 
diurnal  motion)  that  which  it  held  the  moment  before.  The  amount  of 
this  motion  by  which  the  equinox  travels  backward,  or  retrogrades  (as  it 
is  called),  on  the  ecliptic,  is  0®  0'  50-10"  per  annum,  an  extremely 
minute  quantity,  but  which,  by  its  continual  accumulation  from  year  to 
year,  at  last  makes  itself  very  palpable,  and  that  in  a  way  highly  incon- 
venient to  practical  astronomers,  by  destroying,  in  the  lapse  of  a  moderate 
number  of  years,  the  arrangement  of  their  catalogues  of  stars,  and  making 
it  necessary  to  reconstruct  them.  Since  the  formation  of  the  earliest  cata- 
logue on  record,  the  place  of  the  equinox  has  retrograded  already  about 
30°.  The  period  in  which  it  performs  a  complete  tour  of  the  ecliptic,  is 
25,868  years.' 

(313.)  The,  immediate  uranographical  effect  of  the  precession  of  the 
equinoxes  is  to  produce  a  uniform  increase  of  longitude  in  all  the  heavenly 
bodies,  whether  fixed  or  erratic.  For  the  vernal  equinox  being  the  initial 
point  of  longitudes,  as  well  as  of  right  ascension,  a  retreat  of  this  point 
on  the  ecliptic  tells  upon  the  longitudes  of  all  alike,  whether  at  rest  or  in 
motion,  and  produces,  so  far  as  its  amount  extends,  the  appearance  of  a 
motion  in  longitude  common  to  all,  rt.s  if  the  whole  heavens  had  a  slow 
rotation  round  the  poles  of  the  ecliptic  in  the  long  period  above  mentioned, 
similar  to  what  they  have  in  twenty-four  hours  round  those  of  the  equi- 
noctial. This  increase  of  longitude,  the  reader  will  of  course  observe  and 
bear  in  mind,  is,  properly  speaking,  neither  a  real  nor  an  apparent  move- 
ment of  the  stars.  It  is  a  purely  technical  result,  arising  from  the  gradual 
shifting  of  the  zero  point  from  which  longitudes  are  reckoned.  Had  a 
fixed  star  been  chosen  as  the  origin  of  longitudes,  they  would  have  been 
invariable.  ■■    ' 

(314.)  To  form  a  just  idea  of  this  curious  astronomical  phenomenon, 
however,  we  must  abandon,  for  a  time,  the  consideration  of  the  ecliptic, 
as  tending  to  produce  confusion  in  our  ideas ;  for  this  reason,  that  the 
stability  of  the  ecliptic  itself  among  the  stars  is  (as  already  hinted,  art. 
806)  only  approximate,  and  that  in  consequence  its  intersection  with  the 
equinoctial  is  liable  to  a  certain  amount  of  change,  arising  from  ?Vs  fluc- 
tuation, which  mixes  itself  with  what  is  due  to  the  principal  uranogra- 
phical cause  of  the  phenomenon.     This  cause  will  becoiue  at  once  appa- 


2S 

m 


CD 


••wf 

rn 

m-mH 
Sum 

Cmi9 


'  Incipiunt  magni  procedere  menses.  —  Viroii.,  PoUio. 


172 


OUTLINES   OF  ASTRONOMY. 


rent,  if,  instead  of  regarding  the  equinox,  we  fix  our  attention  on  the  pole 
of  the  equinoctial,  or  the  vanishing  point  of  the  earth's  axis. 

(315.)  The  place  of  this  point  among  the  stars  is  easily  determined  at 
any  epoch,  by  the  most  direct  of  all  astronomical  observations,  —  those 
with  the  meridian  or  mural  circle.  By  this  instrument  we  are  enabled  to 
ascertain  at  every  moment  the  exact  distance  of  the  polar  point  from  any 
three  or  more  stars,  and  therefore  to  lay  it  down,  by  triangulating  from 
these  stars,  with  unerring  precision,  on  a  chart  or  globe,  without  the 
least  reference  to  the  position  of  the  ecliptic,  or  to  any  other  circle  not 
naturally  connected  with  it.  Now,  when  this  is  done  with  proper  dili- 
gence and  exactness,  it  results  that,  although  for  short  intervals  of  time, 
such  as  a  few  days,  the  place  of  the  pole  may  be  regarded  as  not  sensibly 
variable,  yet  in  reality  it  is  in  a  state  of  constant,  although  extremely 
slow  motion;  and,  what  is  still  more  remarkable,  this  motion  is  not 
uniform,  but  compounded  of  one  principal  uniform,  or  nearly  uniform, 
part,  and  other  smaller  and  subordinate  periodical  fluctuations :  the 
former  giving  rise  to  the  phenomena  oi  precession  ;  the  latter  to  another 
distinct  phenomenon  called  nutation.  These  two  phenomena,  it  is  true, 
belong,  theoretically  speaking,  to  one  and  the  same  general  head,  and  are 
intimately  connected  together,  forming  part  of  a  great  and  complicated 
chain  of  consequences  flowing  from  the  earth's  rotation  on  its  axis :  but 
it  will  be  conducive  to  clearness  at  present  to  consider  them  separately. 

(316.)  It  is  found,  then,  that  in  virtue  of  the  uniform  p«rt  of  the 
motion  of  the  pole,  it  describes  a  circle  in  the  heavens  around  the  pole  of 
the  ecliptic  as  a  centre,  keeping  constantly  at  thf  same  distance  of  23'^ 
28'  from  it  in  a  direction  from  east  to  west,  and  with  such  a  velocity,  that 
the  annual  angle  described  by  it,  in  this  its  imaginary  orbit,  is  50  10"; 
so  that  the  whole  circle  would  bo  described  by  it  in  the  above-mentioned 
period  of  25,868  years.  It  is  easy  to  perceive  how  such  a  motion  of  tb«? 
pole  will  give  rise  to  the  retrograde  motioB  of  the  equinoxes;  for  in  tb« 
figure,  art.  308,  suppose  the  pole  P  in  the  progress  of  it«  motiop  t»  ^he 
small  circle  P  0  Z  round  K  to  come  to  0,  tkntA,  as  the  sit  motion  of  the 
equinoctial  E  V  Q  is  dete:  mined  by  that  <A  the  pole,  tbi«,  jt  is  evj<Wi»t, 
must  cause  a  displacement  of  the  equinoctial,  vfl^i^fi  will  take  s  neir 
situation,  E  U  Q,  90"  distant  in  every  part  from  the  new  pr/aition  O  of 
the  pole.  The  point  U,  therefore,  Jo  which  the  disp' teed  equinoctial  will 
intersec*^^  the  ecliptic,  i.  e.  the  displaced  equinox,  will  lie  on  tliat  sid*  of 
V,  its  original  position,  towards  which  the  ntotion  of  the  pole  is  direc<*ii, 
or  to  the  westward. 

(317.)  The  precession  of  the  equinoxes  thus  <//iifA\eA,  consists,  f4»^/3, 
in  a  real  but  very  glow  motion  of  the  pole  of  the  hcaveuK  amc«>g  Ibe 


stars,  in  a 
happen  wit 
motion  of 
very  remot 
vanishing 
motion  as 
must  have 
every  part 
of  such  a  n 
or  that  am 
nicely  bala 
hibits,  in 
reader  will 
earth's  axis 
which  it  re 
motion,  and 
driven  throi 
1st,  that  th( 
tion  with  re 
the  earliest 
be  the  case 
of  the  whol 

(318.)  T 
consists  in  t 
polo  and  rec 
call  the  pol 
our  cynosur 
was  12°  frc 
nearer,  to  \ 
slowly  give 
ti*«?  pole, 
brightest  ir 
tion  of  a  pc 

(319  '  i 
wh\4'\x  p»ec( 
tttdes  (A  all 

'  Local  chf 

ot'  rot««jon  w. 


THE  POLE   STAR  NOT  ALWAYS  THE   SAME. 


178 


stars,  in  a  small  circle  round  the  pole  of  the  ecliptic.  Now  this  cannot 
happen  without  producing  corresponding  changes  in  the  apparent  diurnal 
motion  of  the  sphere,  and  the  aspect  which  the  heavens  must  present  at 
very  remote  periods  of  history.  The  pole  is  nothing  more  than  the 
vanishing  point  of  the  earth's  axis.  As  this  point,  then,  has  such  a 
motion  as  we  have  described,  it  necessarily  follows  that  the  earth's  axis 
must  have  a  conical  motion,  in  virtue  of  which  it  points  successively  to 
every  part  of  the  small  circle  in  question.  We  may  form  the  best  idea 
of  such  a  motion  by  noticing  a  child's  peg-top,  when  it  spins  not  upright, 
or  that  amusing  toy  the  te-to-tum,  which,  when  delicately  executed,  rnO 
nicely  balanced,  becomes  an  elegant  philosophical  instrument,  and  ex- 
hibits, in  the  most  beautiful  manner,  the  whole  phenomenon.  The 
reader  will  take  care  not  to  confound  the  variation  of  the  position  of  the 
earth's  axis  in  space  with  a  mere  shifting  of  the  imaginary  line  about 
which  it  revolves,  in  its  interior.  The  whole  earth  participates  in  the 
motion,  and  goes  along  with  the  axis  as  if  it  were  really  a  bar  of  iron 
driven  through  it.  That  such  is  the  case  is  proved  by  the  two  great  facts : 
1st,  that  the  latitudes  of  places  on  the  earth,  or  their  geographical  situa- 
tion with  respect  to  the  poles,  have  undergone  no  perceptible  change  from 
the  earliest  ages.  2dly,  that  the  sea  maintains  its  level,  which  could  not 
be  the  case  if  the  motion  of  the  axis  were  not  accompanied  with  a  motion 
of  the  whole  mass  of  the  earth.' 

(318.)  The  visible  eflFect  of  precession  on  the  aspect  of  the  heavens 
consists  in  the  apparent  approach  of  some  stars  and  constellations  to  the 
pole  and  recess  of  others.  The  bright  :  ar  of  the  Lesser  Bear,  which  we 
call  the  pole  star,  has  not  always  bee/i,  nor  will  always  continue  to  be, 
our  cynosure  :  at  the  time  of  the  construction  of  the  earliest  catalogues  it 
was  12^  from  the  pole  —  it  is  now  only  1°  24',  and  will  approach  yet 
nearer,  to  within  half  a  degree,  after  which  it  will  again  recede,  and 
slowly  give  place  to  others,  which  will  succeed  in  its  companioiiship  to 
Di.«  pole.  After  a  lapse  of  about  12,000  years,  the  star  o  Lyrae,  the 
brightest  in  the  northern  hemisphere,  will  occupy  the  remarkable  situa- 
tion of  a  pole  star  approaching  within  about  5"  of  the  pole. 

(319  1  At  the  date  of  the  erection  of  the  Great  Pyramid  of  Gizeh, 
rhi<'L  js*eeedes  by  3970  years  (say  40'  0)  the  pr* -ent  epoch,  the  lougi- 
mdes  o/  aJl  the  stars  were  less  by  55°  45'  than  at  present.     Calculating 


< 

m 


o 

o 


//Ocai  clmnges  of  the  sea  level,  arising  from  purely  geological  causes,  are  easily 
tl»t**>j{u«faed  from  that  general  and  systematic  alteration  which  a  shiffing  of  the  axis 
of  rotation  would  give  rise  to. 


174  OUTLINES   OF   ASTRONOMY. 

from  this  datum'  tho  place  of  the  pole  of  the  heavens  among  die  stars,  it 
will  be  found  to  fall  near  a  Draconis;  its  distance  from  that  star  being  3° 
44'  25".  This  being  the  most  conspicuous  star  in  the  immediate  neigh- 
bourhood was  therefore  the  pole  star  at  that  epoch.  And  the  latitude  of 
Gizeh  being  just  80°  north,  and  consequently  the  altitude  of  the  north 
pole  there  also  30°,  it  follows  that  the  star  in  question  must  have  had  at 
its  lower  culmination,  at  Gizch,  an  altitude  of  26°  15'  35".  Now  it  is  a 
remarkable  fact,  ascertained  by  the  late  researches  of  Col.  Vyse,  that  '^f 
the  nine  pyramids  still  existing  at  Gizeh,  six  (including  all  the  largest) 
have  the  narrow  passages  by  which  alone  they  can  be  entered,  (all  which 
open  out  on  the  northern  faces  of  their  respective  pyramids)  inclined  to 
the  horizon  downwards  at  angles  as  follows. 

1st,  or  Pyramid  of  Cheops  26°  41 

2d,  or  Pyramid  of  Cephren 25    55 

3d,  or  Pyramid  of  Mycerinus  26      2 

4th,  27      0 

5th, 27    12 

9th, 28      0 

Mean    -    26    47 

Of  the  two  pyramids  at  Abousseir  also,  which  alone  exist  in  a  state  of 
sufficient  preservation  to  admit  of  the  inclinations  of  their  entrance  pas- 
sages being  determined,  one  has  the  angle  27°  5',  the  other  26". 

(320.)  At  the  bottom  of  every  one  of  these  passages  therefore,  the  fJicn 
pole  star  must  have  been  visible  at  its  lower  culmination,  a  circumstance 
which  can  hardly  be  supposed  to  have  been  unintentional,  and  was  doubt- 
less connected  (perhaps  superstitiously)  with  the  astronomical  observation 
of  that  star,  of  whose  proximity  to  the  pole  at  the  epoch  of  the  erection 
of  these  wonderful  structures,  we  are  thus  furnished  with  a  monumental 
record  (*f  the  most  imperishable  nature. 

(321.)  The  nutation  of  the  earth's  axis  is  a  small  and  slow  subordinate 
gyratory  movement,  by  which,  if  subsisting  alone,  the  pole  would  describe 
)ww/>ng  the  stars,  in  a  period  of  about  nineteen  years,  a  miunte  ellipsis, 
having  its  longer  axis  equal  to  18"-5,  and  its  shorter  to  13"-74  j  the  longer 
being  directed  towards  the  pole  of  the  ecliptic,  and  the  shorter,  of  course, 
at  right  angles  to  it.     The  consequence  of  this  real  motion  of  the  pole  is 

'  On  this  calcuklion  the  diminution  of  the  obliquity  of  the  eliptic  in  tW  ♦000  years 
elapsed  has  no  influence.  That  diminution  arises  from  a  change  in  the  pki«e  of  the 
earth's  orbit,  and  has  nothing  to  do  with  the  change  m  the  ^-jsition  of  its  mtr^,  as  re- 
ferred to  the  starry  sphere. 


an  apparent 
pole  in  the 
the  ecliptic 
same  cause  ^ 
equinoctial  ] 
the  right  as 
diminished. 

(322.)  B 
rately,  subsi 
is  describing 
greater  and 
circle  round 
that  is  to  s 
(which,  in  a 
as  seen  fron 
virtue  of  th 
nor  an  exac 
(where,  ho 
to  art.  325.; 

(323.)  T 
the  celestial 
it  impossibh 
earth's  axis 
they  might, 
of  the  Starr; 
poles  of  the 
axis  in  nine: 
nets,  which, 
cannot  withe 
this  idea  fal 
in  the  earth 
subsequent 
of  the  earth 
tion  of  the  i 

(324.)  t 
the  stars,  th 
we  speak  ol 

'  This  argu 
of  nutation,  m 
we  attribute  it 
to  be  kept  in  i 


NUTATION  OF  THE   EARTH'S  AXIS. 


175 


041 

55 
2 
0 

12 
0 

It" 


longer 


pole  is 


as  rc- 


an  apparent  approach  and  recess  of  all  the  stars  in  the  heavens  to  the 
pole  in  the  same  period.  Since,  also,  the  place  of  the  equinox  on 
the  ecliptic  is  determined  by  the  place  of  the  polo  in  the  heavens,  the 
same  cause  will  give  rise  to  a  small  alternate  ridvance  and  recess  of  the 
equinoctial  points,  by  which,  in  the  same  period,  both  the  longitudes  and 
the  right  ascensions  of  the  stars  will  be  also  alternately  increased  and 
d>>ninished. 

(322.)  Both  these  motions,  however,  although  here  considered  sepa- 
rately, subsist  jointly ;  and  since,  while  in  virtue  of  the  nutation,  the  pole 
is  describing  its  little  ellipse  of  18" -5  in  diameter,  it  is  carried  by  the 
greater  and  regularly  progressiva!  motion  of  precession  over  so  much  of  its 
circle  round  the  pole  of  the  ecliptic  as  corresponds  to  nineteen  years, — 
that  is  to  say,  over  an  angle  of  nineteen  times  50" -1  round  the  centre 
(which,  in  a  small  circle  of  23°  28'  in  diameter,  corresponds  to  6'  20", 
as  seen  from  the  centre  of  the  sphere)  :  the  path  which  it  will  pursue  in 
virtue  of  the  two  motions,  subsisting  jointly,  will  be  neither  an  ellipse 
nor  an  exact  circle,  but  a  gently  undulated  ring  like  that  in  the  figure 
(where,  however,  the  undulations  are  much  exaggerated).  (See  fig, 
to  art.  825.) 

(323.)  These  movements  of  precession  and  nutation  are  common  to  all 
the  celestial  bodies,  both  fixed  and  erratic ;  and  this  circumstance  makes 
it  impossible  to  attribute  them  to  any  other  cause  than  a  real  motion  of  the 
earth's  axis  such  as  we  have  described.  Did  they  only  aflFect  the  stars, 
they  might,  with  equal  plausibility,  be  urged  to  arise  from  a  real  rotation 
of  the  starry  heavens,  as  a  solid  shell,  round  an  axis  passing  through  the 
poles  of  the  ecliptic  in  25,868  years,  and  a  real  ecliptic  gyration  of  that 
axis  in  nineteen  years :  but  since  they  also  affect  the  sun,  moon,  and  pla- 
nets, which,  having  motions  independent  of  the  general  body  of  the  stars, 
cannot  without  extravagance  be  supposed  attached  to  the  celestial  concave,' 
iYXd:  idea  falls  to  the  ground ;  and  there  only  remains,  then,  a  real  motion 
in  the  earth  by  which  they  can  be  accounted  for.  It  will  be  shown  in  a 
subsequent  chapter  that  they  are  necessary  consequences  of  the  rotation 
of  the  earth,  combined  with  its  elliptical  figure,  and  the  unequal  attrac- 
tion of  the  sun  and  moon  on  its  polar  and  equatorial  regions. 

(324.)  Uranographically  considered,  as  aflfecting  the  apparent  places  of 
the  stars,  thay  are  of  the  utmost  importance  in  practicd  astronomy.  When 
we  speak  of  the  right  ascension  and  declination  of  a  celestial  object,  it 

'  This  argument,  cogent  as  it  is,  acquires  additional  and  decisive  force  from  the  law 
of  nutation,  which  is  dependent  on  the  position,  for  the  time,  of  the  lunar  orbit.  It 
we  attribute  it  to  a  real  motion  of  the  celestial  sphere,  we  must  then  maintain  that  sphere 
to  be  kept  in  a  constant  state  of  tremor  by  the  motion  of  the  moon. 


t 


CI 

m 


"V! 


rn 


"■*V"1I 


m 


176 


OUTLINES  OF  ASTRONOMY. 


becomes  necessary  to  state  what  q>och  we  intend,  and  whether  we  mean 
the  mean  right  ascension  —  cleared,  that  is,  of  the  periodical  fluctuation  in 
its  amount,  which  arises  from  nutation,  or  the  apparent  right  ascension, 
which,  being  reckoned  from  the  actual  place  of  the  vernal  equinox,  is 
affected  by  the  periodical  advance  and  recess  of  the  equinoctial  point  pro> 
duced  by  nutation — and  so  of  the  other  elements.  It  is  the  practice  of 
astronomers  to  rediice,  as  it  is  termed,  all  their  observations,  both  of  right 
ascension  and  declination,  to  some  common  and  convenient  epoch  —  such 
as  the  beginning  of  the  year  for  temporary  purposes,  or  of  the  decade,  or 
the  century  for  more  permanent  uses,  by  subtracting  from  them  the  whole 
effect  of  precession  in  the  interval ;  and,  moreover,  to  divest  them  of  the 
influence  of  nutation  by  invesrigating  and  subducting  the  amount  of 
change,  both  in  right  ascension  and  declination,  due  to  the  displacement 
of  the  pole  from  the  centre  to  the  circurxtference  of  the  little  ellipse  above 
mentioned.  This  last  process  is  technically  termed  correcting  or  equating 
the  observation  for  nutation ;  by  which  latter  word  is  always  understood, 
in  astronomy,  the  getting  rid  of  a  periodical  cause  of  fluctuation,  and  pre- 
senting a  result,  not  as  it  was  observed,  but  as  it  would  have  been  observed, 
had  that  cause  of  fluctuation  had  no  existence. 

(325.)  For  these  purposes,  in  the  present  case,  very  convenient 
formulae  have  been  derived,  and  tables  constructed.  They  are,  however, 
of  too  technical  a  character  for  this  work ;  we  shall,  however,  point  out 
the  manner  in  which  the  investigation  is  conducted.  It  has  been  shown 
in  art.  809  by  what  means  the  right  ascension  and  declination  of  an 
object  are  derived  from  its  longitude  and  latitude.  Referring  to  the 
figure  of  that  article,  and  supposing  the  triangle  K  P  X  oi  ihograpbically 
projected  on  the  plane  of  the  ecliptic  as  in  the  annexed  figure :  in  the 
triangle  K  P  X,  K  P  is  the  obliquity  of  the  ecliptic,  K  X  the  co-latitude 
(or  complement  of  latitude),  and  the  angle  P  K  X  the  co-longitudt  of  the 
object  X.  These  are  the  data  of  our  question,  of  which  the  second  is 
cc'istant,  and  the  o^her  two  are  varied  by  the  effect  of  precession  and 
nutation :  and  their  a.-iations  (considering  the  minuteness  of  the  latter 
effect  generally,  and  the  small  number  of  years  in  comparison  of  the 
whole  period  of  25,868,  for  which  we  ever  require  to  estimate  the  effect 
of  the  former,)  are  of  that  order  which  may  be  regarded  as  infinitesimal 
in  geometry,  and  treated  as  such  without  fear  of  error.  The  whole  ques- 
tion, then,  is  reduced  to  this: — In  a  spherical  triangle  K  PX,  in  which 
one  side  KX  is  constant,  and  an  angle  K,  .md  adjacent  siile  K  P  vary  by 
given  infinitesimal  changes  of  the  position  of  P :  required  the  changes 
therce  arising  in  the  other  side  P  X,  and  the  angle  K  P  X.  This  is  a 
verj  simple  and  easy  problem  of  spherical  geometry,  and  being  resolveu, 


it  gives  at 
distance  of  ' 
their  variati( 
to  express  i 
longitude,  an 
tion  will  ini: 

(326.)  T 
arc  not  chat 
time  at  the 
Imgitude  ai 
of  the  little 
however,  th 
acquainted  \ 
depends. 

(327.)  A 
cession  and 
reckoned  fro 
fonnly  Jlow 
so  reckoned, 
it  does  not  si 
JoHcs  one  da^ 
*o  the  cquin< 
tion.  We  (1 
apparent  siilt 

(328.)  N, 
celestial  obje 
12 


CORRECTIONS  FOR  PRECESSION  AND  NUTATION. 

Fig.  47. 


1T7 


it  gives  at  once  the  reductions  we  are  seeking ;  for  P  X  being  the  polar 
distance  of  the  object,  and  the  angle  K  P  X  its  right  ascension  pins  90°, 
their  variations  are  the  very  quantities  we  seek.  It  only  remains,  then, 
to  express  in  proper  form  the  amount  of  the  precession  and  nutation  in 
longitude  and  latitude,  when  their  amount  in  right  ascension  and  declina- 
tion will  immediately  be  obtained. 

(326.)  The  precession  in  latitude  ia  zero,  since  the  latitudes  of  objects 
arc  not  changed  by  it :  that  in  longitude  is  a  quantity  proportional  to  the 
time  at  the  rate  of  oO"10  per  annum.  With  regard  to  the  nutation  in 
I'vitfitude  and  latitude,  these  are  no  other  than  the  abscissa  and  ordinate 
of  the  little  ellipse  in  which  the  pole  moves.  The  law  of  its  motion, 
however,  therein,  cannot  bo  understood  till  the  reader  has  been  made 
acquainted  with  the  principal  features  of  the  moon's  motion  on  which  it 
depends.  .  y-    ■ 

(327.)  Another  consequence  of  what  has  been  shown  respecting  pre- 
cession and  nutation  is,  that  sidereal  time,  as  astronomers  use  it,  i.  e.  as 
reckoned  from  the  transit  of  the  equinoctial  point,  is  not  a  mean  or  uni- 
formly ftowimj  quantity,  being  affected  by  nutation;  and  moreover,  that 
,w  reckoned,  even  when  cleared  of  the  periodical  fluctuation  of  nutation, 
i5  does  not  strictly  correspond  to  the  earth's  diurnal  rotation.  As  the  sun 
hues  one  day  in  the  year  on  the  stars,  by  its  direct  motion  in  longitude ; 
v>  the  equinox  f/a.'ns  one  day  in  25,868  years  on  them  by  its  retrograda- 
tion.  We  ought,  therefore,  as  carefully  to  distinguish  between  mean  and 
apparent  sidereal  as  between  mean  and  apparent  solar  time. 

(328.)  Neither  precession  nor  nutation  changes  the  apparent  places  of 
celestial  objects  inter  sc.     We  see  them,  so  far  as  these  causes  go,  as  they 
12 


d 


70 

tmvea 


i 


o 


178 


OUTLINES   OF  ASTRONOMY. 


|H 


are,  though  from  a  station  more  or  less  unstable,  as  we  see  distant  land 
objects  correctly  formed,  though  appearing  to  rise  and  fall  when  viewed 
from  the  heaving  deck  of  a  ship  in  the  act  of  pitching  and  rolling.  But 
there  is  an  optical  cause,  independent  of  refraction  or  of  perspective,  which 
displaces  them  otie  among  the  other,  and  causes  us  to  view  the  heavens 
under  an  aspect  always  to  a  certain  slight  extent  false ;  and  whose  in- 
fluence must  be  estimated  and  allowed  for  before  we  can  obtain  a  precise 
knowledge  of  the  place  of  any  object.  This  cause  is  what  is  called  the 
aberration  of  light )  a  singular  and  surprising  effect  arising  from  this,  that 
we  occupy  a  station  not  at  rest  but  in  rapid  motion )  and  that  the  apparent 
directions  of  the  rays  of  light  are  not  the  same  to  a  spectator  in  motion 
as  to  one  at  rest.  As  the  estimation  of  its  effect  belongs  to  uranography, 
we  must  explain  it  here,  though,  in  so  doing,  we  must  anticipate  some  of 
the  results  to  be  detailed  in  subsequent  chapters. 

(329.)  Suppose  a  shower  of  rain  to  fall  perpendicularly  in  a  dead  calm  j 
a  person  exposed  to  the  shower,  who  would  stand  quite  still  and  upright, 
would  receive  the  drop^  on  his  hat,  which  would  thus  shelter  him,  but  if 
he  ran  forward  in  any  direction  they  would  strike  him  in  the  face.  The 
effect  would  be  the  same  as  if  he  remained  still,  and  a  wind  should  arise 
of  the  same  velocity,  and  drift  them  against  him.     Suppose  a  ball  let  fall 


from  a  point  A  above  a  horizontal  line  E  F,  and  that  at  B  were  placed  to 
receive  it  the  open  mouth  of  an  inclined  hollow  tube  P  Q ;  if  the  tube 
were  held  immoveable  the  ball  would  strike  on  its  lower  side,  but  if  the 
tube  were  carried  forward  in  the  direction  E  F,  with  a  velocity  properly 
adjusted  at  every  instant  to  that  of  the  ball,  vi\x\\Q  preserving  its  inclina- 
fvm.  to  the  horizon,  so  that  when  the  ball  in  its  natural  descent  reached 
C,  the  tube  should  have  been  carried  into  the  position  R  S,  it  is  evident 
that  the  Imll  would,  throughout  its  whole  descent,  be  found  in  the  axis  of 


the  tube ; 
and  carrie 
that  the  b 
axis. 

(330.) 
we  considc 
a  shower  < 
it  us  abso 
from  the  p 
between  tl 
the  other 
them  to  a 
the  cross  y 
point  of  c 
pond  to  t 
area.  Th 
displacem( 

(331.) 
miles  per 
changing  \ 
a  velocity  ( 
that  of  tl 
traversing 
to  the  fori 
Suppose  n 
the  tube  ] 
formed  b 
evident  fn 
be  such  as 
1  :  tan.  2(j 
axis  of  tl 
must  be  2( 

(332.) 
earth's  mo 

•  This  con 
M.  Doppler 
boemischen 
the  luminifei 
render  of  thi 
least  in  the  £ 
At  the  point 
tain  either  tti 


ABERRATION   OF   LIGHT. 


179 


the  tube ;  and  a  spectator  referring  to  the  tube  the  motion  of  the  ball, 
and  carried  along  with  the  former,  unconscious  of  its  motion,  would  fancy 
that  the  bull  hud  been  moving  in  the  inclined  direction  K  S  of  the  tube's 
axis. 

(330.)  Our  eyes  and  telescopes  are  such  tubes.  In  whatever  manner 
we  consider  light,  whether  as  an  advancing  wave  in  a  motionless  ether,  or 
a  shower  of  atoms  traversing  space,  (provided  that  in  both  cases  we  regard 
it  as  absolutely  incapable  of  suffering  resistance  or  corporeal  obstruction 
from  the  particles  of  transparent  media  traversed  by  it,')  if  in  the  interval 
between  the  rays  traversing  the  object  glass  of  the  one  or  the  cornea  of 
the  other  (at  tchich  moment  they  acquire  that  convergence  which  directs 
them  to  a  certain  point  in  fixed  space),  and  their  arrival  at  their  focus, 
the  cross  wires  of  the  one  or  the  retina  of  the  other,  bo  dijvped  aside,  the 
point  of  convergence  (which  remains  unchanged)  will  no  longer  corres- 
pond to  the  intersection  of  the  wires  or  the  central  point  of  our  visual 
area.  The  object  then  will  appear  displaced ;  and  the  amount  of  this 
displacement  is  aberration. 

(331.)  The  earth  is  moving  through  space  with  a  velocity  of  about  19 
miles  per  second,  in  an  elliptic  path  round  the  sun,  and  is  therefore 
changing  the  '.  oction  of  its  motion  at  every  instant.  Light  travels  with 
a  velocity  of  192,000  miles  per  second,  which,  although  much  greater  than 
that  of  the  earth,  is  yet  not  infinitely  so.  Time  is  occupied  by  it  in 
traversing  any  space,  and  in  that  time  the  earth  describes  a  space  which  id 
to  the  former  as  19  to  192,000,  or  as  the  tangent  of  20"-5  to  radius. 
Suppose  now  A  P  S  to  represent  a  ray  of  light  from  a  star  at  A,  and  let 
the  tube  P  Q  be  that  of  a  telescope  so  inclined  forward  that  the  focus 
formsd  by  its  object-gJass  shall  be  received  upon  its  cross  wire,  it  is 
evident  from  what  has  been  said,  that  the  inclination  of  the  tube  must 
be  such  as  to  make  P  S  :  S  Q  : :  velocity  of  light :  velocity  of  the  earth  : : 
1  :  tan.  20" -5;  and,  therefore,  the  angle  S  PQ,  or  P  S  R,  by  which  the 
axis  of  the  telescope  must  deviate  from  the  true  direction  of  the  star, 
must  be  20"-5. 

(332.)  A  similar  reasoning  will  hold  good  when  the  direction  of  the 
earth's  motion  is  not  perpendicular  to  the  visual  ray.    If  S  B  be  the  true 

'  This  condition  is  indispensable.  Without  it  we  fall  into  all  those  difficulties  which 
M.  Doppler  has  so  well  pointed  out  in  his  paper  on  Aberration  (Abhandlungen  der  k. 
boemischen  Gesellschaft  der  Wissenschaften.  Folge  V.  vol.  iii.).  If  light  itself,  or 
the  luminiferous  ether,  be  corporeal,  the  condition  insisted  on  amounts  to  a  formal  sur- 
render of  the  dogma,  either  of  the  extension  or  of  the  impenetrability  of  matter ;  at 
least  in  the  sense  in  which  those  terms  have  been  hitherto  used  by  metaphysicians. 
At  the  point  to  which  science  is  arrived,  probably  few  will  be  found  disposed  to  main- 
tain cither  the  one  or  the  other. 


i 


O 


CO 

tumm 


180 


OUTLINES   OF   ASTRONOMY. 


Fig.  4? 


direction  of  the  visual  ray,  and  A  C  the  position  in  which  the  telcMope 
requires  to  be  held  in  the  apparent  direction,  we  must  still  have  the  pro- 
portion BO  :  B  A  :  :  velocity  of  light :  velocity  of  the  earth  : :  rad. : 
sine  of  20"-5  (for  in  such  small  angles  it  matters  not  whether  we  use  the 
sines  or  tangents).  But  we  have,  also,  by  trigonometry,  B  C  :  B  A  : : 
sine  of  BAG:  sine  of  A  C  B  or  C  B  D,  which  last  is  the  apparent  dis- 
placement caused  by  aberration.  Thus  it  appears  that  the  sine  of  the 
aberration,  or  (since  the  angle  is  extremely  smiill)  the  aberration  itself,  is 
proportional  to  the  sine  of  the  angle  ni.iJe  by  the  earth's  motion  in  space 
with  the  visual  ray,  and  is  therefore  a  maximum  when  the  line  of  sight  is 
perpendicular  to  the  direction  of  the  earth's  motion. 

(333.)  The  uranographical  effect  of  aberration,  then,  is  to  distort  the 
fispect  of  the  heavens,  causing  all  the  stars  to  crowd  as  it  were  directly 
towards  that  point  in  the  heavens  which  is  the  vanishing  point  of  all  lines 
parallel  to  that  in  which  the  earth  is  for  the  time  moving.  As  the  earth 
moves  round  the  sun  in  the  plane  of  the  ecliptic,  this  point  must  lie  in 
that  plane,  90"  in  advance  of  the  earth's  longitude,  or  90°  brhind  the 
sun's,  and  shifts  of  course  continually,  describing  the  circumference  of  the 
ecliptic  in  a  year.  It  is  easy  to  demonstrate  that  the  effect  on  each  par- 
ticular star  will  be  to  make  it  apparently  describe  a  small  ellipse  in  the 
heavens,  havui^  for  its  centre  the  point  in  which  the  st^r  would  be  seen 
if  the  earth  were  at  rest. 

(334.)  Aberration  then  affects  the  apparent  right  ascensions  and  decli- 
nations of  all  the  stars,  and  that  by  quantities  easily  calculable.  The 
formulae  most  convenient  for  that  purpose,  and  which,  systematically 
embracing  at  the  same  time  the  corrections  for  precessioit  and  nutation, 
enable  the  observer,  with  the  utmost  readiness,  to  disencumber  his  obser- 
vations of  right  ascension  and  declination  of  their  influence,  have  been 
constructed  by  Prof.  Bessel,  and  tabulated  in  the  appendix  to  the  first 
volume  of  the  Transactions  of  the  Astronomical  Society,  where  they  will 
be  found  accompanied  with  an  extensive  catalogue  of  the  places,  for  1830, 


of  the  prin 
of  the  kin( 

(886.) 

motion,  an 

it  is  usual 

confounded 

the  studen 

rttical  viev 

The  ray  b; 

moment  wt 

the  tinio  0( 

from  us. 

velocity  mi 

place  at  th( 

same  movi 

Hence  it  is 

case  of  a  i: 

earth's,  cal 

taken  hy  lu 

amount  of 

observed  in 

And  it  is  a 

which  is  thi 

of  the  cart 

inaptly  tern 

the  time  occ 

(386.)  T 
observation 
bndy  as  rea 
adjustment) 
refraction,  j 
correction  fo 

•The  resull 
aberration  are 
minute  diiferei 
gation  of  ligh 
be  at  rc8t  or  i 
tion  of  the  mo 
motion.  In  th 
ly  from  the  ea 
corpuscular  hy 
system  cannot 


ABERRATION   OP  LIGHT. 


181 


rttical  views  respecting  ih 
The  ray  by  which  wc 
njoment  wo  look  at  it.  bt. 
the  time  occupied  by  ligh 


of  the  principal  fixed  stars,  one  of  the  most  useful  and  best  arranged  works 
of  the  kind  which  has  over  appeared. 

(885.)  When  the  body  from  which  the  visual  ray  emanates  is  itself  in 
motion,  an  effect  arises  wliich  is  not  properly  speaking  aberration,  though 
it  is  usually  treated  under  that  head  in  astronomical  books,  and  indeed 
confounded  with  it,  to  the  production  of  some  confusion  in  the  mind  of 
the  student.     The  effect  in     Mcstion  (which  is  independent  of  any  theo- 

'0  of  light ')  may  be  explained  as  follows 
'"''t  is  not  that  which  it  emits  at  the 
it  did  emit  some  time  before,  m«., 
>  rsing  the  interval  which  separates  it 
from  us.  The  aberration  of  such  a  body  then  arising  from  the  earth's 
velocity  must  be  applied  as  a  correction,  not  to  the  line  joining  the  earth's 
place  at  the  moment  of  observation  with  that  occupied  by  the  body  at  the 
scnne  moment,  but  at  that  antecedent  instant  when  the  ray  quitted  it. 
Hence  it  is  easy  to  derive  the  rule  given  by  astronomical  writers  for  the 
case  of  a  moving  object.  From  tin-  known  lawn  of  its  motion  and  tlie 
earth's,  calcntatc  its  apjtarent  or  r-lative  amjxdar  motion  in  the  time 
taken  hy  li(/ht  to  traverse  its  distaiicr  from  the  earth.  This  is  the  total 
amount  of  its  apparent  dinp/arement.  Its  effect  is  to  displace  the  body 
observed  in  a  direction  contrary  to  its  apparent  motion  in  the  heavens. 
And  it  is  a  compound  or  aggregate  <'ffoct  consisting  of  two  parts,  one  of 
which  is  the  aberration,  properly  so  ciilicd,  resulting  from  the  composition 
of  the  earth's  motion  with  that  i»t  light,  the  other  being  what  is  not 
inaptly  termed  the  Equation  of  liyhf,  being  the  allowance  to  be  made  for 
the  time  occupied  by  the  light  in  traversing  a  variable  space. 

(386.)  Tho  conipleti  Reduction,  as  it  is  called,  of  an  astronomical 
observation  consists  in  applying  to  tho  place  of  the  observed  heavenly 
body  as  read  off  on  the  instruments  (supposed  perfect  and  in  perfect 
adjustment)  five  distinct  and  independent  corrections,  viz.  those  for 
refraction,  parallax,  aberration,  precession,  and  nutation.  Of  these  tho 
correction  for  refraction  enables  us  to  declare  what  would  have  been  the 

'  The  results  of  the  undulatory  and  corpuscular  theories  of  light,  in  the  matter  of 
aberration  are,  in  the  main,  the  satue.  We  say  in  the  main.  I'here  is,  however,  a 
minute  difference  even  of  numerical  results.  In  the  undulatory  doctrine,  the  propa- 
gation of  light  takes  place  with  equal  velocity  in  all  directions,  whether  the  luminary 
be  at  rest  or  in  motion.  In  the  corpuscular,  with  an  excess  of  velocity  in  the  direc- 
tion of  the  motion  over  that  in  the  contrary  equal  to  twice  the  velocity  of  the  body's 
motion.  In  the  cases,  then,  of  a  body  moving  with  equal  velocity  directly  to  and  direct- 
ly from  the  earth,  the  aberration  will  be  alike  on  the  undulatory,  but  different  on  the 
corpuscular  hypothesis.  7'he  utmost  difference  which  can  arise  from  this  cause  in  our 
tystem  cannot  amount  to  above  six  thousandths  of  a  second. 


< 

m 


o 


90 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


F.% 


V\^ 


1.0   ^ui  y£ 

•»  itt  111 


1.1 


£  IS2   12.0 


1^        Ui^ 

ll^lilil^li^ 


^ 


^^ 


^/ 


'/ 


FholDgraphic 

Sciences 

Carporation 


33  WIIT  MAM  STRHT 

WltSTIR,N.Y.  14SI0 

(716)  •73-4303 


'^ 


182 


OUTLINES  ^F  ASTRONOMY. 


I'  t. 


observed  place,  were  there  no  atmosphere  to  displace  it.  That  for  parol- 
lax  enables  us  to  say  from  its  place  observed  at  the  surface  of  the  earth, 
where  it  would  have  been  seen  if  observed  from  the  centre.  That  for 
aberration,  where  it  would  have  been  observed  from  a  motionless,  instead 
of  a  moving  station :  while  the  corrections  for  precession  and  nutation 
refer  it  to  fixed  and  determinate  instead  of  constantly  varying  celestial 
circles.  The  great  importance  of  these  corrections,  which  pervade  all 
astronomy,  and  have  to  be  applied  to  every  observation  before  it  can  be 
employed  for  any  practical  or  theoretical  purpose,  renders  this  recapitula- 
tion far  from  superfluous. 

(337.)  Refraction  has  been  already  sufficiently  explained.  Art.  40,  and 
it  is  only,  therefore,  necessary  here  to  add  that  in  its  use  as  an  astronomi- 
cal correction  its  amount  must  be  applied  in  a  contrary  sense  to  that  in 
which  it  affects  the  observation;  a  remark  equally  applicable  to  all  other 
corrections. 

(838.)  The  general  nature  of  parallax  or. rather  of  parallactic  motion 
has  also  been  explained  in  Art.  80.  But  parallax  in  the  uranographical 
sense  of  the  word  has  a  more  technical  meaning.  It  is  understood  to 
express  that  optical  displacement  of  a  body  observed  which  is  due  to  its 
being  observed,  not  from  that  point  which  we  have  fixed  upon  as  a  con- 
ventional central  station  (from  which  we  conceive  the  apparent  motion 
would  be  more  simple  in  its  laws,)  but  from  some  other  station  remote 
from  such  conventional  centre:  not  from  the  centre  of  the  earth,  for 
instance,  but  from  its  surface :  not  from  the  centre  of  the  sun  (which,  as 
we  shall  hereafter  see,  is  for  some  purposes  a  preferable  conventional 
station),  but  from  that  of  the  earth.  In  the  former  case  this  optical  dis- 
placement is  called  the  diurnal  or  geocentric  parallax ;  in  the  latter  the 
annual  or  heliocentric.  In  either  case  parallax  is  the  correction  to  be 
applied  to  the  apparent  place  of  the  heavenly  body,  as  actually  seen  from 
the  station  of  observation,  to  reduce  it  to  its  place  as  it  would  have  been 
seen  at  that  instant  from  the  conventional  station. 

(339.)  The  diurnal  or  geocentric  parallax  at  any  place  of  the  earth's 
surface  is  easily  calculated  if  we  know  the  distance  of  the  body,  and,  vice 
vend,  if  we  know  the  diurnal  parallax  that  distance  may  be  calculated. 
For  supposing  S  the  object,  0  the  centre  of  the  earth,  A  the  station  of 
observation  at  its  surface,  and  C  A  Z  the  direction  of  a  perpendicular  to 
the  surface  at  A,  then  will  the  object  be  seen  from  A  in  the  direction  A 
S,  and  its  apparent  zenith  distance  will  be  Z  A  S ;  whereas,  if  seen  from 
the  centre,  it  will  appear  in  the  direction  C  S,  with  an  angular  distance 
from  the  zenith  of  A  equal  to  Z  C  S;  so  that  Z  A  S  — Z  C  S  or  A  S  C 
is  the  parallax.    Now  since  by  trignometry  C  S  :  C  A  : :  sin  C  A  S 


1,:^ 


or  parol- 
be  earth, 
That  for 
,  instead 
nutation 
celestial 
vade  all 
it  can  be 
icapitula- 

.  40,  and 
itronomi- 
o  that  in 
all  other 

Ic  motion 
graphical 
rstood  to 
iue  to  its 
as  a  con- 
kt  motion 
n  remote 
earth,  for 
which,  as 
iventional 
ptical  dis- 
latter  the 
ion  to  be 
seen  from 
lave  been 

e  earth's 
and,  vice 
calculated, 
station  of 
dicular  to 
rcction  A 
seen  from 
r  distance 
or  ASC 
in  C  A  S 


SUMMABT  OF  URANOaRAPHIOAL  CORRECTIONS. 

Fig.  50. 


188 


=  sin  Z  A  S  :  sin  A  S  0,  it  follows  that  the  sice  of  the  parallax 
Radius  of  earth  ^    *    7  4  Q 

Distance  of  body  *  ,       \  •  ; 

(340.)  The  diurnal  or  geocentric  parallax,  therefore,  at  a  given  place, 
and  for  a  given  distance  of  the  body  observed,  is  proportional  to  the  sine 
of  its  apparent  zenith  distance,  and  is,  therefore,  the  greatest  when  the 
body  is  observed  in  the  act  of  rising  or  setting,  in  which  case  its  parallax 
is  called  its  horizontal  parallax,  so  that  at  any  other  zenith  distance, 
parallax  =  horizontal  parallax  X  sine  of  apparent  zenith  distance,  and 
since  A  C  S  is  always  less  than  Z  A  S  it  appears  that  the  application  of 
the  reduction  or  correction  for  parallax  always  acts  in  diminution  of  the 
apparent  zenith  distance  or  increase  of  the  apparent  altitude  or  distance 
from  the  Nadir,  t.  e.  in  a  contrary  sense  to  that  for  refraction. 

(341.)  In  precisely  the  same  manner  as  the  geocentric  or  diurnal 
parallax  refers  itself  to  the  zenith  of  the  observer  for  its  direction  and 
quantitative  rule,  so  the  heliocentric  or  annual  parallax  refers  itself  for  its 
law  to  the  point  in  the  heavens  diametrically  opposite  to  the  place  of  the 
sun  as  seen  from  the  earth.  Applied  as  a  correction,  its  effect  takes  place 
in  a  plane  passing  through  the  sun,  the  earth,  and  the  observed  body. 
Its  effect  is  always  to  decrease  its  observed  distance  from  that  point  or  to 
increase  its  angular  distance  from  the  sun.  And  its  sine  is  given  by  the 
relation.  Distance  of  the  observed  body  from  the  sun  :  distance  of  the 
earth  from  the  sun  : :  sine  of  apparent  angular  distance  of  the  body  from 
the  sun  (or  its  apparent  elongation)  :  sine  of  heliocentric  parallax.' 

'  This  account  of  the  law  of  heliocentric  parallax  is  in  anticipation  of  what  follows  in 
a  subsequent  chapter,  and  will  be  better  understood  by  the  student  when  somewhat 
farther  advanced. 


mnpq 

o 

""si 


o 


184 


OUTLINES  OF  ASTRONOMT. 


(342.)  On  a  summary  view  of  the  whole  of  the  uranographical  correc- 
tions, they  divide  themselves  into  two  classes,  those  which  do,  and  those 
which  do  not,  alter  the  apparent  configurations  of  the  heavenly  bodies 
inter  se.  The  former  are  real,  the  latter  technical  corrections.  The  real 
corrections  are  refraction,  aberration  and  parallax.  The  technical  are  pre- 
cession and  nutation,  unless,  indeed,  we  choose  to  consider  parallax  as  a 
technical  correction  introduced  with  a  view  to  simplification  by  a  better 
choice  of  our  point  of  sight. 

(348.)  The  corrections  of  the  first  of  these  classes  have  one  peculiarity 
in  respect  of  their  law,  common  to  them  all,  which  the  student  of  prac- 
tical astronomy  will  do  well  to  fix  in  his  memory.  Thet/  all  refer  them- 
selves to  definite  apexes  or  points  of  convergence  in  the  sphere.  Thus, 
refraction  in  its  apparent  effect  causes  all  celestial  objects  to  draw  together 
or  converge  towards  the  zenith  of  the  observer:  geocentric  parallax, 
towards  his  Nadir:  heliocentric,  towards  the  place  of  the  sun  in  the 
heavens :  aberration  towards  that  point  in  the  celestial  sphere  which  is 
the  vanishing  point  of  all  lines  parallel  to  the  direction  of  the  earth's 
motion  at  the  moment,  or  (as  will  be  hereafter  explained)  towards  a  point 
in  the  great  circle  called  the  ecliptic,  90°  behind  the  sun's  place  in  that 
circle.  When  applied  as  corrections  ^  an  observation,  these  directions 
are  of  course  to  be  reversed. 

(344.)  In  the  quantitative  law,  too,  which  this  class  of  corrections 
follow,  a  like  agreement  takes  place,  at  least  as  regards  the  geocentric  and 
heliocentric  parallax  and  aberration,  in  all  three  of  which  the  amount  of 
the  correction  (or  more  strictly  its  sine)  increases  in  the  direct  proportion 
of  sine  of  the  apparent  distance  of  the  observed  body  from  the  apex 
aj,^  ..^riate  to  the  particular  correction  in  question.  In  the  case  of  re- 
fraction the  law  is  less  simple,  agreeing  more  nearly  with  the  tangent  than 
the  sine  of  that  distance,  but  agreeing  with  the  others  in  placing  the 
maximum  at  90°  from  its  apex. 

(345.)  As  respects  the  order  in  which  these  corrections  are  to  be 
applied  to  any  observation,  it  is  as  follows :  1.  Refraction;  2.  Aberration; 
3.  Geocentric  Parallax;  4.  Heliocentric  Parallax;  5.  Nutation;  6.  Pre- 
cession. Such,  at  least,  is  the  order  in  theoretical  strictness.  But  as  the 
amount  of  aberration  and  nutation  is  in  all  cases  a  very  minute  quantity, 
it  matters  not  in  what  order  they  arc  applied ;  so  that  for  practical  conve- 
nience they  are  always  thrown  together  with  the  preceraion,  and  applied 
after  the  others. 


APPAREN 
UIAME' 
CLUDEl 

—  LAy 
AREAS. 
TUDE.  - 
MOTIOf 

—  HEA 
ORBIT. 
OP  THE 

—  PHYf 

—  PROl 
OP  Till 
8URPAC 
OP   SOL. 

(346.) 

path  of  tl 
period  of  ( 
the  earth 
whatever  1 
must  be  c( 
(347.) 
ascension 
by  the  obi 
in  longituc 
if  we  ob» 
transit  and 
wUl  still  b 
motion  is 
mean  solai 


;»  iriiii-f 


OP  THE  sun's  motion. 


185 


CHAPTER  VI. 


«f  '      OF    THE    SUN   S    MOTION. 

APPARENT  MOTION  OP  THE  SUN  NOT  UNIFORM.  —  ITS  APPARENT 
DIAMETER  ALSO  VARIABLE.  —  VARIATION  OP  ITS  DISTANCE  CON- 
CLUDED.—  ITS    APPARENT    ORBIT  AN    ELLIPSE  ABOUT  THE    FOCUS. 

—  LAW  OF  THE  ANGULAR  VELOCITY.  —  EQUABLE  DESCRIPTION  OP 
AREAS.  —  PARALLAX  OP  THE  SUN.  —  ITS  DISTANCE  AND  MAGNI- 
TUDE. —  COPERNICAN  EXPLANATION  OP  THE  SUN'S  APPARENT 
MOTION. — PARALLELISM   OP  THE  EARTH'S  AXIS. — THE    SEASONS. 

—  HEAT  RECEIVED  FROM  THE  SUN  IN  DIFFERENT  PARTS  OF  THE 
ORBIT. — MEAN  AND  TRUE  LONGITUDES  OP  THE  SUN. — EQUATION 
OP  THE  CENTRE. — SIDEREAL,   TROPICAL,   AND  ANOMALISTIC  YEARS. 

—  PHYSICAL   CONSTITUTION   OF  THE   SUN.  —  ITS   SPOTS. — FACUL^. 

—  PROBABLE   NATURE   AND   CAUSE    OF   THE    SPOTS. ATMOSPHERE 

OP  THE  SUN. — ITS  SUPPOSED  CLOUDS.  —  TEMPERATURE  AT  ITS 
SURFACE. — ITS  EXPENDITURE  OF  HEAT.  —  TERRESTRIAL  EFFECTS 
OF   SOLAR  RADIATION. 

(346.)  In  the  foregoing  chapters,  it  has  been  shown  that  the  apparent 
path  of  the  sun  is  a  great  circle  of  the  sphere,  which  it  performs  in  a 
period  of  one  sidereal  year.  From  this  it  follows,  that  the  line  joining 
the  earth  and  sun  lies  constantly  in  one  plane;  and  that,  therefore, 
whatever  be  the  real  motion  from  which  this  apparent  motion  arises,  it 
must  be  confined  to  one  plane,  which  is  called  the  plane  of  the  ecliptic. 

(347.)  We  have  already  seen  (art.  146)  that  the  sun's  motion  in  right 
ascension  among  the  stars  is  not  uniform.  This  is  partly  accounted  for 
by  the  obliquity  of  the  ecliptic,  in  consequence  of  which  equal  variations 
in  longitude  do  not  correspond  to  equal  changes  of  right  ascension.  But 
if  we  observe  the  place  of  the  sun  daily  throughout  the  year,  by  the 
transit  and  circle,  and  from  these  calculate  the  longitude  for  each  day,  it 
will  still  be  found  that,  even  in  its  own  proper  path,  its  apparent  angular 
motion  is  far  from  uniform.  The  change  of  longitude  in  twenty-four 
mean  solar  hours  averages  0°  59'  8''-33 ;  but  about  the  31st  of  Decern- 


z 

m 

o 


HKWJ 

rn 

g«ar- 


c;? 


186 


OUTLINES  OF  ASTRONOMY. 


t 


ber  it  amounts  to  1°  1'  9"-9,  and  about  the  Ist  of  July  is  only  0"  57' 
ll"-5.  Such  are  the  extreme  limits,  and  such  the  mean  value  of  the 
sun's  apparent  angular  velocity  in  its  annual  orbit. 

(348.)  This  variation  of  its  angular  velocity  is  accompanied  with  r>, 
corresponding  change  of  its  distance  from  us.  The  change  of  distance  is 
recognized  by  a  variation  observed  to  take  place  in  its  apparent  diameter, 
when  measured  at  different  seasons  of  the  year,  with  an  instrument 
adapted  for  that  purpose,  called  the  heliometer,^  or,  by  calculating  from 
the  time  which  its  disc  takes  to  traverse  the  meridian  in  the  transit 
instrument.  The  greatest  apparent  diameter  corresponds  to  the  1st  of 
December,  or  to  the  greatest  angular  velocity,  and  measures  32'  35"-6, 
the  least  is  31'  31"'0;  and  corresponds  to  the  1st  of  July;  at  which 
epochs,  as  we  have  seen,  the  angular  motion  is  also  at  its  extreme  limit 
either  way.  Now,  as  we  cannot  suppose  the  sun  to  alter  its  real  size 
periodically,  the  observed  change  of  its  apparent  size  can  only  arise  from 
an  actual  change  of  distance.  And  the  sines  or  tangents  of  such  small 
arcs  being  proportional  to  the  arcs  themselves,  its  distances  from  us,  at 
the  above-named  epoch,  must  be  in  the  inverse  proportion  of  the  apparent 
diameters.  It  appears,  therefore,  that  the  greatest,  the  mean,  and  the 
least  distances  of  the  sun  from  us  are  in  the  respective  proportions  of  the 
numbers  101679,  1.00000,  and  0-98321;  and  that  its  apparent  angular 
velocity  diminishes  as  the  distance  increases,  and  vice  versd. 

(349.)  It  follows  from  this,  that  the  real  orbit  of  the  sun,  as  referred 
to  the  earth  supposed  at  rest,  is  not  a  circle  with  the  earth  in  the  centre. 
The  situation  of  the  earth  within  it  is  excentrtc,  the  excentricity  amount- 
ing to  001679  of  the  mean  distance,  which  may  be  regarded  as  our  unit 
of  measure  in  this  inquiry.  But  besides  this,  the  form  of  the  orbit  is 
not  circular,  but  elliptic.  If  from  any  point  O,  taken  to  represent  th^ 
earth,  we  draw  a  line,  0  A,  in  some  fixed  direction,  from  which  we  then 


rfti;    (■-'■(.'«<? 


■r' 


\ 


tricity, 


Bet  off  a  series  of  angles,  A  O  B,  A  0  0,  &o.  equal  to  the  observed  longi- 
tudes of  the  sun  throughout  the  year,  and  in  these  respective  directions 


-i»ri*:^  ■■ 


1r 


'  'HAio(  the  sun,  and  lurpttv  to  measure. 


FORM   OF  THE  SUN'S  AFPABENT  ORBIT. 


187 


■-.  i  ■■ 


i*^ 


measure  off  from  0  the  distances  0  A,  0  B,  0  C,  &c.  representing  the 
distances  deduced  from  the  observed  diameter,  and  then  connect  all  the 
extremities  A,  B,  C,  &c.  of  these  lines  by  a  continuous  cirve,  it  is  evident 
this  will  be  a  correct  representation  of  the  relative  orbit  of  the  sun  about 
the  earth.  Now,  when  this  is  done,  a  deviation  from  the  circular  figure 
in  the  resulting  curve  becomes  apparent;  it  is  found  to  be  evidently  longer 
than  it  is  broad  —  that  is  to  say,  elliptic,  and  the  point  0  to  occupy,  not 
the  centre,  but  one  of  the  foci  of  the  ellipse.  The  graphical  process  here 
described  is  sufficient  to  point  out  the  general  figure  of  the  curve  in  ques- 
tion ;  but  for  the  purposes  of  exact  verification,  it  is  necessary  to  recur  to 
the  properties  of  the  ellipse,'  and  to  express  the  distance  of  any  one  of 
its  points  in  terms  of  the  angular  situation  of  that  point  with  respect  to 
the  longer  axis,  or  diameter  of  the  ellipse.  This,  however,  is  readily 
done ;  and  when  numerically  calculated,  on  the  supposition  of  the  excen- 
tricity,  being  such  as  above  stated,  a  perfect  coincidence  is  found  to 
subsist  between  the  distances  thus  computed,  and  those  derived  from  the 
measurement  of  the  apparent  diameter. 

(350.)  The  mean  distance  of  the  earth  and  sun  being  taken  for  unity, 
the  extremes  are  1-01679  and  0*98321.  But  if  we  compare,  in  like 
manner,  the  mean  or  average  angular  velocity  with  the  extremes,  greatest 
and  least,  we  shall  find  these  to  be  in  the  proportions  of  1*03386, 1*00000, 
and  0*96670.  The  variation  of  the  sun's  angular  velocity,  then,  is  much 
greater  in  proportion  than  that  of  its  distance  —  fully  twice  as  great ;  and 
if  we  examine  its  numerical  expressions  at  different  periods,  comparing 
them  with  the  mean  value,  and  also  with  the  corresponding  distances,  it 
will  be  found,  that,  by  whatever  fraction  of  its  mean  value  the  distance 
exceeds  the  mean,  the  angular  velocity  will  fall  short  of  its  mean  or  ave- 
rage quantity  by  very  nearly  twice  as  great  a  fraction  of  the  latter,  and 
vice  versd.  Hence  we  are  led  to  conclude  that  the  angular  vrlocity  is  in 
the  inverse  proportion,  not  of  the  distance  simply,  but  of  its  square ;  so 
that,  to  compare  the  daily  motion  in  longitude  of  the  sun,  at  one  point, 
A,  of  its  path,  with  that  at  B,  we  must  state  the  proportion  thus :  — 

0  B'  :  0  A'  : :  daily  motion  at  A  :  daily  motion  at  B.  And  this  is 
found  to  be  exactly  verified  in  every  part  of  the  orbit. 

(851.)  Hence  we  deduce  another  remarkable  conclusion  —  viz.  that  if 
the  sun  be  supposed  really  to  move  around  the  circumference  of  this 
ellipse,  its  actual  speed  cannot  be  uniform,  but  must  be  greatest  at  its 
least  distance  and  less  at  its  greatest..    For,  were  it  uniform,  the  apparent 

•  See  Conic  Sections,  by  the  Rev.  H.  P.  Hamilton,  or  any  other  of  the  very 
numerous  works  on  this  subject. 


ISO 


188 


OUTLINES   OF   ASTRONOMY. 


angular  velocity  would  bo,  of  course,  inversely  proportional  to  the  distance ; 
simply  because  the  same  linear  change  of  place,  being  produced  in  the 
same  time  at  different  distances  from  the  eye,  must,  by  the  laws  of  per- 
spective, correspond  to  apparent  angular  displacements  inversely  as  those 
distances.  Since,  then,  observation  indicates  a  more  rapid  law  of  varia- 
tion in  the  angular  velocities,  it  is  evident  that  mere  change  of  distance, 
unaccompanied  with  a  change  of  actual  speed,  is  insufficient  to  account  for 
it;  and  that  the  increased  proximity  of  the  sun  to  the  earth  must  be 
accompanied  with  an  actual  increase  of  its  real  velocity  of  motion  along 
its  path. 

(352.)  This  elliptic  form  of  the  sun's  path,  the  excentric  position  of 
the  earth  within  it,  and  the  unequal  speed  with  which  it  is  actually 
traversed  by  the  sun  itself,  all  tend  to  render  the  calculation  of  its  longi- 
tude from  theory  (i.  e.  from  a  knowledge  of  the  causes  and  nature  of  its 
motion)  difficult;  and  indeed  impossible,  so  long  as  the  law  of  its  actual 
velocity  continues  unknown.  This  law,  however,  is  not  immediately 
apparent.  It  docs  not  come  forward,  as  it  were,  and  present  itself  at  once, 
like  the  elliptic  form  of  the  orbit,  by  a  direct  comparison  of  angles  and 
distances,  but  requires  an  attentive  consideration  of  the  whole  scries  of 
observations  registered  during  an  entire  period.  It  was  not,  theiefore, 
without  much  painful  and  laborious  calculation,  that  it  was  discovered  by 
Kepler  (who  was  also  the  first  to  ascertain  the  elliptic  form  of  the  orbit), 
and  announced  in  the  following  terms :  —  Let  a  line  be  always  supposed 
to  connect  the  sun,  supposed  in  motion,  with  the  earth,  supposed  at  rest ; 
then,  as  the  sun  moves  along  its  ellipse,  this  line  (which  is  called  in  astro- 
nomy the  radius  vector)  will  describe  or  sweep  over  that  portion  of  the 
whole  area  or  surface  of  the  ellipse  which  is  included  between  its  consec- 
utive positions  :  and  the  motion  of  the  sun  will  be  such  that  equal  areas 
are  thus  swept  over  by  the  revolving  radius  vector  in  equal  timeSf  in  what- 
ever part  of  the  circumference  of  the  ellipse  the  sun  may  be  moving. 

(353.)  From  this  it  necessarily  follows,  that  in  unequal  times,  the  areas 
described  must  be  proportional  to  the  times.  Thus,  in  the  figure  of  art. 
349,  the  time  in  which  the  sun  moves  from  A  to  B,  is  to  the  time  in 
which  it  moves  from  C  to  D,  as  the  area  of  the  elliptic  sector  A  0  B  is  to 
the  area  of  the  sector  DOC. 

(354.)  The  circumstances  of  the  sun's  apparent  annual  motion  may, 
therefore,  be  summed  up  as  follows : — It  is  performed  in  an  orbit  lying  in 
one  plane  passing  through  the  earth's  centre,  called  the  plane  of  the  ecliptic, 
and  whose  projection  on  the  heavens  is  the  great  circle  so  called.  In  this 
plane,  however,  the  actual  path  is  not  circular,  but  elliptical ;  having  the 
earth;  not  in  its  centre,  but  in  one  focus.    The  excentricity  of  this  ellipse 


is  00167 
Imiffcr  di( 
diameter ; 
that  equa 
equal  tim( 
(355.) 
actual  dis 
sions  of  i 
conclusioni 
arrive  at  a 
access, 
formation 
its  centre, 
which  com 
serving  the 
direction  1 
sphere  of  t 
and  refer 


measure  of 
angle  A  S I 
and  B,  witl 
it  is  evideni 
(art.  339)  i 
from  B,  the 
of  the  two 
northern,  tl 
meridian,  tc 
centre.  Hi 
them  of  thi 
to  that  of 
would  be  pi 
the  places  o 


DISTANCE  OF  THE  SUN. 


189 


istanoe ; 
I  in  the 
>  of  per- 
as  those 
[)f  varia- 
distance, 
lount  for 
must  be 
)Q  along 

sition  of 
actually 
its  longi- 
irc  of  its 
its  actual 
aediately 
'  at  once, 
igles  and 
series  of 
iherefore, 
vered  by 
orbit), 
supposed 
at  rest ; 
in  astro- 
of  the 
consec- 
,al  areas 
in  what- 
ing. 

he  areas 
of  art 
time  in 
)Bisto 

)n  may, 
lying  in 
ecliptic, 
In  this 
ng  the 
ellipse 


is  0*01679,  in  parts  of  a  unit  equal  to  the  meon  distance,  or  half  the 
Imujcr  diameter  of  the  ellipse;  i.  e.  about  one  sixtieth  part  of  that  semi- 
diauieter ;  and  the  motion  of  the  sun  in  its  circumference  is  so  regulated| 
that  equal  areas  of  the  ellipse  are  passed  over  by  the  radius  vector  in 
equal  times.  ' 

(855.)  What  we  have  here  stated  supposes  no  knowledge  of  the  sun's 
actual  distance  from  the  earth,  nor,  consequently,  of  the  actual  dimen- 
sions of  its  orbit,  nor  of  the  body  of  the  sun  itself.  To  come  to  any 
conclusions  on  these  points,  we  must  first  consider  by  what  means  we  can 
arrive  at  any  knowledge  of  the  distance  of  an  object  to  which  we  have  no 
access.  Now,  it  is  obvious,  that  its  parallax  alone  can  afford  us  any  in- 
formation on  this  subject.  Suppose  P  A  B  Q  to  represent  the  earth,  C 
its  centre,  and  S  the  sun,  and  A,  B  two  situations  of  a  spectator,  or, 
which  comes  to  the  same  thing,  the  stations  of  two  spectators,  both  ob- 
serving the  sun  S  at  the  same  instant.  The  spectator  A  will  see  it  in  the 
direction  A  S  a,  and  will  refer  it  to  a  point  a  in  the  infinitely  distant 
sphere  of  the  stars,  while  the  spectator  B  will  see  it  in  the  direction  B  S  6, 
and  refer  it  to  h.     The  angle  included  between  these  directions,  or  the 

Fig.  52. 


measure  of  the  <  elestial  are  ah,  by  which  it  is  displaced,  is  equal  to  the 
angle  A  S  B ;  and  if  this  angle  be  known,  and  the  local  situations  of  A 
and  B,  with  the  part  of  the  earth's  surface  A  B  included  between  them, 
it  is  evident  that  the  distance  C  S  may  be  calculated.  Now,  ^ince  A  S  C 
(art.  339)  is  the  parallax  of  the  sun  as  seen  from  A,  and  B  S  C  as  seen 
from  B,  the  angle  A  S  B,  or  the  total  apparent  displacement  is  the  sum 
of  the  two  parallaxes.  Suppose,  then,  two  observers  —  one  in  the 
northern,  the  other  in  the  southern  hemisphere — at  stations  on  the  same 
meridian,  to  observe  on  the  same  day  the  meridian  altitudes  of  the  sun's 
centre.  Having  thence  derived  the  apparent  zenith  distances,  and  cleared 
them  of  the  effects  of  refraction,  if  the  distance  of  the  sun  were  equal 
to  that  of  the  fixed  stars,  the  sum  of  the  zenith  distances  thus  found 
would  be  precisely  equal  to  the  sum  of  the  laLltudes  north  and  south  of 
the  places  of  observation.    For  the  sum  in  question  would  then  be  equal 


*l 


/ 


M  f; 


55 


c^ 


190 


OUTLINES   OF  ASTRONOMY. 


i  'iHi 


to  the  angle  ZCX,  which  is  the  meridional  distance  of  the  stations 
across  the  equator.  But  the  effect  of  parallax  being  in  both  cases  to  in- 
crease  the  apparent  zenith  distances,  their  observed  sum  will  be  greater 
than  the  sum  of  the  latitudes,  by  the  sum  of  the  two  parallaxes,  or  by  the 
angle  A  S  B.  This  angle,  then,  is  obtained  by  subducting  the  sum  of 
the  north  and  south  latitudes  from  that  of  the  zenith  distances ;  and  this 
once  determined,  the  horizontal  parallax  is  easily  found,  by  dividing  the 
angle  so  determined  by  the  sum  of  the  sines  of  the  two  latitudes. 

(856.)  If  the  two  stations  be  not  exactly  on  the  same  meridian  (a  con- 
dition very  difficult  to  fulfil),  the  same  process  will  apply,  if  we  take  care 
to  allow  for  the  change  of  the  sun's  actual  zenith  distance  in  the  interval 
of  time  elapsing  between  its  arrival  on  the  meridians  of  the  stations.  This 
change  is  readily  ascertained,  either  from  tables  of  the  sun's  motion, 
grounded  on  the  experience  of  a  long  course  of  observations,  or  by  actual 
observation  of  its  meridional  altitude  on  several  days  before  and  after  that 
on  which  the  observations  for  parallax  are  taken.  Of  course,  the  nearer 
the  stations  are  to  each  other  in  longitude,  the  less  is  this  interval  of  time, 
and,  consequently,  the  smaller  the  amount  of  this  correction ;  and,  there- 
fore, the  less  injurious  to  the  accuracy  of  the  final  result  is  any  uncertainty 
in  the  daily  change  of  zenith  distance  which  may  arise  from  imperfection 
in  the  solar  tables,  or  in  the  observations  made  to  determine  it. 

(357.)  The  horizontal  parallax  of  the  sun  has  been  concluded  from 
observations  of  the  nature  above  described,  performed  in  stations  the  most 
remote  from  each  other  in  latitude,  at  which  observatories  have  been  in- 
stituted. It  has  also  been  deduced  from  other  methods  of  a  more  refined 
nature,  and  susceptible  of  much  greater  exactness,  to  be  hereafter  de- 
scribed. Its  amount  so  obtained,  is  about  8" -6.  Minute  as  this  quan- 
tity is,  there  can  be  no  doubt  that  it  is  a  tolerably  correct  approximation 
to  the  truth ;  and  in  conformity  with  it,  we  must  admit  the  sun  to  be 
situated  at  a  mean  distance  from  us,  of  no  less  than  23984  times  the 
length  of  the  earth's  radius,  or  about  95000000  miles. 

(358.)  That  at  so  vast  a  distance  the  sun  should  appear  to  us  of  the 
size  it  does,  and  should  so  powerfully  influence  our  condition  by  its  heat 
and  light,  requires  us  to  form  a  very  grand  conception  of  its  actual  mag- 
nitude, and  of  the  scale  on  which  those  important  processes  are  carried  on 
within  it,  by  which  it  is  enabled  to  keep  up  its  liberal  and  unceasing 
supply  of  these  elements.  As  to  its  actual  magnitude  we  can  be  at  no 
loss,  knowing  its  distance,  and  the  angles  under  which  its  diameter  appears 
to  us.  An  object,  placed  at  the  distance  of  95000000  miles,  and  sub- 
tending an  angle  of  32'  3",  must  have  a  real  diameter  of  882000  miles. 
Such,  then,  is  the  diameter  of  this  stupendous  globe.    If  we  compare  it 


with  wha 

shall  fine 

lU^to 

(859.) 

object  of 

some  con 

the  sun  ii 

tare  and 

dark  spot 

by  attend 

tained  th 

plane  of  t 

and  in  th 

west  to  ei 

slower  an 

dimension 

similar  m 

the  existe 

exact  proj 

the  attribi 

lation  roui 

one  hand, 

visible  tie 

alune  in  t 

masses  by 

between  t 

them  be  g 

be  propon 

the  smalle 

paratively 

(360.) 

earth,  or  1 

ference,  so 

posed  sufi 

displaceme 

so  or  not  i 

measurabh 

this,  that  1 

orbit  of  th 

comparisor 

in  conform 


m 


THE  earth's  annual  MOTION. 


191 


stations 
ses  to  in- 
>e  greater 
or  by  the 
I  sum  of 

and  this 
iding  the 

IS. 

m  (a  con- 
take  care 
le  interval 
ns.    This 
s  motion, 
by  actual 
after  that 
the  nearer 
al  of  time, 
tnd,  there- 
uncertainty 
t  perfection 

ided  from 

3  the  most 

e  been  in- 

ire  refined 

•eafter  de- 

his  quan- 

oximation 

san  to  be 

times  the 

us  of  the 
y  its  heat 
itual  mag- 
carried  on 
unceasing 
Q  bo  at  no 
er  appears 
,  and  sub- 
lOO  miles, 
ompare  it 


with  what  we  have  already  ascertained  of  the  dimensions  of  our  ovro,  we 
shall  find  that  in  linear  magnitude  it  exceeds  the  earth  in  the  proportion 
111^  to  1,  and  in  bulk  in  that  of  1884472  to  1. 

(859.)  It  is  hardly  possible  to  avoid  associating  our  conception  of  an 
object  of  definite  globular  figure,  and  of  such  enormous  dimensions,  with 
some  corresponding  attribute  of  massiveness  and  material  solidity.  That 
the  sun  is  not  a  mere  phantom,  but  a  body  having  its  own  peculiar  struc- 
ture and  economy,  our  telescopes  distinctly  inform  us.  They  show  us 
dark  spots  on  its  surface,  which  slowly  change  their  places  and  forms,  and 
by  attending  to  whose  situation,  at  different  times,  astronomers  have  ascer- 
tained that  the  sun  revolves  about  an  axis  nearly  perpendicular  to  the 
plane  of  the  ecliptic,  performing  one  rotation  in  a  period  of  about  25  days, 
and  in  the  same  direction  with  the  diurnal  rotation  of  the  earth,  i.  e.  from 
west  to  east.  Here,  then,  we  have  an  analogy  with  our  own -globe;  the 
slower  and  more  majestic  movement  only  corresponding  with  the  greater 
dimensions  of  the  machinery,  and  impressing  us  with  the  prevalence  of 
similar  mechanical  laws,  and  of,  at  least,  such  a  community  of  nature  as 
the  existence  of  inertia  and  obedience  to  force  may  argue.  Now,  in  the 
exact  proportion  in  which  we  invest  our  idea  of  this  immense  bulk  with 
the  attribute  of  inertia,  or  weight,  it  becomes  difficult  to  conceive  its  circu- 
lation round  so  comparatively  small  a  body  as  the  earth,  without,  on  the 
one  hand,  dragging  it  along,  and  displacing  it,  if  bound  to  it  by  some  in- 
visible tie )  or,  on  the  other  hand,  if  not  so  held  to  it,  pursuing  its  course 
alone  in  space,  and  leaving  the  earth  behind.  If  we  connect  two  sdlid 
masses  by  a  rod,  and  fling  them  aloft,  we  see  them  circulate  about  a  point 
between  them,  which  is  their  common  centre  of  gravity ;  but  if  one  of 
them  be  greatly  more  ponderous  than  the  other,  this  common  centre  will 
be  proportionally  nearer  to  that  one,  and  even  within  its  surface ;  so  that 
the  smaller  one  will  circulate,  in  fact,  about  the  larger,  which  will  be  com- 
paratively but  little  disturbed  from  its  place. 

(360.)  Whether  the  earth  move  round  the  sun,  the  sun  round  the 
earth,  or  both  round  their  common  centre  of  gravity,  will  make  no  dif- 
ference, so  far  as  appearances  are  concerned,  provided  the  stars  be  sup- 
posed sufficiently  distant  to  undergo  no  sensible  apparent  parallactic 
displacement  by  the  motion  so  attributed  to  the  earth.  Whether  they  are 
so  or  not  must  still  be  a  matter  of  inquiry ;  and  from  the  absence  of  any 
measurable  amount  of  such  displacement,  we  can  conclude  nothing  but 
this,  that  the  scale  of  the  sidereal  universe  is  so  great,  that  the  mutual 
orbit  of  the  earth  and  sun  may  be  regarded  as  an  imperceptible  point  in 
comparison  with  the  distance  of  its  nearest  members.  Admitting,  then, 
in  conformity  with  the  laws  of  dynamics,  that  two  bodies  connected  with 


^, 


/^; 


'39 

rua4 


192 


OUTLINES  or  ASTRONOMT. 


•nd  reyolTing  about  each  other  in  free  space  do,  in  taet,  reyolve  abont  their 
common  centre  of  gravity,  which  remains  immoveable  by  their  mutual 
action,  it  becomes  a  matter  of  further  inquiry,  whereaboutt  between  them 
this  centre  is  situated.  Mechanics  teach  us  that  its  place  will  divide  their 
mutual  'distance  in  the  inverse  ratio  of  their  weight*  or  TMutet;^  and 
calculatii  ^  grounded  on  phenomena,  of  which  an  account  will  be  given 
further  on,  inform  us  that  this  ratio,  in  the  case  of  the  sun  and  earth,  ii 
actually  that  of  854936  to  1,  —  the  sun  being,  in  that  proportion,  more 
ponderous  than  the  earth.  From  this  it  will  follow  that  the  common  point 
about  which  they  both  circulate  is  only  267  miles  from  the  sun's  centre, 
or  about  ^^^Q^th  part  of  its  own  diameter. 

(861.)  Henceforward,  then,  in  conformity  with  the  above  statements, 
and  with  the  Gopernican  view  of  our  system,  we  must  learn  to  look  upon 
the  sun  as  the  comparatively  motionless  centre  about  which  the  earth  per- 
forms an  annual  elliptic  orbit  of  the  dimensions  and  exccntricity,  and  with 
ft  velocity,  regulated  according  to  the  law  above  assigned ;  the  sun  occu- 
pying  one  of  the  foci  of  the  ellipse,  and  from  that  station  quietly  dissemi- 
nating on  all  sides  its  light  and  heat ;  while  the  earth  travelling  round  it, 
and  presenting  itself  differently  to  it  at  different  times  of  the  year  and 
day,  passes  through  the  varieties  of  day  and  night,  summer  and  winter, 
which  we  enjoy. 

(362.)  In  this  annual  motion  of  the  earth,  its  axis  preserves,  at  all 
times,  the  same  direction  as  if  the  orbitual  movement  had  no  existence ; 
and  is  carried  round  parallel  to  itself,  and  pointing  always  to  the  same 


■'-t'. 


vanishing  point  in  the  sphere  of  the  fixed  stars.  This  it  is  which  gives 
rise  to  the  variety  of  seasons,  as  wo  shall  now  explain.  In  so  doing,  we 
shall  neglect  (for  a  reason  which  will  be  presently  explained)  the  ellipticity 
of  the  orbit,  and  suppose  it  a  circle,  with  the  sun  in  the  centre. 

,._■-„_  „^.._  *Principia,  lib.  i.  Itx.  iii.  cor.  14.  ^       ,-.'• 


'M 


(868.) 

of  t?io  ear 

of  March, 

June,  or 

autumnal 

solstice. 

earth,  aboi 

with  its  ai 

lighten  on( 

shaded  poi 

dark,  and  \ 

positions. 

intersectior 

in  the  equi 

treme  confi 

day  over  ht 

and  as  the 

half  its  diu 

duration  of 

term  equim 

position  C. 

(864.)  I 

mmmer  soli 

the  earth's  i 

the  enlighte 

therefore,  tl 

fore,  at  this 

day  at  the  n 

this  pole  as 

or  within  wl 

hand,  the  o{ 

the  antarctti 

at  this  scasoi 

here  oontinu 

(365.)  ^ 

between  the 

nearer  any  p 

its  diurnal  ( 

the  dark  hei 

shorter  its  ni 

more  and  a 

13 


i. 


OF  THE  SEASONS. 


198 


}ing,  we 
llipticity 


(863.)  Let,  then,  S  represent  the  lun,  and  A,  6,  C,  D,  four  positions 
of  t'lii  earth  iu  its  orbit  00°  apart,  viz.  A  that  which  it  has  on  tho  2l8t 
of  March,  or  at  tho  time  of  tho  vernal  equinox;  B  that  of  the  2l8t  of 
June,  or  the  summer  solstice;  C  that  of  the  21st  of  September,  or  the 
autumnal  equinox;  and  D  that  of  the  2l8t  of  December,  or  the  winter 
Bolfitioe.  In  each  of  these  positions  let  PQ  represent  the  axis  of  the 
earth,  about  which  its  diurnal  rotation  is  performed  without  interfering 
with  its  annual  motion  in  its  orbit.  Then,  since  the  sun  can  only  en- 
lighten one  half  of  the  surface  at  once,  viz.  that  turned  towards  it,  the 
shaded  portions  of  the  globe  in  its  several  positions  will  represent  the 
dark,  and  the  bright,  the  enlightened  halves  of  the  earth's  surface  in  these 
positions.  Now,  1st,  in  the  position  A,  the  sun  is  vertically  over  the 
intersection  of  the  equinoctial  F  E  and  the  ecliptic  H  G.  It  is,  therefore, 
in  the  equinox ;  and  in  this  position  the  poles  P  Q,  both  fall  on  the  ex- 
treme confines  of  the  enlightened  side.  In  this  position,  therefore,  it  is 
day  over  half  the  i^orth^iu  and  half  the  southern  hemisphere  at  once; 
and  as  the  earth  revolves  on  its  axis,  every  point  of  its  surface  describes 
half  its  diurnal  course  in  light,  and  half  in  darkness ;  in  other  words,  the 
duration  of  day  and  night  is  here  equal  over  the  whole  globe :  hence  the 
term  equinox.  The  same  holds  good  at  the  autumnal  equinox  on  the 
position  0. 

(864.)  B  is  the  position  of  the  earth  at  the  time  of  the  northern 
mmmer  solstice.  Here  the  north  pole  P,  and  a  considerable  portion  of 
the  earth's  surface  in  its  neighbourhood,  as  far  as  B,  are  situated  vnlJdn 
the  enlightened  half.  As  tho  earth  turns  on  its  axis  iu  this  position, 
therefore,  the  whole  of  that  part  remains  constantly  enlightened ;  there- 
fore, at  this  point  of  its  orbit,  or  at  this  season  of  the  year,  it  is  continual 
day  at  the  north  pole,  and  in  all  that  region  of  the  earth  which  encircles 
this  pole  as  far  as  B  —  that  is,  to  the  distance  of  23°  28'  from  tho  pole, 
or  within  what  is  called  in  geography,  the  arctic  circle.  On  the  other 
band,  the  opposite  or  south  pole  Q,  with  all  the  region  comprised  within 
the  antarctic  circle,  as  far  as  23°  28'  from  the  south  pole,  are  ii^mersed 
at  this  season  in  darkness  during  the  entire  diurnal  rotation,  so  that  it  is 
here  continual  night. 

(865.)  With  regard  to  that  portion  of  the  surface  comprehended 
between  the  arctio  and  antarotio  circles,  it  is  no  less  evident  that  the 
nearer  any  point  is  to  the  north  pole,  the  larger  will  be  the  portion  of 
its  diurnal  course  comprised  within  the  bright,  and  the  smaller  within 
the  dark  hemisphere ;  that  is  to  say,  the  longer  will  be  its  day,  and  the 
shorter  its  night.  Every  station  north  of  the  equator  will  have  a  day  of 
more  and  a  night  of  less  than  twelve  hours'  duration,  and  vice  versfi, 
18 


^ 


CZ 


50 


«ryJJ 

SI 

5*? 


194 


OUTLINES   OP  ASTRONOMY. 


All  these  pbenomena  are  exactly  inverted  when  the  eaxth  comes  to  the 
opposite  point  D  of  its  orbit. 

(366.)  Now,  the  temperature  of  any  part  of  the  earth's  surface 
depends  mainly  on  its  exposure  to  the  sun's  rays.  Whenever  the  sun  is 
above  the  horizon  of  any  place,  that  place  is  receiving  heat ;  when  below, 
parting  with  it,  by  the  process  called  radiation ;  and  the  whole  quantities 
received  and  parted  with  in  the  year  (secondary  causes  apart)  must 
balance  each  other  at  every  station,  or  the  equilibrium  of  temperature 
(that  is  to  say,  the  constancy  which  is  observed  to  prevail  in  the  annual 
averages  of  temperature  as  indicated  by  the  thermometer)  would  not  be 
supported.  Whenever,  then,  the  sun  remains  more  than  twelve  hours 
above  the  horizon  of  any  place,  and  less  beneath,  the  general  temperature 
of  that  place  will  be  above  the  average ;  when  the  reverse,  below.  As 
the  earth,  then,  moves  from  A  to  B,  the  days  growing  longer,  and  the 
nights  shorter,  in  the  northern  hemisphere,  the  temperature  of  every  part 
of  that  hemisphere  increases,  and  we  pass  from  spring  to  summer;  while, 
at  the  same  time,  the  reverse  obtains  in  the  southern  hemisphere.  As 
the  earth  passes  from  B  to  C,  the  days  and  nights  again  approach  to 
equality  —  the  excess  of  temperature  in  the  northern  hemisphere  above 
the  mean  state  grows  less,  as  well  as  its  defect  in  the  southern ;  and  at 
the  autumnal  equinox  C,  the  mean  state  is  once  more  attained.  From 
thence  to  D,  and,  finally,  round  again  to  A,  all  the  same  phenomena,  it 
is  obvious,  must  again  occur,  but  reversed,  —  it  being  now  winter  in  the 
northern  and  summer  in  the  southern  hemisphere. 

(367.)  All  this  is  exactly  consonant  to  observed  fact.  The  continual 
day  within  the  polar  circles  in  summer,  and  night  in  winter,  the  general 
increase  of  temperature  and  length  of  day  as  the  sun  approaches  the 
elevated  pole,  and  the  reversal  of  the  seasons  in  the  northern  and  southern 
hemispheres,  are  all  facts  too  well  known  to  require  further  comment. 
The  positions  A,  C  of  the  earth  correspond,  as  we  have  said,  to  the 
equinoxes ;  those  at  B,  1)  to  the  solstices.  This  term  must  be  explained. 
If,  at  any  point,  X,  of  the  orbit,  we  draw  X  P  the  earth's  axis,  and  X  S 
to  the  sun,  it  is  evident  that  the  angle  P  X  S  will  be  the  sun's  polar 
distance.  Now,  this  angle  is  at  its  maximum  in  the  position  D,  and  at 
its  minimum  at  B;  being  in  the  former  case=90°+23«'  28=103°  28', 
and  in  the  latter  90°— 23°  28=66°  32'.  At  these  points  the  sun 
ceases  to  approach  to  or  to  recede  from  the  pole,  and  hence  the  name 
solstice. 

(368.)  The  elliptic  form  of  the  earth's  orbit  has  but  a  very  trifling 
share  in  producing  the  variation  of  temperature  corresponding  to  the 
difference  of  seasons     This  assertion  may  at  first  sight  seem  incompati- 


EQUAL  SUPPLY  OF  HEAT  TO   BOTH   HEMISPHERES. 


195 


s  to  the 

I  surface 
be  sun  is 
sn  below, 
quantities 
rt)  must 
aperature 
le  annual 
,d  not  be 
Lve  hours 
nperature 
low.     As 
>,  and  the 
3very  part 
er;  while, 
here.     As 
>proach  to 
jere  above 
■n ;  and  at 
d.     From 
lomena,  it 
iter  in  the 


le 


continual 
general 
)aches  the 

southern 
comment, 
d,  to  the 
explained. 
,  and  X  S 
iin's  polar 

D,  and  at 
H03"»  28', 

I  the  sun 

the  name 

iry  trifling 
Dg  to  the 
incompati* 


ble  with  what  we  know  of  the  laws  of  the  communication  of  heat  from 
a  luminary  placed  at  a  variable  distance.  Heat,  like  light,  being  equally 
dispersed  from  the  sun  in  all  directions,  and  being  spread  over  the  surface 
of  a  sphere  continually  enlarging  as  wo  recede  from  the  centre,  must,  of 
course,  diminish  in  intensity  according  to  the  inverse  proportion  of  the 
surfice  of  the  sphei-e  over  which  it  is  spread ;  that  is,  in  the  inverse  pro- 
portion of  the  square  of  the  distance.  But  we  have  seen  (art.  350)  that 
this  is  also  the  proportion  in  which  the  angular  velocity  of  the  earth 
about  the  sun  varies.  Hence  it  appears,  that  the  momentary  mpply  of 
heat  received  by  the  earth  from  the  sun  varies  in  the  exact  proportion  of 
angular  velocity,  i.  e.  of  the  momentary  increase  of  longitude :  and  from 
this  it  follows,  that  equal  amounts  of  heat  are  received  from  the  sun  in 
passing  over  equal  angles  round  it,  in  whatever  part  of  the  ellipse  those 
angles  may  be  situated.    Let,  then,  S  represent  the  sun ;  A  Q  M  P  the 


earth's  orbit;  A  its  nearest  point  to  the  sun,  or,  as  it  is  called,  the  peri- 
helion of  its  orbit;  M  the  farthest,  or  the  aphelion;  and  therefore  AS 
M  the  axis  of  the  ellipse.  Now,  suppose  the  orbit  divided  into  two 
segments  by  a  straight  line  P  S  Q,  drawn  through  the  sun,  and  anyhow 
situated  as  to  direction ;  then,  if  we  suppose  the  earth  to  circulate  in  the 
direction  PAQMP,  it  will  have  passed  over  180°  of  lon^tude  in 
moving  from  P  to  Q,  and  as  many  in  inoving  from  Q  to  P.  It  appears, 
therefore,  from  what  has  been  shown,  that  the  supplies  of  heat  received 
from  the  sun  will  be  equal  in  the  two  segments,  in  whatevw  direction  the 
line  P  S  Q  be  drawn.  They  will,  indeed,  be  described  in  unequal  times ; 
that  in  which  the  perihelion  A  lies  in  a  shorter,  and  the  other  in  a  longer, 
in  proportion  to  their  unequal  area :  but  the  greater  proximity  of  the  sun 
in  the  smaller  segment  compensates  exactly  for  its  more  rapid  description, 
and  thus  an  equilibrium  of  heat  is,  as  it  were,  maintained.  Were  it  not 
for  this,  the  cxcentricity  of  the  orbit  would  materially  influence  the  tran- 
sition of  seasons.    The  fluctuation  of  distance  amounts  to  nearly  ^^^th  Qf 


O 


T** 


"'^ 


IF!'*'' 

MOW* 

a? 


196 


OUTLINES  OP  ASTRONOMY. 


its  meaD  quantity,  and,  consequently,  the  fluctuation  in  the  sun's  direct 
heating  power  to  double  this,  or  j'^th  of  the  whole.  Now,  the  perihelion 
of  the  orbit  is  situated  nearly  at  the  place  of  the  northern  winter  solstice ; 
so  that,  were  it  not  for  the  compensation  we  have  just  described,  the  effect 
would  be  to  exaggerate  the  difference  of  summer  and  winter  in  the 
southern  hemisphere,  and  to  moderate  it  in  the  northern ;  thus  producing 
a  more  violent  alternation  of  climate  in  the  one  hemisphere,  and  an 
approach  to  perpetual  sprinjg  in  the  other.  As  it  is,  however,  no  such 
inequality  subsists,  but  an  equal  and  impartial  distribution  of  heat  and 
light  is  accorded  to  both. 

(369.)  This  does  not  prevent,  however,  the  direct  impression  of  the 
solar  heat  in  the  height  of  summer,  —  the  glow  and  ardour  of  his  rays, 
under  a  perfectly  clear  sky,  at  noon,  in  equal  latitudes  and  under  equal 
circumstances  of  exposure, —  from  being  very  materially  greater  in  the 
southern  hemisphere  than  in  the  northern.  One  fifteenth  is  too  considera- 
ble a  fraction  of  the  whole  intensity  of  sunshine  not  to  aggravate  in  a 
serious  degree  the  sufferings  of  those  who  are  exposed  to  it  in  thirsty 
deserts,  without  shelter.  The  accounts  of  these  sufferings  in  the  interior 
of  Australia,  for  instance,  are  of  the  most  frightful  kind,  and  would  seem 
far  jO  exceed  what  have  ever  been  undergone  by  travellers  in  the  northern 
deserts  of  Africa.' 

(370.)  A  conclusion  of  a  very  remarkable  kind,  recently  drawn  by  Pro- 
fessor Dove  from  the  comparison  of  the  thermometric  observations  at 
different  seasons  in  very  remote  regions  of  the  globe,  may  appear  on  first 
sight  at  variance  with  what  is  above  stated.  That  eminent  meteorologist 
has  shown,  by  taking  at  all  seasons  the  mean  of  the  temperatures  of  points 
diametrically  opposite  to  each  other,  that  the  mean  temperature  of  the 
wlwle  earth's  iurface  in  June  considerably  exceeds  that  in  December. 
This  result,  which  is  at  variance  with  the  greater  proximity  of  the  sun  in 
December,  is,  however,  due  to  a  totally  diffierent  and  very  powerful  cause, 
—  the  greater  amount  of  land  in  that  hemisphere  which  has  its  summer 
solstice  in  June  (i.  e.  the  northern,  see  art.  362) ;  and  the  fact  is  so 
explained  by  him.  The  effect  of  land  under  sunshine  is  to  throw  hebt 
into  the  general  atmosphere,  and  so  distribute  it  by  the  carrying  power  of 
the  latter  over  the  whole  earth.  Water  is  much  les&  effective  in  this 
respect,  the  heat  penetrating  its  depths,  and  being  there  absorbed ;  so  that 

*  See  the  account  of  Captain  Sturt's  exploration  in  Athenaeum,  No.  1012.  "  The 
ground  was  almost  a  molten  surface,  and  if  a  match  accidentally  fell  upon  it,  it  imme- 
diately ignited."  The  author  has  observed  the  temperature  of  the  surface  soil  in 
South  Africa  as  high  as  159°  Fahrenheit.  An  ordinary  lucifer  match  does  not  ignite 
when  simply  pressed  upon  a  smooth  surface  at  212°,  but  in  the  act  of  withdrawing  it, 
it  takes  fire,  and  the  slightest  friction  upon  such  a  surface  of  course  ignites  it. 


MEAN  TEMPERATURE  OF  THE  EARTH'S  SURFACE.    197 


's  direct 
jrihelion 
solstice ; 
,he  effect 
r  in  the 
reducing 
and  an 
no  such 
heat  and 

»n  of  the 
his  rays, 
der  equal 
iT  in  the 
3onsidera- 
vate  in  a 
in  thirsty 
10  interior 
ould  seem 
i  northern 

a  by  Pro- 

ations   at 

ar  on  first 

■eorologist 

I  of  points 

re  of  the 

)ecember. 

he  sun  in 

ful  cause, 

s  summer 

fact  is  so 

irow  hdat 

power  of 

e  in  this 

y ,  so  that 

2.  "  The 
t,  it  imme- 
ace  soil  in 
not  ignite 
Irawing  it, 


the  surface  never  acquires  a  very  elevated  temperature  even  under  the 
equator. 

(371.)  The  great  key  to  simplicity  of  conception  in  astronomy,  and, 
indeed,  in  all  sciences  where  motion  is  concerned,  consists  in  contempla- 
ting every  movement  as  referred  to  points  which  are  either  permanently 
fixed,  or  so  nearly  so,  as  that  their  motions  shall  be  too  small  to  interfere 
materially  with  and  confuse  our  notions.     In  the  choice  of  these  primary 
points  of  reference,  too,  we  must  endeavour,  as  far  as  possible,  to  select 
such  as  have  simple  and  symmetrical  geometrical  relations  of  situation  with 
respect  to  the  curves  described  by  the  moving  parts  of  the  system,  and 
which  are  thereby  fitted  to  perform  the  office  of  natural  centres  —  advan- 
tageous stations  for  the  eye  of  reason  and  theory.     Having  learned  to 
attribute  an  orbitual  motion  to  the  earth,  it  loses  this  advantage,  which  is 
transferred  to  the  sun,  as  the  fixed  centre  about  which  its  orbit  is  per- 
formed.    Precisely  as,  when  embarrassed  by  the  earth's  diurnal  motion, 
we  have  learned  to  transfer,  in  imagination,  our  station  of  observation 
from  its  surface  to  its  centre,  by  the  application  of  the  diurnal  parallax ; 
so,  when  we  come  to  inquire  into  the  movements  of  the  planets,  we  shall 
find  ourselves  continually  embarrassed  by  the  orbitual  motion  of  our  point 
of  view,  unless,  by  the  consideration  of  the  annual  or  heliocentric  paral- 
lax, we  consent  to  refer  all  our  observations  on  them  to  the  centre  of  the 
sun,  or  rather  to  the  common  centre  of  gravity  of  the  sun,  and  the  other 
bodies  which  are  connected  with  it  in  our  system.     Hence  arises  the  dis- 
tinction between  the  geocentric  and  heliocentric  place  of  an  object.     The 
former  refers  its  situation  in  space  to  an  imaginary  sphere  of  infinite 
radius,  having  the  centre  of  the  earth  for  its  centre  —  the  latter  to  one 
concentric  with  the  sun.     Tlius,  when  we  speak  of  the  heliocentric  longi' 
tudes  and  latitudes  of  objects,  we  suppose  the  spectator  situated  in  the  sun 
and  referring  them  by  circles  perpendicular  to  the  plane  of  the  ecliptic, 
to  the  great  circle  marked  out  in  the  heavens  by  the  infinite  prolon^tion 
of  that  plane. 

(372.)  The  point  in  the  imaginary  concave  of  an  infinite  heaven,  to 
which  a  spectator  in  the  sun  refers  the  earth,  must,  of  course,  be  diame- 
trically opposite  to  that  to  which  a  spectator  on  the  earth  refers  the  sun's 
centre;  consequently  the  heliocentric  latitude  of  the  earth  is  always 
nothing,  and  i/a  heliocentric  longitude  always  equal  to  the  sun^s  geocentric 
longitude  ■{■1S0°.  The  heliocentric  equinoxes  and  solstices  are,  therefore, 
the  same  as  the  geocentric  reversely  named ;  and  to  conceive  them,  we 
have  only  to  imagine  a  plane  passing  through  the  sun's  centre,  parallel  to 
the  earth's  equator,  and  prolonged  infinitely  on  all  sides.   The  line  of  inter- 


A< 


55 

'"'hi 

►'■A.*.!' 

o 
CI 


198 


OUTLINES  OF  ASTBONOMT. 


Bection  of  this  plane  and  the  plane  of  the  ecliptic  is  the  line  of  equinoxes, 
and  the  solstices  are  90°  distant  from  it. 

(373.)  The  position  of  the  longer  axis  of  the  earth's  orbit  is  a  point 
of  great  importance.  In  the  figure  (art.  368)  let  E  C  L I  be  the  ecliptic, 
E  the  vernal  equinox,  L  the  autumnal  (i.  e.  the  points  to  which  the  earth 
is  referred  from  Oie  sun  when,  its  heliocentric  longittcdes  are  0°  and  180° 
re^ectively).  Supposing  the  earth's  motion  to  be  performed  in  the  direc- 
tion E  C  L  I,  the  angle  E  S  A,  or  the  longitude  of  the  perihelion,  in  the 
year  1800  was  99°  30'  5" :  we  say  in  the  year  1800,  because,  in  point  of 
fact,  by  the  operation  of  causes  hereafter  to  be  explained,  its  position  is 
subject  to  an  extremely  slow  variation  of  about  12"  per  annum  to  the 
eastward,  and  which  in  the  progress  of  an  immensely  long  period — of  no 
less  than  20984  years  —  carries  the  axis  A  S  M  of  the  orbit  completely 
round  the  whole  circumference  of  the  ecliptic.  But  this  motion  must  be 
disregarded  for  the  present,  as  well  as  many  other  minute  deviations,  to  be 
brought  into  view  when  they  can  be  better  understood. 

(374.)  Were  the  earth's  orbit  a  circle,  described  with  a  uniform 
velocity  about  the  sun  placed  in  its  centre,  nothing  could  be  easier  than 
to  calculate  its  position  at  any  time  with  respect  to  the  line  of  equinoxes, 
or  its  longitude,  for  we  should  only  have  to  reduce  to  numbers  the  pro< 
portion  following  j  viz.  One  year  :  the  time  elapsed  : :  360°  :  the  arc  of 
longitude  passed  over.  The  longitude  so  calculated  is  called  in  astronomy 
the  mean  longitude  of  the  earth.  But  since  the  earth's  orbit  is  neither 
circular,  nor  uniformly  described,  this  rule  will  not  give  us  the  true  place 
in  the  orbit  of  any  proposed  moment.  Nevertheless,  as  the  excentricity 
and  deviation  from  a  circle  are  small,  the  true  place  will  never  deviate 
very  far  from  that  so  determined  (which  for  distinction's  sake,  is  called 
the  mean  place^,  and  the  former  may  at  all  times  be  calculated  from  the 
latter,  by  applying  to  it  a  correction  or  equation  (as  it  is  termed),  whoso 
amount  is  never  very  great,  and  whose  computation  is  a  question  of  pure 
geometry,  depending  on  the  equable  description  of  areas  by  the  earth 
about  the  sun.  For  since,  in  elliptic  motion  according  to  Kepler's  law 
above  stated,  ai'eas  not  a^igles  are  described  uniformly,  the  proportion 
must  now  be  stated  thus ; — One  year  :  the  time  elapsed  : :  the  whole  area 
of  the  ellipse  :  the  area  of  the  sector  swept  over  by  the  radius  vector  in 
that  time.  This  area,  therefore,  becomes  known,  and  it  is  then,  as  above 
observed,  a  problem  of  pure  geometry  to  ascertain  the  ant/le  about  the  sun 
(A  S  V,fj.  art.  368),  which  corresponds  to  any  proposed  fractional  area  of 
the  whole  ellipse  supposed  to  be  contained  in  the  sector  APS.  Suppose 
we  set  out  from  A  the  perihelion,  then  will  the  angle  A  S  P  at  first 
increase  more  rapidly  than  the  m.ean„  hngitudCf  and  will,  therefore,  during 


OP  THE   sun's   mean   AND  TRUE   LONGITUDES. 


199 


the  Avhole  semi-revolution  from  A  to  M,  exceed  it  in  amount ;  or,  in  other 
words,  the  true  place  will  be  in  advance  of  the  mean:  at  M,  one  half  the 
year  will  have  elapsed,  and  one  half  the  orbit  have  been  described, 
whether  it  be  curcular  or  elliptic.  Here,  then,  the  mean  and  true  places 
coincide ;  but  in  all  the  other  half  of  the  orbit,  from  M  to  A,  the  true 
place  will  fall  short  of  the  mean,  since  at  M  the  angular  motion  is  slowest, 
and  the  true  place  from  this  point  begins  to  lag  behind  the  mean  —  to 
make  up  with  it,  however,  as  it  approaches  A,  where  it  once  more  over- 
takes  it. 

(375.)  The  quantity  by  which  the  true  longitude  of  the  earth  differs 
from  the  mean  longitude  is  called  the  equation  of  the  centre,  and  is  addi- 
tive  during  all  the  half-year,  in  which  the  earth  passes  from  A  to  M, 
beginning  at  0°  0'  0",  increasing  to  a  maximum,  and  again  .diminishing 
to  zero  at  M ;  after  which  it  becomes  subtractive,  attains  a  maximum  of 
subtractive  magnitude  between  M  and  A,  and  again  diminishes  to  0  at  A. 
Its  maximum,  both  additive  and  subtractive,  is  1°  55'  33"-3. 

(376.)  By  applying,  then,  to  the  earth's  mean  longitu  le,  the  equation 
of  the  centre  corresponding  to  any  given  time  at  which  we  would  ascer- 
tain its  place,  the  true  longitude  becomes  known ;  and  since  the  sun  is 
always  seen  from  the  earth  in  180°  more  longitude  than  the  earth  from 
the  sun,  in  this  way  also  the  sun's  true  place  in  the  ecliptic  becomes 
known.  The  calculation  of  the  equation  of  the  centre  is  performed  by  a 
table  constructed  for  that  purpose,  to  be  found  in  all  "  Solar  Tables." 

(377.)  The  maximum  value  of  the  equation  of  the  centre  depends  only 
on  the  ellipticity  of  the  orbit,  and  may  be  expressed  in  terms  of  the  ex- 
centricity.  Vice  versd,  therefore,  if  the  former  quantity  can  be  ascer- 
tained by  observation,  the  latter  may  be  derived  from  it ;  because,  when- 
ever the  law,  or  numerical  connection,  between  two  quantities  is  known, 
the  one  can  always  be  determined  from  the  other.  Now,  by  assiduous 
observation  of  the  sun's  transits  over  the  meridian,  we  can  ascertain,  for 
every  day,  its  exact  right  ascension,  and  thence  conclude  its  longitude 
(art.  309).  After  this,  it  is  easy  to  assign  the  angle  by  which  this 
observed  longitude  exceeds  or  falls  short  of  the  mean ;  and  the  greatest 
amount  of  this  excess  or  defect  which  occurs  in  the  whole  year,  is  the 
maximum  equation  of  the  centre.  This,  as  a  means  of  ascertaining  the 
excentricity  of  the  orbit,  is  a  far  more  easy  and  accurate  method  than 
that  of  concluding  the  sun's  distance  by  measuring  its  apparent  diameter. 
The  results  of  the  two  methods  coincide,  however,  perfectly. 

(378.)  If  the  ecliptic  coincided  with  the  equinoctial,  the  effect  of  the 
equation  of  the  centre,  by  disturbing  the  uniformity  of  the  sun's  apparent 
motion  in  longitude,  would  cause  an  inequality  in  its  time  of  coming  on 


KsaM 


200 


OUTLINES   OP  ASTRONOMY. 


the  meridian  on  successive  days.  When  the  sun's  centre  comes  to  the 
meridinn,  it  is  apparent  noon,  and  if  its  motion  in  longitude  were  uni- 
form, and  the  ecliptio  coincident  with  the  equinoctial,  this  would  always 
coincide  with  mean  noon,  or  the  stroke  of  12  on  a  well-regulated  solar 
clock.  But,  independent  of  the  want  of  uniformity  in  its  motion,  the 
obliquity  of  the  ecliptic  gives  rise  to  another  inequality  in  this  respect ;  in 
consequence  of  which,  the  sun,  even  supposing  its  motion  in  the  ecliptic 
uniform,  would  yet  alternately,  in  its  time  of  attaining  the  meridian,  anti- 
cipate and  fall  short  of  the  mean  noon  as  shown  by  the  clock.  For  the 
right  ascension  of  a  celestial  object  forming  a  side  of  a  right-angled  sphe- 
rical triangle,  of  which  its  longitude  is  the  hypothenuse,  it  is  clear  that 
the  uniform  increase  of  the  latter  must  necessitate  a  deviation  from  uni- 
formity in  the  increase  of  the  former. 

(379.)  These  two  causes,  then,  acting  conjointly,  produce,  in  fact,  a 
very  considerable  fluctuation  in  the  time  as  shown  per  clock,  when  the  sun 
really  attains  the  meridian.  It  amounts,  in  fact,  to  upwards  of  half  an 
hour;  apparent  noon  sometimes  taking  place  as  much  as  16^  min.  before 
mean  noon,  and  at  others  as  much  as  14^  min.  after.  This  difference 
between  apparent  and  mean  noon  is  called  the  equation  of  time,  and  is 
calculated  and  inserted  in  ephemerides  for  every  day  of  the  year,  under 
that  title :  or  else,  which  comes  to  the  same  thing,  the  moment,  in  mean 
tim£,  of  the  sun's  culmination  for  each  day,  b  set  down  as  an  astrono- 
mical phaenomenon  to  be  observed.  r     '• 

(380.)  As  the  sun,  in  its  apparent  annual  course,  is  carried  along  the 
ecliptic,  its  declination  is  continually  varying  between  the  extreme  limits 
of  23°  27'  30"  north,  and  as  much  south,  which  it  attains  at  the  sol- 
stices. It  is  consequently  always  vertical  over  some  part  or.  other  of  that 
zone  or  belt  of  the  earth's  surface  which  lies  between  the  north  and  south 
parallels  of  23°  27'  30".  These  parallels  are  called  in  geography  the 
tropics;  the  northern  one  that  of  Cancer,  and  the  southern,  of  Capri- 
corn ;  because  the  sun,  at  the  respective  solstices,  is  situated  in  the  divi- 
sions, or  signs  of  the  ecliptic  so  denominated.  Of  these  signs  there  are 
twelve,  each  occupying  30°  of  its  circumference.  They  commence  at  the 
vernal  equinox,  and  are  named  in  order — Aries,  Taurus,  Gemini,  Cancer, 
Leo,  Virgo,  Libra,  Scorpio,  Sagittarius,  Capricornus,  Aquarius,  Pisces.' 
They  are  denoted  also  by  the  following  symbols:  —  T.  y.  n,  ss,  i\,  Ttj?,  =g:, 
^>  ^>  VSi  0X>  X-  Longitude  itself  is  also  divided  into  signs,  degrees,  and 
minutes,  &c.     Thus  6»  27°  0'  corresponds  to  177°  0'. 

'  They  may  be  remembered  by  the  following  memorial  hexameters :  ^         . 
Sunt  Aries,  Taurus,  Gemini,  Cancer,  Leo,  Virgo, 
4'  Libraque,  Scorpius,  Arcitenens,  Caper,  Amphora,  Pisces. 


es  to  the 
mrero  uni- 
Id  always 
itcd  solar 
)tion,  the 
}spect;  in 
10  ecliptic 
lian,  anti- 
For  the 
gled  sphe- 
clear  that 
from  uni- 

in  fact,  a 
n  the  sun 
)f  half  an 
lin.  before 
diflferenco 
ne,  and  is 
jar,  under 
in  mean 
astrono- 

along  the 
me  limits 
the  sol- 
3r  of  that 
and  south 
•aphy  the 
)f  Capri- 
the  divi- 
there  are 
ice  at  the 
i,  Cancer, 
Pisces.' 

a.  n^  =. 

jrees,  and 


SIDEREAL,   TROPICAL,  AND  ANOMALISTIC   YEARS. 


201 


(381.)  These  Sujna  are  purely  technical  subdivisions  of  the  ecliptic, 
commencing  from  the  actual  equinox,  and  are  not  to  be  confounded  with 
the  constellations  so  called  (and  sometimes  so  aymbolized).  The  constel- 
lations  of  the  zodiac,  as  they  now  stand  arranged  on  the  ecliptic,  are  all  a 
full  "sign"  in  advance  or  anticipation  of  their  symbolic  cognomens  thereon 
marked.  Thus  the  constellation  Aries  actually  occupies  the  sign  Taurus 
H,  tlie  constellation  Taurus,  the  sign  Gemini  n,  and  so  on,  the  signs 
having  retreated'  among  the  stars  (together  with  the  equinox  their  origin), 
by  the  effect  of  precession.  The  bright  star  Spica  in  the  constellation 
Virgo  (o  Virginis),  by  the  observations  of  Hipparchus,  128  years  b.  c, 
preceded,  or  was  westward  of  the  autumnal  equinox  in  longitude  by  6". 
In  1750  it  followed  or  stood  eastward  of  the  same  equinox  by  20"  21'. 
Its  place  then,  as  referred  to  the  ecliptic  at  the  former  epoch,  would  be  in 
longitude  5*  24"  0',  or  in  the  24th  degree  of  the  sign  Si,  whereas  in  the 
latter  epoch  it  stood  in  the  21st  degree  of  HK,  the  equinox  having  retreated 
by  26"  21'  in  the  interval,  1878  years,  elapsed.  To  avoid  this  source  of 
misunderstanding,  the  use  of  "  signs"  and  their  symbols  in  the  reckoning 
of  celestial  longitudes  is  now  almost  entirely  abandoned,  and  the  ordinary 
reckoning  (by  degrees,  &c.  from  0  to  360)  adopted  in  its  place,  and  the 
names  Aries,  Virgo,  &c.  are  becoming  restricted  to  the  constellations  so 
called.' 

(382.)  When  the  sun  is  in  either  tropic,  it  enlightens,  as  we  have  seen, 
the  pole  on  that  side  the  equator,  and  shines  over  or  beyond  it  to  the 
extent  of  23"  27'  30".  The  parallels  of  latitude,  at  this  distance  from 
either  pole,  are  called  the  polar  circles,  and  are  distinguished  from  each 
other  by  the  names  arctic  and  antarctic.  The  regions  within  these 
circles  are  sometimes  termed  frigid  zones,  while  the  belt  between  the 
tropics  is  called  the  torrid  zone,  and  the  intermediate  belts  temperate  zones. 
These  last,  however,  are  merely  names  given  for  the  sake  of  naming ;  as, 
in  fact,  owing  to  the  different  distribution  of  land  and  sea  in  the  two  hemi- 
spheres, zones  of  climate  are  not  co-terminal  with  zones  of  latitude.     - . 

(383.)  Our  seasons  are  determined  by  the  apparent  passages  of  the  sun 
across  the  equinoctial,  and  its  alternate  arrival  in  the  northern  and  south- 
em  hemisphere.  Were  the  equinox  invariable,  this  would  happen  at 
intervals  precisely  equal  to  the  duration  of  the  sidereal  year ;  but,  in  fact, 

^  Setreated  is  here  used  with  reference  to  longitude,  not  to  the  apparent  diurnal 
motion. 

'  When,  however,  the  place  of  the  sun  is  spoken  of,  the  old  usage  prevails.  Thus, 
if  we  say  "  the  sun  is  in  Aries,"  it  would  be  interpreted  to  mean  between  0°  and  30' 
of  longitude.  So,  also,  "  the  first  point  of  Aries"  is  still  understood  to  mean  the 
vernal,  and  "  the  first  point  of  Libra,"  the  autumnal  equinox;  and  so  in  a  few  othar 
cases. 


f^- 


202 


OUTLINES   OF  ASTRONOMT. 


l!         S 


I:  ■?•     ;   .■  ■ 


owing  to  the  slow  conical  motion  of  tho  eai  th's  axis  described  in  art.  317, 
the  equinox  retreats  on  the  ecliptic,  and  mrets  the  advancing  sun  some- 
what before  the  whole  sidereal  circuit  is  completed.  The  annual  retreat 
of  the  equinox  is  dO"'l,  and  this  arc  is  described  by  the  sun  in  the  eclip- 
tic in  20'»  10*-9.  By  so  much  shorter^  then,  is  the  periodical  return  of 
our  seasons  than  the  true  sidereal  revolution  of  the  earth  round  the  sun. 
As  the  latter  period,  or  sidereal  year,  is  equal  to  365*  C*  9"  9»-6,  it  fol- 
lows, then,  that  the  former  must  be  only  365*  b^  48"  49»'7 ;  and  this  is 
what  is  meant  by  the  tropical  year. 

(384.)  We  have  already  mentioned  that  the  longer  axis  of  the  ellipse 
described  by  the  earth  has  a  slow  motion  of  11" -S  per  annum  in  advance. 
From  this  it  results,  that  when  the  earth,  setting  out  from  the  perihelion, 
has  completed  one  sidereal  period,  the  perihelion  will  have  moved 
forward  by  ll"-8,  which  arc  must  be  described  by  the  earth  before  it  can 
again  reach  the  perihelion.  In  so  doing,  it  occupies  4"  39*  7,  and  this 
must  therefore  be  added  to  the  sidereal  period,  to  give  the  interval  between 
two  consecutive  returns  to  the  perihelion.  This  interval,  then,  is  365* 
Qh  13m  49»-3j>  and  is  what  is  called  the  anomalistic  year.  All  these 
periods  have  their  uses  in  astronomy;  but  that  in  which  mankind  in 
general  are  most  interested  is  tlie  tropical  year,  on  which  the  return  of 
the  seasons  depends,  and  which  we  thus  perceive  to  be  a  compound  phe- 
nomenon, depending  chiefly  and  directly  on  the  annual  revolution  of  the 
earth  round  the  sun,  but  subordinately  also,  and  indirectly,  on  its  rotation 
round  its  own  axis,  which  is  what  occasions  the  precession  of  the  equi- 
noxes; thus  affording  an  instructive  example  of  the  way  in  which  a 
motion,  once  admitted  in  any  part  of  our  system,  may  be  traced  in  its 
influence  on  others  with  which  at  first  sight  it  could  not  possibly  be  sup- 
posed to  have  any  thing  to  do. 

(385.)  As  a  rough  consideration  of  the  appearance  of  the  earth  points 
out  the  general  roundness  of  its  form,  and  more  exact  inquiry  has  led  ua 
first  to  the  discovery  of  its  elliptic  figure,  and,  in  the  further  progress  of 
refinement,  to  the  perception  of  minuter  local  deviations  from  that  figure ; 
so,  in  investigating  the  solar  motions,  the  first  notion  we  obtain  is  that  of 
an  orbit,  generally  speaking,  round,  and  not  far  from  a  circle,  which,  on 
more  careful  and  exact  examination,  proves  to  be  an  ellipse  of  small  excen- 
tricity,  and  described  in  conformity  with  certain  laws,  as  above  stated. 
Still  minuter  inquiry,  however,  detects  yet  smaller  deviations  again  from 
this  form  and  from  these  laws,  of  which  avc  have  a  specimen  in  the  slow 
motion  of  the  axis  of  the  orbit  spoken  of  in  art.  372 ;  and  which  are 

'  These  numbers,  as  well  as  all  the  other  numerical  data  of  our  system,  are  taken 
from  Mr.  Baily's  Astronomical  Tables  and  Formulie,  unless  the  contrary  is  expressed. 


PHTSIOAL  CONSTITUTION  OF  THE  SUN. 


208 


generally  comprehended  under  the  name  of  perturbations  and  secular  in- 
equalities. Of  thtise  deviations,  and  their  causes,  we  shall  speak  here- 
after at  length.  It  is  the  triumph  of  physical  astronomy  to  have  rendered 
a  complete  account  of  them  all,  and  to  have  left  nothing  unexplained, 
either  in  the  motions  of  the  sun  or  in  those  of  any  other  of  the  bodies  of 
our  system.  But  the  nature  of  this  explanation  cannot  bo  understood  till 
we  have  developed  the  law  of  gravitation,  and  carried  it  into  its  more 
direct  consequences.  This  will  be  the  object  of  our  three  following  chap- 
ters; in  which  we  shall  take  advantage  of  the  proximity  of  the  moon, 
and  its  immediate  connection  with  and  dependence  on  the  earth,  to  render 
it,  as  it  were,  a  stepping-stone  to  the  general  explanation  of  the  planet- 
ary movements.  We  shall  conclude  this  by  describing  what  is  known  of 
the  physical  constitution  of  the  sun. 

(386.)  When  viewed  through  powerful  telescopes,  provided  with 
coloured  glasses,  tiO  take  off  the  beat,  which  would  otherwise  injure  our 
eyes,  the  sun  is  observed  to  have  frequently  large  and  perfectly  black 
spots  upon  it,  surrounded  with  a  kind  of  border,  less  completely  dark, 
called  a  penumbra.  Some  of  these  are  represented  at  a,  b,  c,  d,  in  Plate 
I.  fig.  2.,  at  the  end  of  this  volume.  They  are,  however,  not  permanent. 
When  watched  from  day  to  day,  or  even  from  hour  to  hour,  they  appear 
to  enlarge  or  contract,  t^<  change  their  forms,  and  at  length  to  disappear 
altogether,  or  to  break  out  anew  in  parts  of  the  surface  where  none  were 
before.  In  such  cases  of  disappearance,  the  central  dark  spot  always  con- 
tracts into  a  point,  and  vanishes  before  the  border.  Occasionally  they 
break  up,  or  divide  into  two  or  more,  and  in  those  cases  offer  every  evi- 
dence of  that  extreme  mobility  which  belongs  only  to  the  fluid  state,  and 
of  that  excessively  violent  agitation  which  seems  only  compatible  with  the 
atmospheric  or  gaseous  state  of  matter.  The  scale  on  which  their  move- 
ments take  place  is  immense.  A  single  second  of  angular  measure,  as 
seen  from  the  earth,  corresponds  on  the  sun's  disc  to  461  miles ;  and  a 
circle  of  this  diameter  (containing  therefore  nearly  167000  square  miles) 
is  the  least  space  which  can  be  distinctly  discerned  on  the  sun  as  a  visible 
Spots  have  been  observed,  however,  whose  linear  diameter  has 


area. 


been  upwards  of  45000  miles;'  and  even,  if  some  records  are  to  be 
trusted,  of  very  much  greater  extent.  That  such  a  spot  should  close  up 
in  six  weeks'  time  (for  they  seldom  last  much  longer),  its  borders  must 
approach  at  the  rate  of  njore  than  1000  miles  a  day. 

(387.)  Many  other  circumstances  tend  to  corroborate  this  view  of  the 
subject.     The  part  of  the  sun's  disc  not  occupied  by  spots  is  far  from 


I. 


S33 


urn 


CD 


•  Mayer,  Obs.  Mar.  15,  1758. 
eter=^)r  diatn.  soils. 


'  Ingens  macula  in  sole  conspiciebatur,  cujus  diam- 


204 


OUTLINES   OP  ASTRONOMY. 


UDiforiuIy  bright.  Its  ground  ia  finely  mottled  with  an  appearance  of 
minute,  durk  dota,  or  jxircn,  which,  when  attentively  watched,  are  found 
to  be  in  a  constant  stuto  of  change.  There  is  nothing  which  represents 
so  faithfully  thia  appearance  as  the  slow  subsidence  of  some  flocculent 
chemical  precipitates  in  a  transparent  fluid,  when  viewed  perpendicularly 
from  above :  so  faithfully,  indeed,  that  it  is  hardly  possible  not  to  be  im> 
pressed  with  the  idea  of  a  luminous  medium  intermixed,  but  not  con- 
founded, with  a  transparent  and  non-luminous  atmosphere,  either  floating 
as  clouds  ir  our  air,  or  pervading  it  in  vast  sheets  and  columns  like  flame, 
or  the  streamers  of  our  northern  lights,  directed  in  lines  perpendicular  to 
the  surface. 

(388.)  La.^tly,  in  the  neighbourhood  of  great  spots,  or  extensive  groups 
of  them,  large  spaces  of  the  surface  are  often  observed  to  be  covered  with 
strongly  marked  curved  or  branching  streaks,  more  luminous  than  the 
rest,  called  faculse,  and  among  these,  if  not  already  existing,  spots  fre< 
quently  break  out.  They  may,  perhaps,  be  regarded  with  most  proba- 
bility, as  the  ridges  of  immense  waves  in  the  luminous  regions  of  the 
sun's  atmosphere,  indicative  of  violent  agitation  in  their  neighbourhood. 
They  are  most  commonly,  and  best  seen,  towards  the  borders  of  the 
visible  disc,  and  their  appearance  is  as  represented  in  Plate  I.  fig.  1. 

(389.)  But  what  are  the  spots?  Many  fanciful  notions  have  been 
broached  on  this  subject,  but  only  one  seems  to  have  any  degree  of 
physical  probability,  viz.  that  they  are  the  dark,  or  at  least  comparatively 
dark,  solid  body  of  the  sun  itself,  laid  bare  to  our  view  by  those  immense 
fluctuations  in  the  luminous  regions  of  its  atmosphere,  to  which  it  appears 
to  be  subject.  Respecting  the  manner  in  which  this  disclosure  takes 
place,  different  ideas  again  have  been  advocated.  Lalande  (art.  3240) 
suggests,  that  eminences  in  the  nature  of  mountains  are  actually  laid 
bare,  and  project  above  the  luminous  ocean,  appearing  black  above  it, 
while  their  shoaling  declivities  produce  the  penumbrse,  where  the  lumi- 
nous fluid  is  less  deep.  A  fatal  objection  to  this  theory  is  the  uniform 
shade  of  the  penumbra  and  its  sharp  termination,  both  inwards,  where  it 
joins  the  spot,  and  outwards,  where  it  borders  on  the  bright  surface.  A 
more  probable  view  baa  been  taken  by  Sir  William  Hcrschel,'  who  con- 
siders the  luminous  strata  of  the  atmosphere  to  be  sustained  far  above 
the  level  of  the  solid  body  by  a  transparent  elastic  medium,  carrying  on 
its  upper  surface  (or,  rather,  to  avoid  the  former  objection,  at  some  con- 
siderably lower  level  within  its  depth)  a  cloudy  stratum  which,  being 
strongly  illuminated  from  above,  reflects  a  considerable  portion  of  the 
light  to  our  eyeS;  and  forms  a  penumbra,  while  the  solid  body  shaded  by 

'Phil.  Trans.  1801. 


NATURE  OF  THE  SUN'S  SPOTS. 


206 


Fig.  56. 


the  clouds,  reflects  none.  (See  fg.)  The  temporary  removal  of  both 
the  strata,  but  more  of  the  upper  than  the  lower,  he  supposes  efiected  by 
powerful  upward  currents  of  the  atmosphere,  arising,  perhaps,  from 
spiracles  in  the  body,  or  from  local  agitations.   '       • 

(390.)  When  the  spots  are  attentively  watched,  their  situation  on  the 
disc  of  the  sun  is  observed  to  change.  They  advance  regularly  towards 
its  western  limb  or  border,  where  they  disappear,  and  are  replaced  by 
others  which  enter  at  the  eastern  limb,  and  which,  pursuing  their  respec- 
tive courses,  in  their  turn  disappear  at  the  western.  The  apparent 
rapidity  of  this  movement  is  not  uniform,  as  it  would  be  were  the  spots 
dark  bodies  passing,  by  an  independent  motion  of  their  own,  between  the 
earth  and  the  sun ;  but  is  swiftest  in  the  middle  of  their  paths  across 
the  disc,  and  very  slow  at  its  borders.  This  is  precisely  what  would  be 
the  case  supposing  them  to  appertain  to  and  make  part  of  the  visible 
surface  of  the  sun's  globe,  and  to  be  carried  round  by  a  uniform  rotation 
of  that  globe  on  its  axis,  so  that  each  spot  should  describe  a  circle  parallel 
to  the  sun's  equator,  rendered  elliptic  by  the  effect  of  perspective.  Their 
apparent  paths  also  across  the  disc  conform  to  this  view  of  their  nature, 
being,  generally  speaking,  ellipses,  much  elongated,  concentric  with  the 
sun's  disc,  each  having  one  of  its  chords  for  its  longer  axis,  and  all  these 
axes  parallel  to  each  other.  At  two  periods  of  the  year  only  do  the 
spots  appear  to  describe  straight  lines,  viz.  on  and  near  to  the  11th  of 
June  and  the  12th  of  December,  on  which  days,  therefore,  the  plane  of 
the  circle,  which  a  spot  situated  on  the  sun's  equator  describes  (and  con- 
sequently, the  plane  of  that  equator  itself,)  passes  through  the  earth. 
Hence  it  is  obvious,  that  the  plane  of  the  sun's  equator  is  inclined  to  that 
of  the  ecliptic,  and  intersects  it  in  a  line  which  passes  through  the  place 
of  the  earth  on  these  days.     The  situation  of  this  line,  or  ilin  line  of  the 


O 


en? 


ht5 


206 


OUTLINES   OF  ASTRONOMT. 


nntUa  of  the  imu's  rquntor  as  it  id  called,  is,  therefore,  dofW»oiI  by  tlio 
lougitudos  of  the  earth  as  seen  from  the  sun  at  those  epochs,  whi>  h  ure 
respectively  ''')''  \l\'  and  200°  21'  (=80°  21'+ 180")  being,  )f  course, 
diauietrically  opposite  in  direction. 

(391.)  The  inclination  of  the  sun's  axis  (that  of  the  plane  of  \t^ 
equator)  to  the  ecliptic  is  determined  by  ascertaining  the  proportion  of 
the  longer  and  the  shorter  diameter  of  the  apparent  ellipse,  described  by 
any  remarkable,  well-defined  spot ;  in  order  to  do  which,  its  apparent 
place  on  the  sun's  disc  must  K  -  pf  nisely  ascertained  by  micrometrio 
measures,  repeated  from  dt>>  io  day  a.;  1  'Ug  as  it  continues  visible  (usually 
about  12  or  18  days,  acci.li'i  to  the  magnitude  of  the  spots,  which 
always  vanish  by  the  (fftct  of  foreshortening  before  they  attain  the  actual 
border  of  the  disc^-  ^hl  the  larger  spots  being  traceable  closer  to  the  limb 
than  the  smaller.')  The  reflation,  of  such  observations,  or  the  oonclu- 
sion  from  them  of  the  element  in  question,  is  complicated  with  the  effect 
of  the  earth's  motion  in  the  interval  of  the  observations,  and  with  its 
situation  in  the  ecliptic,  with  respect  to  the  line  of  nodes.  For  simplicity, 
we  will  suppose  tho  earth  situated  as  it  is  on  the  10th  of  March,  in  a  line 
at  right  angles  to  that  of  the  nodes,  i.  e.  in  the  heliocentric  longitude 
170°  21',  and  to  remain  there  stationary  during  the  whole  passage  of  a 
spot  across  the  disc.     In  this  case  the  axis  of  rotation  of  the  sun  will  be 

Fig.  56. 


situated  in  a  plane  passing  through  the  earth  and  at  right  angles  to  the 
plane  of  the  ecliptic.  Suppose  C  to  represent  the  sun's  centre,  P  C  p 
its  axis,  E  C  the  line  of  sight,  P  N  Q  A  p  S  a  section  of  the  sun  passing 


'  The  great  spot  of  December,  1719,  is  stated  to  have  been  seen  aa  a  notch  in  the 
limb  of  the  sun. 


OP  THE  8UN*8   ROTATION   ON   ITS  AXIS. 


20T 


ed  hy  the 
whicij  ttie 
of  course, 

ine  of  it." 
portioa  of 
scribed  by 
s  apparent 
licrometrio 
le  (usually 
ots,  which 
the  actual 
lO  the  limb 
he  conolu- 
i  the  effect 
d  with  its 
simplicity, 
1,  in  a  lino 
I  longitude 
.saago  of  a 
lun  will  be 


^les  to  the 
tre,  P  C  p 
in  passing 

notch  in  the 


through  the  earth,  and  Q  a  xpot  sirtwuted  on  its  equator,  and  in  that  plane, 
•nd  consequeotly  in  the  iiiiildic  o^  ftfi  apparent  path  across  the  disc.  If  « 
the  axis  of  rotiition  were  pcrp«>«<licular  to  the  ecliptic,  as  N  S,  this  spot 
W'^uld  be  at  A,  and  would  b«  seen  projected  on  C,  the  centre  of  the  sun. 
It  is  uctUitlly  at  Q,  proje"t«d  npon  1),  at  an  apparent  distance  0  D  to  the 
norfh  of  the  lontro,  which  is  the  apparent  smaller  semi-axis  of  the  ellipse 
described  by  the  spot,  which  being  kao\  ■.  by  micromotrio  measurement, 

the  value  of  ^-^  or  the  cosine  of  Q  C  N,  ♦bo  inoUnatiau  of  the  sun's 

equator  becmuw  known,  C  N  being  'ho  apj  "^nt  <  rai-diamotor  of  the 
sun  at  the  time.  At  this  epoch,  inoreo\  fii  the  \orthern  half  of  the  circle 
described  by  the  spot  is  visible  (the  souti  rn  pMuaing  behind  the  body  of 
the  sun,)  and  the  south  polo  2>  ^  the  n  is  *  ithin  the  visible  hemi- 
sphere. Thii»  is  the  case  in  the  whole  ii  om  December  11th  to 
July  12th,  daring  which,  the  visual  my  W^  tpoi  the  southern  side  of 
the  sun's  equ  .tor.  The  contrary  happens  >ther  half  year,  from 
July  12th  to  December  11th,  and  this  is  wh  is  understood  when  we  say 
that  the  aM-am/intj  node  (denoted  Q)  of  the  »  ^  s  equator  lies  in  80°  21' 
longitude — a  spot  on  the  equator  passing  that  do  being  then  in  the  act 
of  ancending  fro  in  the  southern  to  the  norther  ide  of  the  plane  of  the 
ecliptic — such  being  the  conventional  language 
of  these  matters. 

(892.)  If  the  observations  are  made  at  other 
are  the  less  favourable  for  this  purpose  the  mor  remote  they  are  from 
the  epochs  here  as  igned);  when,  moreover,  as  in  strietness  is  necessary, 
the  motion  of  the  earth  in  the  interval  of  the  measM'-'^s  is  allowed  for  (as 
for  a  change  of  the  point  of  sight) ;  the  calculatiou.  requisite  lo  deduce 
the  situation  of  the  axis  in  space,  and  the  duration  of  the  revolution 
around  it,  become  much  more  intricate,  and  it  would  be  beyond  the  scope 
of  this  work  to  enter  into  them.'  According  to  the  best  determinations 
we  possess,  the  inclination  of  the  sun's  equator  to  the  ecliptic  is  about  7** 
20'  (its  nodes  being  as  above  stated),  and  the  period  of  rotation  25  days 
7  hours  48  minutes.* 

(893.)  The  region  of  the  spots  is  confined,  generally  speaking,  within 
about  25**  on  either  side  of  the  sun's  equator;  beyond  30°  they  are  very 

*  See  the  theory  in  Leland's  Astronomy,  art.  3258,  and  the  formulae  of  computation 
in  a  paper  by  Petersen  Schumacher's  Nachrichten,  No.  419. 

'>  Bianchi  (Schumacher's  Nach.  483),  agreeing  with  Laugier.    Leiambre  makes  it 
CS"*  0**  17" ;  Petersen,  25''  4*'  30".    The  inclination  of  the  axis  is  uncertain  to  half  a 
degree,  and  the  node  to  several  degrees.    The  continual  changes  in  the  spots  them 
selves  cause  this  uncertainty. 


>nomers  in  speaking 
•asons  (which,  however, 


SB. 

2 


•SO 

rn 

CO 

£2? 


208 


OUTLINES   OF  ASTRONOMY. 


rarely  seen ;  in  the  polar  regions,  never.  The  actual  equator  of  the  sun 
itis  also  less  frequently  visited  by  spots  than  the  adjacent  zones  on  either 
side,  and  a  very  material  difference  in  their  frequency  and  magnitude 
subsists  in  its  northern  and  southern  hemisphere,  those  on  the  northern 
preponderating  in  both  respects.  The  zone  comprised  between  the  11th 
and  15  th  degree  to  the  northward  of  the  equator  is  particulai-ly  fertile  in 
large  and  durable  spots.  These  circumstances,  as  well  as  the  frequent 
occurrence  of  a  more  or  less  regular  arrangement  of  the  spots,  when 
numerous,  in  the  manner  of  belts  parallel  to  the  equator,  point  evidently 
to  physical  peculiarities  in  certain  parts  of  the  sun's  body  more  favourable 
than  in  others  to  the  production  of  the  spots,  on  the  one  hand ;  and  on 
the  other,  to  a  general  influence  of  its  rotation  on  its  axis  as  a  determining 
cause  of  their  distribution  and  arrangement,  and  would  appear  indicative 
of  a  system  of  movements  in  the  fluids  which  constitute  its  luminous 
surface  bearing  no  remote  analogy  to  our  trade  winds  —  from  whatever 
cause  arising.     (See  art.  239.  et  scq.) 

(394.)  The  duration  of  individual  spots  is  commonly  not  great;  some 
are  formed  and  disappear  within  the  limit  of  a  single  transit  across  the 
disc — but  such  are  for  the  most  part  small  and  insignificant.  Frequently 
they  make  one  or  two  revolutions,  being  recognized  at  their  reappearance 
by  their  situation  with  respect  to  the  equator,  their  configurations  inter  sc, 
their  size,  or  other  peculiarities,  as  well  aa  by  the  interval  elapsing  be- 
tween their  disappearance  at  one  limb  and  reappearance  on  the  other.  In 
a  few  rare  cases,  however,  they  have  been  watched  round  many  revolu- 
tions. The  great  spot  of  1779  appeared  during  six  months,  and  one  and 
the  same  grovp  was  observed  in  1840  by  Schwabe  to  return  eight 
times.*  It  has  been  surmised,  with  considerable  apparent  probability,  that 
some  spots,  at  least,  are  generated  again  and  again,  at  distant  intervals  of 
time,  over  the  same  identical  points  of  the  sun's  body  (as  hurricanes,  for 
example,  are  known  to  affect  given  localities  on  the  earth's  surface,  and  to 
pursue  definite  tracks).  The  uncertainty  which  still  prevails  with  respect 
to  the  exact  duration  of  its  rotation  renders  it  very  difficult  to  obtain  con- 
vincing evidence  of  this  j  nor,  indeed,  can  it  be  expected,  until  by  bring- 
ing together  into  one  connected  view  the  recorded  state  of  the  sun's  sur- 
face during  a  very  long  period  of  time,  and  comparing  together  remarka- 
ble spots  which  have  appeared  on  the  same  parallel,  some  precise  periodic 
time  shall  be  found  which  shall  exactly  conciliate  numerous  and  well- 
characterized  appearances.  The  inquiry  is  one  of  singular  interest,  as 
there  can  be  no  reasonable  doubt  that  the  supply  of  light  and  heat 

*  Schum.  Nach.  No.  418,  p.  150.    The  recent  papers  of  Biela,  Capocci,  Schwabe, 
PastorfT,  and  Schmidt,  in  that  collection,  will  be  found  highly  interesting. 


afforded  i 
which  nr 
some  waj 
(395.) 
the  spots 
atmosphe 
disc  of  th 
enough  tc 
contempli 
the  disc  a 
is  shown 
nified,  so 
of  white 
pearance 
rays  havi 
of  some 
their  pass: 
and  indcc 
total  eclip 
produced 
earth  and 
very  smal 
place,  wer 
about  the 
after  abun 
moon  to 
this  from 
fading  gm 
where  the 
concentric 
fully  seen 
addition  — 
elsewhere ; 
(as  represi 
limb  of  th 
which  the: 
naked  eye 
degree  of  i 
most  excesi 
bly  their  e 
(396.)  ' 
14 


OF  THE   sun's   spots. 


209 


the  sun 

on  either 

lagnitude 

northern 

the  11th 

fertile  in 

frequent 

)t3,  when 

evidently 

'avourable 

I ;  and  on 

termining 

indicative 

luminous 

I  whatever 

eat;  some 
across  the 
frequently 
ippearance 
IS  inter  se, 
ipsing  be- 
)ther.     In 
ay  revolu- 
id  one  and 
urn  eight 
Dility,  that 
itervals  of 
icanes,  for 
ice,  and  to 
th  respect 
(btain  con- 
by  bring- 
sun's  sur- 
reraarka- 
»e  periodic 
and  well- 
Qterest,  as 
and  heat 

i,  Schwabe, 


afforded  to  our  globe  stands  in  intimate  connexion  with  those  processes 
which  are  taking  place  on  the  solar  surface,  and  to  which  the  spots  in 
some  way  or  other  owe  their  origin. 

(395.)  Above  the  luminous  surface  of  the  sun,  and  the  region  in  which 
the  spots  reside,  there  are  strong  indications  of  the  existence  of  a  gaseous 
atmosphere  having  a  somewhat  imperfect  transparency.  When  the  whole 
disc  of  the  sun  is  seen  at  once  through  a  telescope  magnifying  moderately 
enough  to  allow  it,  and  with  a  darkening  glass  such  as  to  suffer  it  to  be 
contemplated  with  perfect  comfort,  it  is  very  evident  that  the  borders  of 
the  disc  are  much  less  luminous  than  the  centre.  That  this  is  no  illusion 
is  shown  by  projecting  the  sun's  image  undarkened  and  moderately  mag- 
nified, so  as  to  occupy  a  circle  two  or  three  inches  in  diameter,  on  a  sheet 
of  white  paper,  taking  care  to  have  it  well  in  focus,  when  the  same  ap- 
pearance will  be  observed.  This  can  only  arise  from  the  circumferential 
rays  having  undergone  the  absorptive  action  of  a  much  greater  thickness 
of  some  imperfectly  transparent  envelope  (due  to  greater  obliquity  of 
their  passage  through  it)  than  the  central.  —  But  a  still  more  convincing 
and  indeed  decisive  evidence  is  offered  by  the  phaenomena  attending  a 
total  eclipse  of  the  sun.  ■  Such  eclipses  (as  will  be  shown  hereafter)  are 
produced  by  the  interposition  of  the  dark  body  of  the  moon  between  the 
earth  and  sun,  the  moon  being  large  enough  to  cover  and  surpass,  by  a 
very  small  breadth,  the  whole  disc  of  the  sun.  Now  when  this  takes 
place,  were  there  no  vaporous  atmosphere  capable  of  reflecting  any  light 
about  the  sun,  the  sky  ought  to  appear  totally  dark,  since  (as  will  here- 
after abundantly  appear)  there  is  not  the  smallest  reason  for  believing  tho 
moon  to  have  any  atmosphere  capable  of  doing  so.  So  far,  however,  is 
this  from  being  the  case,  that  a  bright  ring  or  corona  of  light  is  seen, 
fading  gradually  away,  as  represented  in  PI.  I.  fig.  3.,  which  (in  cases 
where  the  moon  is  not  centrally  superposed  on  the  sun)  is  observed  to  be 
concentric  with  the  latter,  not  the  former  body.  This  corona  was  beauti- 
fully seen  in  the  eclipse  of  July  7,  1842,  and  with  this  most  remarkable 
addition  —  witnessed  by  every  spectator  in  Pavia,  Milan,  Vienna,  and 
elsewhere :  there  distinct  and  very  conspicuous  rose-coloured  protuberances 
(as  represented  in  the  figure  cited)  were  seen  to  project  beyond  the  dark 
limb  of  the  moon,  likened  by  some  to  flames,  by  others  to  mountains,  but 
which  their  enormous  magnitude  (for  to  have  been  seen  at  all  by  tho 
naked  eye  their  height  must  have  exceeded  40,000  miles),  and  their  faint 
degree  of  illumination,  clearly  prove  to  have  been  cloudy  masses  of  the 
most  excessive  tenuity^  and  which  doubtless  owed  their  support,  and  proba- 
bly their  existence,  to  such  an  atmosphere  as  we  are  now  speaking  of. 

(396.)  That  the  temperature  at  the  visible  surface  of  the  sun  cannot 
14 


"353 

WI<JJ 


210 


t) 


OUTLINES   OF  ASTRONOMY. 


be  otherwise  than  very  elevated,  much  more  so  than  any  artificial  heat 
produced  in  our  furnaces,  or  by  chemical  or  galvanic  processes,  we  have 
indications  of  several  distinct  kinds :  1st,  From  the  law  of  decrease  of 
radiant  heat  and  light,  which,  being  inversely  as  the  squares  of  the  dis- 
tances, it  follows,  that  the  heat  received  on  a  given  area  exposed  at  the 
distance  of  the  earth,  and  on  an  equal  area  at  the  visible  surface  of  the 
sun,  must  be  in  the  proportion  of  the  area  of  the  sky  occupied  by  the 
sun's  apparent  disc  to  the  whole  hemisphere,  or  as  1  to  about  800000. 
A  far  less  intensity  of  solar  radiation,  collected  in  the  focus  of  a  burning 
glass,  suffices  to  dissipate  gold  and  platina  in  vapour.  2dly,  From  the 
facility  with  which  the  calorific  rays  of  the  sun  traverse  glass,  a  property 
which  is  found  to  belong  to  the  heat  of  artificial  fires  in  the  direct  pro- 
portion of  their  intensity.'  Sdly,  From  the  fact,  that  the  most  vivid 
flames  disappear,  and  the  most  intensely  ignited  solids  appear  only  as 
black  spots  on  the  disc  of  the  sun  when  held  between  it  and  the  eye.- 
From  the  last  remark  it  follows,  that  the  body  of  the  sun,  however  dark 
it  may  appear  when  seen  through  its  spots,  may,  nevertheless,  be  in  a 
state  of  most  intense  ignition.  It  does  not,  however,  follow  of  necessity 
that  it  miist  be  so.  The  contrary  is  at  least  physically  possible.  A  per- 
fectly rejlective  canopy  would  effectually  defend  it  from  the  radiation  of 
the  luminous  regions  above  its  atmosphere,  and  no  heat  would  be  con- 
ducted downwards  through  a  gaseous  medium  increasing  rapidly  in 
density.  That  the  penumbral  clouds  are  highly  reflective,  the  fact  of 
their  visibility  in  such  a  situation  can  leave  no  doubt. 

(397.)  As  the  magnitude  of  the  sun  has  been  measured,  and  (as  we 
shall  hereafter  see)  its  weight,  or  quantity  of  ponderable  matter,  ascer- 
tained, so  also  attempts  have  been  made,  and  not  wholly  without  success, 
from  the  heat  actually  communicated  by  its  rays  to  given  surfaces  of 
material  bodies  exposed  to  their  vertical  action  on  the  earth's  surface,  to 
estimate  the  total  expenditure  of  heat  by  that  luminary  in  a  given  time. 
The  result  of  such  experiments  has  been  thus  announced.  Supposing  a 
cylinder  of  ice  45  miles  in  diameter,  to  be  continually  darted  into  the  sun 
with  the  velocity  of  light,  and  that  the  water  produced  by  its  fusion  were 


'  By  direct  measurement  with  the  aclinometer,  I  find  that  out  of  1000  calorific  eolar 
rays,  816  penetrate  a  sheet  of  plate  glass  0'12  inch  thick ;  and  that  of  1000  rays  which 
have  passed  through  one  such  plate,  859  are  capable  of  passing  through  another.  H. 
1827. 

'The  ball  of  ignited  quicklime,  in  Lieutenant  Drummond's  oxy-hydrogen  lamp, 
gives  the  nearest  imitation  of  the  solar  splendour  which  has  yet  been  produced.  The 
appearance  of  this  against  the  sun,  was,  however,  as  described  in  an  imperfect  trial  at 
which  I  was  present.  The  experiment  ought  to  be  repeated  under  favourable  circum- 
stances.—iVb(e  to  the  ed.  of  1833. 


ticial  heat 
1,  we  have 
iecrcase  of 
of  the  dis- 
sed  at  the 
face  of  the 
ied  by  the 
Lt  300000. 
'  a  burning 
,  From  the 
a  property 
direct  pro- 
most  vivid 
Bar  only  as 
d  the  eye.^ 
Dwever  dark 
3SS,  be  in  a 
of  necessity 
tie.     A  per- 
radiation  of 
uld  be  con- 
rapidly  in 
the  fact  of 

,  and  (as  we 
attcr,  ascer- 
lout  success, 
surfaces  of 
s  surface,  to 
given  time. 
Supposing  a 
into  the  sun 
fusion  were 

calorific  solar 
DOO  rays  which 
another.    H. 

ydrogen  lamp, 

Toduced.    The 

iperfect  trial  at 

mrable  circum- 


TERRESTRIAL   EFFECTS   OF  THE   SUN'S   RADIATION.         211 

continually  carried  off,  the  heat  now  given  off  constantly  by  radiation 
would  then  be  wholly  expended  in  its  liquefaction,  on  the  one  hand,  so  us 
to  leave  no  radiant  surplus ;  while,  on  the  other,  the  actual  temperature 
at  its  surface  would  undergo  no  diminution. 

(398.)  This  immense  escape  of  heat  by  radiation,  we  may  remark,  will 
fully  explain  the  constant  state  of  tumultuous  agitation  in  which  the  fluids 
composing  the  visible  surface  are  maintained,  and  the  continual  geceration 
and  filling  in  of  the  pores,  without  having  recourse  to  internal  causes. 
The  mode  of  action  here  alluded  to  is  perfectly  represented  to  the  eye  in 
the  disturbed  subsidence  of  a  precipitate,  as  described  in  art.  387,  when 
the  fluid  from  which  it  subsides  is  warm,  and  losing  heat  from  its  surface. 

(399.)  The  sun's  rays  are  the  ultimate  source  of  almost  every  motion 
which  takes  place  on  the  surface  of  the  earth.  By  its  heat  are  produced 
all  winds,  and  thojj^  disturbances  in  the  electric  equilibrium  of  the  atmo- 
sphere which  give  rise  to  the  phenomena  of  lightning,  and  probably  also 
to  those  of  terrestrial  magnetism  and  the  aurora.  By  their  vivifying 
action  vegetables  are  enabled  to  draw  support  from  inorganic  matter,  and 
become,  in  their  turn  the  support  of  animals  and  of  man,  and  the  sources 
of  those  great  deposits  of  dynamical  efficiency  which  are  laid  up  for 
human  use  in  our  coal  strata.'  By  them  the  waters  of  the  sea  are  made 
to  circulate  in  vapour  through  the  air,  and  irrigate  the  land,  producing 
springs  and  nvers.  By  them  are  produced  all  disturbances  of  the 
chemical  equilibrium  of  the  elements  of  nature,  which,  by  a  series  of 
compositions  and  decompositions,  give  rise  to  new  products,  and  originate 
a  transfer  of  materials.  Even  the  slow  degradation  of  the  solid  con- 
stituents of  the  surface,  in  which  its  chief  geological  changes  consist,  is 
almost  entirely  due  on  the  one  hand  to  the  abrasion  of  wind  and  rain,  and 
the  alternation  of  heat  and  frost ;  on  the  other  to  the  continual  beating 
of  the  sea  waves,  agitated  by  winds,  the  results  of  solar  radiation.  Tidal 
action  (itself  partly  due  to  the  sun's  agency)  exercises  here  a  compara- 
tively slight  influence.  The  effect  of  oceanic  currents  (mainly  originating 
in  that  influence,)  though  slight  in  abrasion,  is  powerful  in  diffusing  and 
transporting  the  matter  abraded ;  and  when  we  consider  the  immense 
transfer  of  matter  so  produced,  the  increase  of  pressure  over  large  spaces 
in  the  bed  of  the  ocean,  and  diminution  over  corresponding  portions  of 
the  land,  we  are  not  at  a  loss  to  perceive  how  the  clastic  power  of  sub- 
terranean fires,  thus  repressed  on  the  one  hand  and  relieved  on  the  other, 
may  break  forth  in  points  where  the  resistance  is  barely  adequate  to  their 
retention,  and  thus  bring  the  phenomena  of  even  volcanic  activity  under 
the  general  law  of  solar  influence.' 

'  So  in  the  edition  of  1633.  »  So  in  the  edition  of  1833. 


m 


«V1 


CD 


212 


OUTLINES   OP  ASTRONOMY. 


(400.)  The  great  mystery,  however,  is  to  conceive  how  so  enorBfiJUS  a 
conflagration  (if  such  it  be)  can  be  kept  up.  Every  discovery  in  chemi- 
cal science  here  leaves  us  completely  at  a  loss,  or  rather,  seems  to  remove 
farther  the  prospect  of  probable  explanation.  If  conjecture  might  be 
hazarded,  we  should  look  rather  to  the  known  possibility  of  an  indefinite 
generation  of  heat  by  friction,  or  to  its  excitement  by  the  electric  dis- 
charge, than  to  any  actual  combustion  of  ponderable  fuel,  whether  solid 
or  gaseous,  for  the  origin  of  the  solar  radiatic..' 


ft 


'Electricity  traversing  excessively  rarefied  air  or  vapours,  gives  out  light,  and, 
doubtless,  also  heat.  May  not  a  continual  current  of  electric  matter  be  constantly 
circulating  in  the  sun's  immediate  neighbourhood,  or  traversing  the  planetary  spaces, 
and  exciting,  in  the  upper  regions  of  its  atmosphere,  those  phenomena  of  which,  on 
however  diminutive  a  scale,  we  have  yet  an  unequivocal  manifestation  in  our  aurora 
borealis.  The  possible  analogy  of  the  solar  light  to  that  of, the  aurora  has  been 
distinctly  insisted  on  by  the  late  SirW.  Herschel,  in  his  paper  already  cited.  It  would 
be  a  highly  curious  subject  of  experimental  inquiry,  how  far  a  mere  reduplication  of 
sheets  of  flame,  at  a  distance  one  behind  the  other  (by  which  their  light  might  bo 
brought  to  any  required  intensity,)  would  communicate  to  the  heat  of  the  resulting 
compound  ray  the  penetrating  character  which  distinguishes  the  solar  calorific  rnys. 
We  may  also  observe,  that  the  tranquillity  of  the  sun's  polar,  as  compared  with  its 
equatortal  regions  (if  its  spots  be  really  atmospheric.)  cannot  be  accounted  for  by  its 
rotation  on  its  axis  only,  but  must  arise  from  some  cause  external  to  the  luminous  sur- 
face of  the  sun,  as  we  see  the  belts  of  Jupiter  and  Saturn,  and  our  trade-winds  arise 
from  a  cause,  external  to  these  planets,  combining  itself  with  their  rotation,  which 
alone  can  produce  no  motions  when  once  the  form  of  equilibrium  is  attained. 

The  prismatic  analysis  of  the  solar  beam  exhibits  in  the  spectrum  a  series  of  "  (ixed 
Hnes,"  totally  unlike  those  which  belong  to  the  light  of  any  known  terrestrial  flame. 
1'his  may  hereafter  lead  us  to  a  clearer  insight  into  its  origin.  But,  before  we  can 
draw  any  conclusions  from  such  an  indication,  we  must  recollect  that  previous  to 
reaching  us  it  has  und'^rgone  the  whole  absorptive  action  (»f  our  atmosphere,  as  well 
as  of  the  sun's.  Of  the  latter  we  know  nothing,  and  may  conjecture  every  thing ; 
but  of  the  blue  colour  of  the  former  we  are  sure ;  and  if  this  be  an  inherent  (t.  e.  an 
absorptive)  colour,  the  air  must  be  expected  to  act  on  the  spectrum  after  the  analogy 
of  other  coloured  media,  which  often  (and  especially  light  blue  media)  leave  unab- 
sorbed  portions  separated  by  dark  intervals.  It  deserves  inquiry,  therefore,  whether 
some  or  all  the  fixed  lines  observed  by  Wollaaton  and  Fraunhofer  may  not  have  their 
ongin  in  our  own  atmosphere.  Experiments  made  on  lofty  mountains,  or  the  cars  of  bal- 
loons, on  the  one  hand,  and  on  the  other  with  reflected  beams  which  have  been  made 
to  traverse  several  miles  of  additional  air  near  the  surface,  would  decide  this  point. 
The  absorptive  effect  of  the  sun's  atmosphere,  and  possibly  also  of  the  medium  sur- 
rounding it  (whatever  it  be)  which  resists  the  motions  of  comets,  cannot  be  thus 
eliminated. — Note  to  the  edition  of  1833. 


OF   THE  MOON. 


218 


rmaus  a 
1  chcmi- 
» remove 
aigbt  be 
ndcfinite 
jtric  dis- 
bar solid 


light,  and, 
constantly 
jry  spaces, 

which,  on 
our  aurora 

has  been 
.  It  would 
slicalion  of 
U  might  he 
le  resulting 
lorific  rays, 
■ed  with  its 
d  for  by  its 
minous  sur- 
Iwinds  arise 
lion,  which 

8  of  "fixed 
itrial  flame, 
ore  we  can 
previous  to 
ire,  as  well 
very  thing ; 
■ent  (t.  c.  an 
the  analogy 
eave  unab- 
re,  whether 
have  their 
carsofbal- 
been  made 
this  point, 
ledium  sut- 
lot  be  thus 


CHAPTER  VII. 

OP  THE   MOON. — ITS   SIDEREAli   TERIOD. — ITS  APPARENT  DIAMETER. 

—  ITS  PARALLAX,  DISTANCE,  AND  REAL  DIAMETER.  —  FIRST  AP- 
PROXIMATION TO  ITS  ORBIT.  —  AN  ELLIPSE  ABOUT  THE  EARTH  IN 
THE  FOCUS.  —  ITS  EXCENTRICITY  AND  INCLINATION.  —  MOTION  OP 
ITS  NODES  AND  APSIDES. — OF  OCCULT ATIONS  AND  SOLAR  ECLIPSES 
GENERALLY.  —  LIMITS  WITHIN  WHICH  THEY  ARE  POSSIBLE.  —  THEY 
PROVE  THE  MOON  TO  BE  AN  OPAKE  SOLID. — ITS  LIGHT  DERIVED 
FROM  THE  SUN.  —  ITS  PHAvSES.  —  SYNODIC  REVOLUTION  OR  LUNAR 
MONTH. — OP  ECLIPSES  MORE  PARTICULARLY.  —  THEIR  PHENOMENA. 

—  THEIR  PERIODICAL  RECURRENCE.  —  PHYSICAL  CONSTITUTION  OP 
THE  MOON. — ITS  MOUNTAINS  AND  OTHER  SUPERFICIAL  FEATURES. 
— ^INDICATIONS  OF  FORMER  VOLCANIC  ACTIVITY. — ITS  ATMOSPHERE. 

—  CLIMATE.  —  RADIATION  OF  HEAT  FROM  ITS  SURFACE. — ROTATION 
ON  ITS  OWN  AXIS.  —  LIBRATION. — APPEARANCE  OP  THE  EARTH 
FROM  IT. 

(401.)  The  moon,  like  the  sun,  appears  to  advance  among  the  stars 
with  a  movement  contrary  to  the  general  diurnal  motion  of  the  heavens, 
but  much  more  rapid,  so  as  to  be  very  readily  perceived  (as  we  have 
before  observed)  by  a  few  hours'  cursory  attention  on  any  moonlight 
night.  By  this  continual  advance,  which,  though  sometimes  quicker, 
sometimes  slower,  is  never  intermitted  or  reversed,  it  makes  the  tour  of 
the  heavens  in  a  mean  or  average  period  of  27''  T"*  43""  ll'O,  returning, 
in  that  time,  to  a  position  among  the  stars  nearly  coincident  with  that  it 
had  before,  and  which  would  be  exactly  so,  but  for  reasons  presently  to 
be  stated. 

(402.)  The  moon,  then,  like  the  sun,  apparently  describes  an  orbit 
round  the  earth,  and  this  orbit  cannot  be  very  different  from  a  circle,  be- 
cause the  apparent  angular  diameter  of  the  full  moon  is  not  liable  to  any 
great  extent  of  variation.  '     ,.; 

(403.)  The  distance  of  the  moon  from  the  earth  is  concluded  from  its 
horizontal  parallax,  which  may  be  found  either  directly,  by  observations 
at  remote  geographical  stations,  exactly  similar  to  those  described  in  art. 
355,  in  the  case  of  the  sun,  or  by  means  of  the  phaenomena  called  occul- 


G2 


pa 


1 


;^i 


214 


OUTLINES   OF  ASTRONOMY. 


tations,  from  wbich  also  its  apparent  diameter  is  most  readily  and  cor- 
rectly found.  From  such  observations  it  results  that  the  mean  or  average 
distance  of  the  centre  of  the  moon  from  that  of  the  earth  is_5i):.l).6i3,Qf 
the  earth's  equatorial  radii,  or  about  237,000  miles.  This  distance,  : 
great  as  it  is,  is  little  more  than  one-fourth  of  the  diameter  of  the  sun's 
body,  so  that  the  globe  of  the  sun  would  nearly  twice  include  the  whole 
orbit  of  the  moon;  a  consideration  wonderfully  calculated  to  raise  our 
ideas  of  that  stupendous  luminary  ! 

(404.)  The  distance  of  the  moon's  centre  from  an  observer  at  any 
station  on  the  earth's  surface,  compared  with  its  apparent  angular  diameter 
as  measured  from  that  station,  will  give  its  real  or  linear  diameter.  Now, 
the  former  distance  is  easily  calculated  when  the  distance  from  the  earth's 
centre  is  known,  and  the  apparent  zenith  distance  of  the  moon  also  deter- 
mined by  observation ;  for  if  we  turn  to  the  figure  of  art.  339,  and  suppose 
S  the  moon,  A  the  station,  and  C  the  earth's  centre,  the  distance  S  C,  and 
the  earth's' radius  C  A,  two  sides  of  the  triangle  A  C  S  are  given,  and  the 
angle  CAS,  which  is  the  supplement  of  Z  A  S,  the  observed  zenith  dis- 
tance, whence  it  is  easy  to  find  A  S,  the  moon's  distance  from  A.  From 
such  observations  and  calculations  it  results,  that  the  real  diameter  of  the 
moon  is  2100  miles,  or  about  0-2729  of  that  of  the  earth,  whence  it  follows. 
•  that,  the  bulk  of  rtie  latter  heiug  considered  as  1,  that  of  the  former  will 
be  00204,  or  about  ^.  The  difference  of  the  apparent  diameter  of  the 
moon,  as  seen  /rom  the  earth's  centre  and  from  any  point  of  its  surface, 
is  technically  called  the  augmentation  of  the  apparent  diameter,  and  Its 
maximum  occurs  when  the  moon  is  in  the  zenith  of  the  spectator.  Her 
mean  angular  diameter,  as  seen  from  the  centre,  is  31'  7",  and  is  always 
=  0-545  X  her  horizontal  parallax. 

(405.)  By  a  series  of  observations,  such  as  described  in  art.  403,  if 
continued  during  one  or  more  revolutions  of  the  moon,  its  real  distance 
may  be  ascertained  at  every  point  of  its  orbit ;  and  if  at  the  same  time  its 
apparent  places  in  the  heavens  be  observed,  and  reduced  by  means  of  its 
parallax  to  the  earth's  centre,  their  angular  intervals  will  become  known, 
so  that  the  path  of  the  moon  may  then  be  laid  down  on  a  chart  supposed 
to  represent  the  plane  in  which  its  orbit  lies,  just  as  was  explained  in  the 
case  of  the  solar  ellipse  (art.  349.)  Now,  when  this  is  done,  it  is  found 
that,  neglecting  certain  small  (though  very  perceptible)  deviations  (Of 
which  a  satisfactory  account  will  hereafter  be  rendered),  the  form  of  the 
apparent  orbit,  like  that  of  the  sun,  is  elliptic,  but  considerably  more 
eccentric,  the  eccentricity  amounting  to  0-05484  of  the  mean  distance,  or 
the  major  semi-axis  of  the  ellipse,  and  the  earth's  centre  being  situated  in 
its  focus.  V   .    . 


OF  THE   moon's   MOTION. 


216 


'  1 


and  cor- 
)r  average 

distance,  J 
the  sun's 
the  wbole 

raise  our 

er  at  any 
,r  diameter 
«r.     Now, 
the  earth's 
also  deter- 
nd  suppose 
se  S  C,  and 
en,  and  the 
zenith  dis- 
A.    From 
leter  of  the 
30  it  follows, 
former  will 
leter  of  the 
its  surface, 
ter,  and  its 
ator.     Her 
i  is  always 

art.  403,  if 
>eal  distance 
imc  time  its 
means  of  its 
jme  known, 
art  supposed 
ained  in  the 
,  it  is  found 
viations  (of 
form  of  the 
erably  more 
distance,  or 
g  situated  in 


(406.)  The  plane  in  which  this  orbit  lies  is  not  the  ecliptic,  however, 
bijt  is  inclined  to  it  at  an  angle  of  5°  8'  48",  which  is  called  the  iucU;. 
-iuttion!  of  the  lunar  orbit,  and  intersects  it  in  two  opposite  points,  which 
are  called  its  nodes — the  asccndinf/ node  being  that  in  which  the  moon 
passes  from  the  southern  side  of  the  ecliptic  to  the  northern,  and  the 
descending  the  reverse.  The  points  of  the  orbit  at  which  the  moon  is 
nearest  to,  and  farthest  from,  the  earth,  are  called  respectively  its  perigee 
-am  a^wyec,  and  the  line  joining  them  and  the  earth  of  «ue  line  of  apsides. 
I  (40T.)  There  are,  however,  several  remarkable  circumstances  which 
interrupt  the  closeness  of  the  analogy,  which  cannot  fail  to  strike  the 
reader,  between  the  motion  of  the  moon  around  the  earth,  and  of  the 
earth  around  the  sun.  In  the  latter  case,  the  ellipse  described  remains, 
during  a  great  many  revolutions,  unaltered  in  its  position  and  dimensions; 
or,  at  least,  the  changes  which  it  undergoes  are  not  perceptible  but  in  a 
course  of  very  nice  observations,  which  have  disclosed,  it  is  true,  the 
existence  of  "  perturbations,"  but  of  so  minute  an  order,  that,  in  ordinary 
parlance,  and  for  common  purposes,  we  may  leave  them  unconsidered. 
But  this  cannot  be  done  in  the  case  of  the  moon.  Even  in  a  single  revo- 
lution, its  deviation  from  a  perfect  ellipse  is  very  sensible.  It  does  not 
return  to  the  same  exact  position  among  the  stars  froui  which  it  set  out, 
thereby  indicating  a  continual  change  in  the  ^>/aH<^  of  its  orbit.  And,  in 
effect,  if  we  trace  by  observation,  frOm  month  to  month,  the  point  where 
it  traverses  the  ecliptic,  we  shall  fiud  that  the  nodes  of  its  orbit  are  in  a 
continual  state  of  retreat  upon  the  ecliptic.  Suppose  O  to  be  the  earth, 
and  A  bad  that  portion  of  the  plane  of  the  ecliptic  which  is  intersected 
by  the  moon,  in  its  alternate  passages  through  it,  from  south  to  north,  and 
vice  versd ;  and  let  A  B  C  D  E  F  be  a  portion  of  the  moon's  orbit,  em- 


bracing a  complete  sidereal  revolution.  Suppose  it  to  set  out  from  the 
ascending  node,  A ;  then,  if  the  orbit  lay  all  in  one  plane,  passing  through 
0,  it  would  have  a,  the  opposite  point  in  the  ecliptic,  for  its  descending 
node ;  after  passing  which,  it  would  again  ascend  at  A.  But,  in  fact,  its 
real  path  carries  it  not  to  a,  but  along  a  certain  curve,  A  B  C.  to  C,  a 


Cii** 


B*', 


n 


216 


OUTLINES   OP  ASTRONOMY. 


h'' 


i^ 
!! 


point  in  the  ecliptic  less  than  180°  distant  from  A ;  «o  that  the  angle 
A  0  C,  or  the  arc  of  longitude  described  between  the  ascending  and  the 
descending  node,  is  somewhat  less  than  180°.  It  then  pursues  its  course 
below  the  ecliptic,  along  the  curve  C  D  E,  and  rises  again  above  it,  not  at 
the  point  c,  diametrically  opposite  to  C,  but  at  a  point  E,  less  advanced  in 
longitude.  On  the  whole,  then,  the  arc  described  in  longitude  between 
two  consecutive  passages  from  south  to  north,  through  the  plane  of  the 
ecliptic,  falls  short  of  360°  by  the  angle  A  0  E  j  or,  in  other  words,  the 
ascending  node  appears  to  have  retreated  in  one  lunation  on  the  plane  of 
the  ecliptic  by  that  amount.  To  complete  a  sidereal  revolution,  then,  it 
must  still  go  on  to  describe  an  arc,  E  F,  on  its  orbit,  which  will  no  longer, 
however,  bring  it  exactly  back  to  A,  but  to  a  point  somewhat  above  it,  or 
having  north  latittide. 

(408.)  The  actual  amount  of  this  retreat  of  the  moon's  node  is  about 
3'  10"-64  per  diem,  on  an  average,  and  in  a  period  of  6793  39  mean 
solar  days,  or  about  18-6  years,  the  ascending  node  is  carried  round  in  a 
direction  contrary  to  the  moon's  motion  in  its  orbit  (or  from  east  to  west) 
over  a  whole  circumference  of  the  ecliptic.  Of  course,  in  the  middle  of 
this  period  the  position  of  the  orbit  must  have  been  precisely  reversed 
from  what  it  was  at  the  beginning.  Its  apparent  path,  then,  will  lie 
among  totally  different  stars  and  constellations  at  different  parts  of  this 
period ;  and  this  kind  of  spiral  revolution  being  continually  kept  up,  it 
will,  at  one  time  or  other,  cover  with  its  disc  every  point  of  the  heavens 
within  that  limit  of  latitude  or  distance  from  the  ecliptic  which  its  inclina- 
tion permits;  that  is  to  say,  a  belt  or  zone  of  the  heavens,  of  lO''  18'  in 
breadth,  having  the  ecliptic  for  its  middle  line.  Nevertheless,  :t  still 
remains  true  that  the  actual  place  of  the  moon,  in  consequence  of  this 
motion,  deviates  in  a  single  revolution  very  little  from  what  it  would  be 
were  the  nodes  at  rest.  Supposing  the  moon  to  set  out  from  its  node  A, 
its  latitude,  when  it  comes  to  F,  having  completed  a  revolution  in  longi- 
tude, will  not  exceed  8'j  which,  though  small  in  a  single  revolution, 
accumulates  in  its  effect  in  a  succession  of  many :  it  is  to  account  for,  and 
represent  geometrically,  this  deviation,  that  the  motion  of  the  nodes  is 
devised.  ,  .  ^ 

(409.)  The  noon's  orbit,  then,  is  not,  strictly  speaking,  an  ellipse 
returning  into  itself,  by  reason  of  the  variation  of  the  plane  in  whichMt 
lies,  and  the  motion  of  its  nodes.  But  even  laying  aside  this  considera- 
tion, the  axis  of  the  ellipse  is  itself  constantly  changing  its  direction  in 
space,  as  has  already  been  stated  of  the  solar  ellipse,  but  muoh  more 
rapidly  j  making  a  complete  revolution,  in  the  same  direction  with-  the 
moon's  own  motion,  in  3232'5753  mean  solar  days,  or  about  nine  years, 


being  al 
This  is  I 
apsides. 
to  produ( 
included 
the  mT)on 
it  becom( 
and  a  hal 
apogee  of 
_    (410.) 
is  to  rega 
at  the  sa 
revolutioi 
that  plant 
exactly  si 
produced 
(411.) 
cally  spea 
stars  are  i 
that  at  on 
and  plane 
of  the  eai 
throw  it  a 
the  centn 
exempt  fr 
in  this  he 
pied  in  th 
the  most 
astronomj 
even  in  s( 
were,  obli 
upon  it  as 
nution  of 
if  at  midi 
centrally 
the  earth 
the  very  i 
when  the 
light,  pro] 
in  its  cent 

(412.) 


MOTION   OF  THE   NODES  AND   APSIDES. 


217 


:he  angle 
r  and  the 
its  course 
it,  not  at 
vanced  in 
I  between 
me  of  the 
^ords,  the 
!  plane  of 
n,  then,  it 
no  longer, 
bove  it,  or 

e  is  about 
^30  mean 
ound  in  a 
St  to  west) 
middle  of 
ly  reversed 
n,  will  lie 
rts  of  this 
kept  up,  it 
le  heavens 
its  inclina- 
IC^  18"  in 
iss,  it  still 
nee  of  this 
t  would  be 
ts  node  A, 
a  in  longi- 
revolution, 
int  for,  and 
ie  nodes  is 

an  ellipse 
in  which' it 
s  considera-^ 
lirection  in 
much  more 
n  with-  the 

nine  years, 


being  about  3°  oi  igular  motion  in  a  whole  revolution  of  the  moon. 
This  is  a  phenomenon'  known  by  the  name  of  the  revolution  of  the  moon's 
apsides.  Its  cause  will  be  hereafter  explained.  Its  immediate  effect  is 
;to  produce  a  variation  in  the  moon's  distance  from  the  earth,  which  is  not 
included  in  the  laws  of  exact  elliptic  motion.  In  a  single  revolution  of 
the  mT)on,  this  variation  of  distance  is  trifling ;  but  in  the  course  of  many 
it  becomes  considerable,  as  is  easily  seen,  if  wo  consider  that  in  four  years 
and  a  half  the  position  of  the  axis  will  be  completely  reversed,  and  the 
apogee  of  the  moon  will  occur  where  the  perigee  occurred  before. 

(410.)  The  best  way  to  form  a  distinct  conception  of  the  moon's  motion 
is  to  regard  it  as  describing  an  ellipse  about  the  earth  in  the  focus,  and, 
at  the  same  time,  to  regard  this  ellipse  itself  to  be  in  a  twofold  state  of 
revolution ,  1st,  in  its  own  plane,  by  a  continual  advance  of  its  axis  in 
that  plane ;  and  2dly,  by  a  continual  tilting  motion  of  the  plane  itself, 
exactly  similar  to,  but  much  ^nore  rapid  than,  that  of  the  earth's  equator 
produced  by  the  conical  motion  of  its  axis  described  in  art.  317. 

(411.)  As  the  moon  is  at  a  very  moderate  distance  from  us  (astronomi- 
cally speaking),  and  is  in  fact  our  nearest  neighbour,  while  the  sun  and 
stars  are  in  comparison  immensely  beyond  it,  it  must  of  necessity  happen, 
that  at  one  time  or  other  it  must  j)ass  over  and  occxdt  or  eclipse  every  star 
and  planet  within  the  zone  above  described  (and,  as  seen  from  the  surface 
of  the  earth,  even  somewhat  beyond  it,  by  reason  of  parallax,  which  may 
throw  it  apparently  nearly  a  degree  either  way  from  its  place  as  seen  from 
the  centre,  according  to  the  observer's  station).  Nor  is  the  sun  itself 
exempt  from  being  thus  hidden,  whenever  any  part  of  the  moon's  disc, 
in  this  her  tortuous  course,  couies  to  overlap  any  part  of  the  space  occu- 
pied in  the  heavens  by  that  luminary.  On  these  occasions  is  exhibited 
the  most  striking  and  impressive  of  all  the  occasional  phenomena  of 
astronomy,  an  eclipse  of  the  sun,  in  which  a  greater  or  less  portion,  or 
even  in  some  rare  conjunctures  the  whole,  of  its  disc  is  obscured,  and,  as  it 
were,  obliterated,  by  the  superposition  of  that  of  the  moon,  which  appears 
upon  it  as  a  circularly-terminated  black  spot,  producing  a  temporary  dimi- 
nution of  daylight,  or  even  nocturnal  darkness,  so  that  the  stars  appear  as 
if  at  midnight.  In  other  cases,  when,  at  the  moment  that  the  moon  is 
centrally  superposed  on  the  sun,  it  so  happens  that  her  distance  from 
the  earth  is  such  as  to  render  her  angular  diameter  less  than  the  sun's, 
the  very  singular  phenomenon  of  an  annular  solar  eclipse  takes  place, 
when  the  edge  of  the  sun  appears  for  a  few  minutes  as  a  narrow  ring  of 
light,  projecting  on  all  sides  beyond  the  dark  cinjle  occupied  by  the  moon 
in  its  centre.  / 

(412.)  A  solar  eclipse  can  only  happen  when  the  sun  and  moon  are  in 


C3 


218 


OUTLINES   OF  ASTRONOMY. 


conjunction,  that  is  to  say,  have  tho  same,  or  nearly  the  same,  position  ia 
the  heavens,  or  tho  same  longitude.  It  appears  by  art.  409  that  this 
condition  cun  only  bo  fulfilled  at  tho  time  of  a  neio  moon,  though  it  by  no 
means  follows,  that  at  cvcri/  conjunction  there  must  be  an  eclipse  of  the 
sun.  If  the  lunar  orbit  coincided  with  tho  ecliptic,  this  would  be  the 
case,  but  as  it  is  inclined  to  it  at  an  angle  of  upwards  of  5°,  it  is  evident 
that  the  conjunction,  or  equality,  of  longitudes,  may  take  place  when  tho 
moon  is  in  the  part  of  her  orbit  too  remote  from  the  ecliptic  to  permit  the 
discs  to  meet  and  overlap.  It  is  easy,  however,  to  assign  the  limits 
within  which  an  eclipse  is  possible.  To  this  end  we  must  consider,  that, 
by  tho  effect  of  parallax,  the  moon's  ajtparcnt  edge  may  be  thrown  in 
any  direction,  according  to  a  spectator's  geographical  station,  by  anj/ 
amount  not  exceeding  the  horizontal  parallax.  Now,  this  comes  to  tho 
same  (so  fi.i  as  the  possibility  of  an  eclipse  is  concerned)  as  if  the  ap- 
parent diameter  of  the  moon,  seen  from  the  earth's  centre,  were  dilated 
by  twice  lii  horizontal  parallax ;  for  if,  when  so  dilated,  it  can  touch  or 
overlap  the  sun,  there  must  be  an  eclipse  at  some  part  or  other  of  the 
earth's  surface.  If,  then,  at  the  moment  of  the  nearest  conjunction,  the 
geocentric  distance  of  the  centres  of  the  two  luminaries  do  not  exceed  the 
sum  of  their  semidiamcters  and  of  the  moon's  horizontal  parallax,  there 
will  be  an  eclipse.  This  sum  is,  at  its  maximum,  about  1°  34'  27".  In 
the  spherical  triangle  S  N  M,  then,  in  which  S  is  the  sun's  centre,  M  the 
moon's,  S  N  the  ecliptic,  M  N  tho  moon's  orbit,  and  N  the  node,  we  may 

Fig.  58. 


suppose  the  angle  N  S  M  a  right  angle,  S  M  =  1°  34'  27",  and  tho  angle 
M  N  S  =  5°  8'  48",  the  inclination  of  the  orbit.  Hence  we  calculate 
SN,  which  comes  out  16°  58'.  If,  then,  at  ^Ha  moment  of  the  new 
moon,  the  moon's  node  is  farther  from  the  sun  in  longitude  than  this 
limit,  there  can  be  no  eclipse ;  if  within,  there  may,  and  probably  will,  at 
some  part  or  other  of  the  earth.  To  a.scertain  precisely  whether  there 
will  or  not,  and,  if  there  be,  how  great  will  be  the  part  eclipsed,  the  solar 
and  lunar  tables  must  be  consulted,  the  place  of  the  node  and  the  semi- 
diameters  exactly  ascertained,  and  the  local  parallax,  and  apparent  aug- 
mentation of  the  moon's  diameter  due  to  the  difference  of  her  distance 


from  the 
to  a  sixti 
is  easy,  fr 
of  the  tw 

(413.) 
considcrat 
seen  from 
equal  to  t 
hapjun  m 
spot,  carri 
mented  sc 
tions,  whi 

(414.) 
highly  in 
teach  us  tl 
defined  su 
that  at  th 
pursues  h( 
narrow,  th 
though  un 
bright,  th( 
the  directi 
a  star  occt 
telescope, 
to  expect 
moon,  at 
in  mid-air 
it  happen! 
of  its  lig 
one,  even 
too,  when 
the  bright 
crescent, 
less  surpr 
case. 

'  Woodho 

'There  i 
often  been 
within  tlie 
depth.     I  I 
quivocnl  tt's 
star  may  sh 


OCCULT ATION    OF    A    ST 


IT  n«  Mciili^ 


219 


)sition  in 
that  this 

it  by  no 
se  of  tho 
d  be  the 
13  evident 
when  tho 
ermit  the 
he  limits 
ider,  that, 
ihrown  in 
,  by  any 
nes  to  tho 
if  the  ap- 
re  dilated 
1  touch  or 
lier  of  the 
lotion,  the 
jxceed  the 
Uax,  there 

•27".  In 
tre,  M  the 
e,  we  may 


1  the  angle 
e  calculate 
)f  the  new 
than  this 
ibly  will,  at 
icther  there 
d,  the  solar 
d  the  scmi> 
parent  aug- 
ler  distance 


from  the  observer  and  from  tho  ccnti  4  the  eai  *k  (which  may  amount 
to  a  sixtieth  part  of  her  horizontal  dmii  t<tcr),  dcturmined;  after  which  it 
is  easy,  from  tho  above  considerations,  to  c^iiculatu  tho  amount  overlapped 
of  the  two  discs,  and  their  moment  of  contact. 

(418. )  The  calculation  of  the  occultation  of  a  star  depends  on  similar 
considerations.  An  occultation  is  ^joitst'^/*?,  when  the  moon's  course,  m 
seen  from  the  earth's  centre,  carries  her  within  a  distance  from  tlio  star 
equal  to  the  sum  of  her  scmidiameter  and  horizontal  parallax  ,  and  it  will 
hupjH'ii  at  ant/  pat'ficular  »pot,  when  her  apparent  path,  as  seen  from  that 
spot,  carries  her  centre  within  a  distance  equal  to  the  sum  of  her  amj- 
nientcil  semidiamcter  and  actual  parallax.  The  details  of  those  calcula- 
tions, which  arc  somewhat  troublesome,  must  be  sought  elsewhere.' 

(414.)  The  phenomenon  of  a  solar  eclipse  and  of  an  occultation  are 
highly  interesting  and  instructive  in  a  physical  point  of  view.     They 
teach  us  that  the  moon  is  an  opaque  body,  terminated  by  a  real  and  sharply 
defined  surface  intercepting  light  like  a  solid.     They  prove  to  us,  also, 
that  at  those  times  when  we  cannot  sec  the  moon,  she  really  exists,  and 
pursues  her  course,  and  that  when  we  sec  her  only  as  a  crescent,  however 
narrow,  the  whole  globular  body  «*s  there,  filling  up  the  deficient  outline, 
though  unseen.     For  occultations  take  place  indifferently  at  the  dark  and 
bright,  the  visible  and  invisible  outline,  whichever  happens  to  bo  towards 
the  direction  in  which  tiie  moon  is  moving ;  with  this  only  difference,  that 
a  star  occulted  by  the  bright  limb,  if  the  phenomenon  be  watched  with  a 
telescope,  gives  notice,  by  its  gradual  approach  to  the  visible  edge,  when 
to  expect  its  disappearance,  while,  if  occulted  at  the  dark  limb,  if  the 
moon,  at  least,  be  more  than  a  few  days  old,  it  is,  as  it  were,  extinguished 
in  mid-air,  without  notice  or  visible  cause  for  its  disappearance,  which,  as 
it  happens  instantaneousli/,  and  without  the  slightest  previous  diminution 
of  its  light,  is  always  surprising ;  and,  if  the  star  be  a  large  and  bright 
one,  even  startling  from  its  suddenness.     The  re-appearance  of  the  star, 
too,  when  the  moon  has  passed  over  it,  takes  place  in  those  eases  when 
the  bright  side  of  the  moon  is  foremost,  not  at  the  concave  outline  of  the 
crescent,  but  at  the  invisible  outline  of  the  complete  circle,  and  is  scarcely 
less  surprising,  from  its  suddenness,  than  its  disappearance  in  the  other 
case. 

'  Woodhouse's  Astronomy,  vol.  i.    See  also  Trans.  Ast.  Soc.  vol.  i.  p.  325. 

"  There  is  an  optical  illusion  of  a  very  strange  and  unaccountable  nature  which  has 
often  been  remarked  in  occultations.  The  star  appears  to  advance  actually  upon  and 
within  the  edge  of  the  disc  before  it  disappears,  and  that  sometimes  to  a  considerable 
depth.  I  have  never  myself  witnessed  this  singular  effect,  but  it  rests  on  most  une- 
quivocal testimony.  I  have  called  it  an  optical  illusion;  but  it  is  barely  porsiblc  that  a 
star  may  shine  on  such  occasions  through  deep  fissures  in  the  substance  of  tho  moon. 


iCV 


.^ 


atii  1,1(1.' 


220 


OUTLINES   OF  A8TR0X0MT. 


'(i 


^a 


I 
I 


(415.)  Tho  existcnco  of  the  complete  circle  of  the  disc,  even  when 
Iho  moon  h  not  full,  docs  not,  however,  rest  only  on  tho  evidence  of 
occtltations  and  eclipses.  It  may  be  seen,  when  the  moon  is  crescent  or 
waning,  i\  few  days  before  and  after  the  ncto  moov,  with  tho  naked  eye, 
as  a  pale  round  body,  to  which  the  crescent  seems  attached,  and  some- 
what  projecting  beyond  its  outline  (which  is  an  optical  illusion  arising 
°i  .m  tho  greater  intensity  of  its  light.)  Tho  cause  of  this  appearance 
will  presently  bo  explained.  Meanwhile  the  fact  is  sufficient  to  show 
that  the  moon  is  not  inhercnti)/  luminous  like  tho  sur.,  but  that  her  light 
is  of  an  adventitious  nature.  And  its  crescent  form,  increasing  regularly 
from  a  narrow  semicircular  line  to  a  complete  circular  disc,  corresponds  to 
the  appearance  a  globe  would  present,  one  hemisphere  of  which  was 
black,  the  other  white,  when  differently  turned  towards  the  eye,  ho  as  to 
present  a  greater  or  less  portion  of  each.  Tho  obvious  conclusion  from 
this  is,  that  the  moon  is  such  a  globe,  one  half  of  which  is  brightened  by 
the  rays  of  some  luminary  sufficiently  distant  to  enlighten  tho  complete 
hemisphere,  and  sufficiently  intense  to  give  it  the  degree  of  splendour  we 
see.  Now,  the  sun  alone  is  competent  to  such  an  effect.  Its  distance 
and  light  suffice ;  and,  moreover,  it  is  invariably  observed  that,  when  a 
crescent,  the  bright  edge  is  towards  the  sun,  and  that  in  proportion  as 
the  moon  in  her  monthly  course  becomes  more  and  more  distant  from  the 
sun,  the  breadth  of  tho  crescent  increases,  and  vice  versd. 

(416.)  The  sun's  distance  being  23984  radii  of  tho  earth,  and  the 
moon's  only  60,  the  former  is  nearly  400  times  the  latter.  Lines,  there- 
fore, drawn  from  the  sun  to  every  part  of  the  moon's  orbit  may  be 
regarded  as  very  nearly  parallel.'  Suppose,  now,  0  to  be  the  earth, 
A  B  C  D,  &c.  various  positions  of  the  moon  in  its  orbit,  and  S  the  sun, 
at  tho  vast  distance  above  stated ;  as  is  shown,  then,  in  the  figure,  the 
hemisphere  of  tho  lunar  globe  turned  towards  it  (on  tho  right)  will  be 
bright,  the  opposite  dark,  wherever  it  may  stand  in  its  orbit.  Now,  in 
the  position  A,  when  in  conjunction  with  the  sun,  tho  dark  part  is 
entirely  turned  towards  0,  and  the  bright  from  it.     In  this  case,  then, 

The  occiiltations  of  close  double  stars  ought  to  be  narrowly  watched,  to  see  whether 
both  individuals  are  thus  projected,  as  well  as  for  other  purposes  connected  with  their 
theory.  I  will  only  hint  ut  one,  viz.  that  a  double  star,  too  dote  to  be  seen  divided 
with  any  telescope,  may  yet  be  detected  to  be  double  by  the  mode  of  its  disapppear* 
ance.  Should  a  considerable  star,  for  instance,  instead  of  undergoing  instantaneous 
and  complete  extinction,  go  out  by  two  distinct  steps,  following  close  upon  each  other; 
first  losing  a  portion,  then  the  whole  remainder  of  its  light,  we  may  be  sure  it  is  a 
double  star,  though  we  cannot  see  the  individuals  separately. — Note  to  the  edit,  of  1833. 
'  The  angle  subtended  by  the  moon's  orbit,  as  seen  from  the  sun,  (in  the  mean  state 
of  things,)  is  only  IT  12". 


the  moon  is 
half  the  bri 
same  in  the 
of  tho  moor 
earth,  the  w 
fiifl  moon. 
bright  face  ] 
face,  then  g 
comes  rouni 
(417.)  T 
called,  arise, 
one  side  by 
the  light  so 
stance  thus  i 
earth.     It  is 
blue  sky. 
from  such  a 
last  rays  of 
seeming  bri 
such  a  ligh 
greater  appa 

'  The  actual 
sandstone  rod 
the  grey  perpe 
in  the  opposit 
brightness  fror 
altitudes  and  t 
both  luminarie 

'The  apparc 
from  the  mooi 
therefore,  are  i 


PHASES   OF  TUB   MOON   EXPLAINED. 


221 


iron  wbon 
idcnco  of 
resccnt  or 
akcd  cyo, 
md  somo- 
)D  arising 
ppcaranco 
t  to  show 
her  light 
;  regularly 
csponds  to 
rhich  was 
'e,  HO  as  to 
ibion  from 
;htened  hy 
5  complete 
iendour  wo 
la  distance 
it,  when  a 
sportion  as 
it  from  the 

and  the 
nes,  there- 
it  may  be 
the  earth, 
S  the  sun, 
figure,  the 
it)  will  be 

Now,  in 
rk  part  is 
case,  then, 

SCO  whether 
cd  with  their 
seen  divided 
I  disapppcar- 
nstantaneous 
I  each  other ; 
sure  it  is  a 
edit,  of  1833. 
le  mean  state 


Fig.  60. 


the  moon  is  not  seen,  it  is  nrw  moon.  When  the  tac^^  has  come  to  C, 
half  the  bright  and  half  the  dark  hemisphere  arc  .         o  ' ),  aud  the 

same  in  the  opposite  situation  0  :  these  are  the     •  '  d  fjuartcrs 

of  the  moon.  Lastly,  when  at  E,  the  whole  briglit  i.il.^  id  towjirds  the 
earth,  the  whole  dark  side  from  it,  and  it  is  then  seen  wholly  bright  or 
full  moon.  In  the  intermediate  positions  B  D  F  II,  the  portions  of  the 
bright  face  presented  to  0  will  be  at  first  less  than  half  the  visible  sur- 
face, then  greater,  and  finally  less  again,  till  it  vanishes  altogether,  as  it 
comes  round  again  to  A. 

(417.)  These  monthly  changes  of  appearance,  or  j>/*f/.«ic.s,  as  they  are 
called,  arise,  then,  from  the  moon,  an- opaque  body,  being  illuminated  on 
one  side  by  the  sun,  and  reflecting  from  it,  in  all  directions,  a  portion  of 
the  light  so  received.  Nor  let  it  be  thought  surprising  that  a  solid  sub- 
stance thus  illuminated  should  appear  to  diine,  and  again  illuminate  the 
earth.  It  is  no  more  than  a.  white  cloud  does  standing  off  upon  the  clear 
blue  sky.  By  day,  the  moon  can  hardly  be  distinguished  in  brightness 
from  such  a  cloud ;  and,  in  the  dusk  of  the  evening,  clouds  catching  the 
last  rays  of  the  sun  appear  with  a  dazzling  splendour,  not  inferior  to  the 
seeming  brightness  of  the  moon  at  night.'  That  the  earth  sends  also 
such  a  light  to  the  moon,  only  probably  more  powerful  by  reason  of  its 
greater  apparent  size',  is  agreeable  to  optical  principles,  and  explains  the 

'  The  actual  illumination  of  the  lunar  surface  is  not  much  superior  to  that  of  weathered 
sandstone  rock  in  full  sunshine.  I  have  frequently  compared  the  moon  setting  behind 
the  grey  perpendicular  fafade  of  the  Table  Mountain,  illuminated  by  the  sun  just  risen 
in  the  opposite  quarter  of  the  horizon,  when  it  has  been  scarcely  distinguish,  blc  in 
brightness  from  the  rock  in  contact  with  it.  The  sun  and  moon  being  nearly  at  equal 
altitudes  and  the  atmosphere  perfectly  free  from  cloud  or  vapour,  its  effect  is  alike  on 
both  luminaries.  (H.  1848). 

'The  apparent  diameter  of  the  moon  is  32'  from  the  earth ;  that  of  the  earth  seen 
from  the  moon  is  twice  her  horizontal  parallax,  or  1°  54'.  The  apparent  surfaces, 
I  therefore,  are  as  (114)*:  (32)',  or  as  13  :  1  nearly.    ' 


ISP" 


222 


OUTLINES   OF  ASTRONOMY. 


If 


^i 


II 


appearance  of  the  dark  portion  of  the  young  or  waning  moon  completing 
its  crescent  (art.  413).  For,  when  the  moon  is  nearly  new  to  the  earth, 
the  latter  (so  to  speak)  is  nearly  full  to  the  former  j  it  then  illuminates  its 
dark  half  by  strong  earth-Uglit ;  and  it  is  a  portion  of  this,  reflected  back 
again,  which  makes  it  visible  to  us  in  the  twilight  sky.  As  the  moon 
gains  age,  the  earth  offers  it  a  less  portion  of  its  bright  side,  and  the  phe- 
nomenon in  question  dies  away. 

(418.)  The  lunar  month  is  determined  by  the  recurrence  of  its  phases:  * 
-it  reckons  from  new  moon  to  new  moon ;  that  is,  from  leaving  its  coDJunc<v 
tion  with  the  sun  to  its  return  to  conjunction.  If  the  sun  stood  still,  like 
a  fixed  star,  the  interval  between  two  conjunctions  would  be  the  same  as 
the  period  of  the  moon's  sidereal  revolution  (art.  401) ;  but,  as  the  sun 
apparently  advances  in  the  heavens  in  the  same  direction  with  the  moon, 
only  slower,  the  latter  has  more  than  a  complete  sidereal  period  to  perform 
to  come  up  with  the  sun  again,  and  will  require  for  it  a  longer  time,  which 
is  the  lunar  month,  or,  as  it  is  generally  termed  in  astronomy,  a  synodiml 
period.  The  difference  is  easily  calculated  by  considering  that  the  super- 
fluous arc  (whatever  it  be)  is  described  by  the  sun  with  the  velocity  of 
0°'08565  jL>e/' rfi'em,  in  the  same  time  that  the  moon  describes  that  arc 
^>^H.s-  a  complete  revolution,  with  her  velocity  of  13°'17640per  diem;  and, 
the  times  of  description  being  identical,  the  spaces  are  to  each  other  in  the 
proportion  of  the  velocities.  Let  V  and  v  be  the  mean  angular  velocities, 
X  the  superfluous  arc;  then  Y  '.  v  :'.  \  •\-  x'.x)  and  V  — v  :  u  : :  1  :a;. 


X 


whence  x  is  found,  and  —  =  the  time  of  describing  x,  or  the  difference  of 

the  sidereal  and  synodical  periods.  From  these  data  a  slight  knowledge 
of  arithmetic  will  suffice  to  derive  the  arc  in  question,  and  the  time  of  its 
description  by  the  moon ;  which  being  the  excess  of  the  synodic  over  the 
sidereal  period,  the  former  will  be  had,  and  will  appear  to  be  29''  12" 
44'"  2-87. 

(419.)  Supposing  the  position  of  the  nodes  of  the  moon's  orbit  to 
permit  it,  when  the  moon  stands  at  A  (or  at  the  new  moon),  it  will  inter- 
cept a  part  or  the  whole  of  the  sun's  rays,  and  cause  a  solar  eclipse.  On 
the  other  band,  when  at  E  (or  at  the  full  moon),  the  earth  0  will  inter- 
cept the  rays  of  the  sunj  and  cast  a  shadow  on  the  moon,  thereby  causing 
a  lunar  eclipse.  And  this  is  perfectly  consonant  to  fact,  such  eclipses 
never  happening  but  at  the  exact  time  of  the  full  moon.  But,  what  is 
still  more  remarkable,  as  confirmatory  of  the  position  of  the  earth's  sphe- 
ricity,  this  shadow,  which  we  plainly  see  to  enter  upon  and,  as  it  were, 
eat  away  the  disc  of  the  moon,  is  always  terminated  by  a  circular  outline, 
though,  from  the  greater  size  of  the  circle,  it  is  only  partially  seen  at  any 


on  eove.y 
to  be  sens 


SOLAR  AND   LUNAR   ECLIPSES. 


223 


completing 
the  earth, 
iininates  its 
iected  back 
1  the  moon 
nd  the  phe- 

'its  phases:  * 
its  conjunci^ 
)d  still,  like 
the  same  as 
,,  as  the  sun 
,  the  moon, 
d  to  perform 
time,  which 
a  si/nodical 
it  the  super- 
5  velocity  of 
bcs  that  arc 
•  diem;  and, 
other  in  the 
ar  velocities, 
):v::l:x, 

difference  of 

it  knowledge 

e  time  of  its 

odic  over  the 

be  29'»  12" 

)n*8  orbit  to 
it  will  inter- 
eclipse.  On 
0  will  inter- 
ireby  causing 
such  eclipses 
But,  what  is 
earth's  sphe- 
d,  as  it  were, 
•cular  outline, 
y  seen  at  any 


one  time.     Now,  a  body  which  always  casts  a  circular  shadow  must  itself 
be  spherical. 

(420.)  Eclipses  of  the  sun  are  best  understood  by  regarding  the  sun 
and  moon  as  two  independent  luminaries,  each  moving  according  to  known 
laws,  and  viewed  from  the  earth :  but  it  is  also  instructivfe  to  consider 
eclipses  generally  as  arising  from  the  shadow  of  one  body  thrown  on  ano- 
ther by  a  luminary  much  larger  than  either.  Suppose  then,  A  B  to 
rppresent  the  sun,  and  C  D  a  spherical  body,  whether  earth  or  moon,  illu- 
minated by  it.  If  we  join  and  prolong  AC,  B D ;  since  A B  is  grteater 
than  C  D,  these  lines  will  meet  in  a  point  E,  more  or  less  distant  from 
the  body  C  D,  according  to  its  size,  and  within  the  space  C  E  D  (which 
represents  a  cone,  since  C  D  and  A  B  are  spheres),  there  will  be  a  total 
shadow.  This  shadow  is  called  the  umbra,  and  a  spectator  situated  within 
it  can  see  no  part  of  the  sun's  ^isc.    Beyond  the  umbra  are  two  diverging 


Fig.  00. 


spaces  (or  rather,  a  portion  of  a  single  conical  space,  having  K  for  its 

vertex),  where  if  a  spectator  be  situated,  as  at  M,  he  will  see  a  portion 

only  (A  0  N  P)  of  the  sun's  surface,  the  rest  (B  0  N  P)  being  obscured 

by  the  earth.     He  will,  therefore,  receive  only  partial  sunshine ;  and  the 

more,  the  nearer  bo  is  to  the  exterior  borders  of  that  cone  which  is  called 

the  penumbra.     Beyond  this  he  will  see  the  whole  sun,  and  be  in  full 

illumination.     All  these  circumstances  may  be  perfectly  well  shown  by 

holding  a  small  globe  up  in  the  sun,  and  receiving  its  shadow  at  different 

distances  on  a  sheet  of  paper. 

(421.)  In  a  lunar  eclipse  (represented  in  the  upper  figure),  the  moon 

is  seen  to  enter'  ihQ penumbra  first,  and,  by  degrees,  get  involved  in  the 

umbra,  the  former  bordering  the  latter  like  a  smoky  haze.    At  this  period 

of  the  eclipse,  and  while  yet  a  considerable  part  of  the  moon  remains 

'  The  actual  contact  with  the  penumbra  is  never  seen  ;  tiie  defalcation  of  light  cornea 
on  E>o  ve.y  gradually  that  it  is  not  till  when  already  deeply  immersed,  that  it  is  perceived 
to  be  sensibly  darkened. 


^tm^ 


«V1 


c^ 


224 


OUTLINES  OF  ASTRONOMY. 


unobscured,  the  portion  involved  in  the  umbra  is  invisible  to  the  naked 
eye,  though  still  perceptible  in  a  telescope,  and  of  a  dark  grey  hue.  But 
as  the  eclipse  advances,  and  the  enlightened  part  diminishes  in  extent,  and 
grows  gradually  more  and  more  obscured  by  the  advance  of  the  penumhra, 
the  eye,  relieved  from  its  glare,  becomes  more  sensible  to  feeble  impres- 
sions of  light  and  colour ;  and  pheno  .ena  of  a  remarkable  and  instruc- 
tive character  begin  to  be  developed.  The  umbra  is  seen  to  be  very  far 
from  totally  dark :  and  in  its  faint  illumination  it  exhibits  a  gradation  of 
colour,  being  bluish,  or  even  (by  contrast)  somewhat  greenish,  towards 
the  borders  for  a  space  of  about  4'  or  5'  of  apparent  angular  breadth 
inwards,  thence  passing,  by  delicate  but  rapid  gradation,  through  rose  red 
to  a  fiery  or  copper-coloured  glow,  like  that  of  dull  red-hot  iron.  As 
the  eclipse  proceeds  this  glow  spreads  over  the  whole  surface  of  the  moon, 
which  then  becomes  on  some  occasions  so  strongly  illuminated,  as  to  cast 
a  very  sensible  shadow,  and  allow  the  spots  on  its  surface  to  be  perfectly 
well  distinguished  through  a  telescope. 

(422.)  The  cause  of  these  singular,  and  sometimes  very  beautiful 
appearances,  is  the  refraction  of  the  sun's  light  in  passing  through  our 
atmosphere,  which  at  the  same  time  becomes  coloured  with  the  hues  of 
sunset  by  the  absorption  of  more  or  less  of  the  violet  and  blue  rays,  as  it 
passes  through  strata  nearer  or  more  remote  from  the  earth's  surface,  and 
therefore,  more  or  less  loaded  with  vapour.  To  show  this,  let  A  D  a  be 
a  section  of  the  cone  of  the  umht^fl,  and  F  B  Ji/  of  the  penumhra,  through 
their  common  axis  D  E  S,  passing  through  the  centres  E  S  of  the  earth 
and  sun,  and  let  K  M  Jc  be  a  section  of  these  cones  at  a  distance  E  M  from 
E,  equal  to  the  radius  of  the  moon's  orbit,  or  60  radii  of  the  earth.' 
Taking  this  radius  for  unity,  since  E  S,  the  distance  of  the  sun,  is  23984, 
and  the  semidiameter  of  the  sun  111  J  such  units,  we  readily  calculate 
D  E=218,  D  M=158,  for  the  distances  at  which  the  apex  of  the  geome- 
trical umbra  lies  behind  the  earth  and  the  moon  respectively.  We  also 
find  for  the  measure  of  the  angle  E  D  B,  15'  46",  and  therefore  D  B  E= 
89°  44'  14",  whence  also  we  get  M  C  (the  linear  semidiameter  of  the 
umbra)=0-72t)  (or  in  miles  28G4),  and  the  angle  C  E  M,  its  apparent 
angular  semidiameter  as  seen  from  E=41'  30".  And  instituting  similar 
calculations  for  the  geometrical  penumbra  we  get  M  K=1005  (3970 
miles),  and  K  E  M  57'  36";  and  it  may  be  well  to  remember  that  the 
doubles  of  these  angles,  or  the  mean  angular  diameters  of  the  umbra  and 
penumbra,  are  described  by  the  moon  with  its  mean  velocity  in  2"  43", 
and  3"  47"  respectively,  which  are  therefore  the  respective  durations  of 

'  The  figure  is  unavoidably  drawn  out  of  all  proportion,  and  the  angles  violently 
exaggerated.    The  reader  should  endeavour  to  draw  the  figure  in  its  true  proportions. 


that  at 
suing  the 
tions  Bz^ 
each  1°  i 

n 


be  naked 
le.     But 
tent,  and 
mumhraf 
e  impres- 
l  instruc- 
e  very  far 
idation  of 
1,  towards 
ir  breadth 
h  rose  red 
iron.     As 
the  moon, 
as  to  cast 
le  perfectly 

r   beautiful 
hrougli  our 
he  hues  of 
>  rays,  as  it 
iurface,  and 
1  A  D  a  be 
m,  through 
f  the  earth 
e  E  M  from 
the  earth.' 
n,  is  23984, 
ly  calculate 
'  the  geame- 
We  also 
,reDBE= 
leter  of  the 
its  apparent 
ting  similar 
005  (3970 
)er  that  the 
umbra  and 
y  in  2"  43", 
durations  of 

igles  violently 
;e  proportions. 


PHENOMENA  OF  A  LUNAR  ECLIPSE. 
Fig.  61. 


225 


the  total  and  partial  obscuration  of  any  one  point  of  the  moon's  disc  in 
traversing  centrally  the  geometrical  shadow. 

(423.)  Were  the  earth  devoid  of  atmosphere,  the  whole  of  the  phe- 
nomena of  a  lunar  eclipse  would  consist  in  these  partial  or  total  obscura- 
tions. Within  the  space  C  c  the  whole  of  the  light,  and  within  K  C  and 
ck  &  greater  or  less  portion  of  it,  would  be  intercepted  by  the  solid  body 
Bb  of  the  earth.  The  refracting  atmosphere,  however,  extends  from 
B,  5,  to  a  certain  unknown,  but  very  small  distance  B  H,  &  A,  which,  acting 
as  a  convex  lens,  of  gradually  (and  very  rapidly)  decreasing  density,  dis- 
perses all  that  comparatively  small  portion  of  light  which  falls  upon  it 
over  a  space  bounded  externally  by  Hff,  parallel  and  very  nearly  coinci- 
dent with  B  F,  ind  internally  by  a  line  B  z,  the  former  representing  the 
extreme  exterior  ray  from  the  limb  a  of  the  sun,  the  latter,  the  extreme 
interior  ray  from  the  limb  A.  To  avoid  complication,  however,  we  will 
trace  only  the  courses  of  rays  which  just  graze  the  ^  rface  at  B,  viz:  3z 
from  the  upper  border.  A,  and  B  v  from  the  lower,  a,  of  the  sun.  Each 
of  these  rays  is  bent  inwards  from  its  original  course  by  double  the 
amount  of  the  horizontal  refraction  (38')  i.  e.  by  1°  6',  because,  in 
passing  from  B  out  of  the  atmosphere,  it  undergoes  a  deviation  equal  to 
that  at  entering,  and  in  the  same  direction.  Instead,  therefore,  of  pur- 
suing the  courses  B  D,  B  F,  these  rays  respectively  will  occupy  the  posi- 
tions B  2^,  B  V,  making,  with  the  aforesaid  lines,  the  angles  D  B  &,  F  B  v, 
each  1°  6'.  Now  we  have  found  DBE  =  89°  44'  14"  and  therefore 
15 


230 


226 


OUTLINES   OF  ASTRONOMY. 


m 


111 


i 
1 

4- 


FBE(  =  DBE+  angular  diam.  of  0)  =  ^^°  1"'  17",  consequently 
the  angles  E  By  and  E  B  o  will  be  respectively  88°  38'  14"  and  89°  11' 
17"  from  which  we  conclude  Fjz  =  42-03  and  Ev—  88-89,  the  former 
falling  short  of  the  moon's  orbit  by  17-07,  and  the  latter  surpassing  it  by 
28-89  radii  of  the  earth. 

(424.)  The  penumbra,  therefore,  of  rays  refracted  at  B,  will  be  spread 
over  the  space  v  B  i/,  that  at  H  over  u  H  d,  and  at  the  intermediate 
points,  over  similar  intermediate  spaces,  and  through  this  compound  of 
superposed  penumbraj  the  moon  passes  during  the  whole  of  its  path 
through  the  geometrical  shadow,  never  attaining  the  absolute  umbra 
B  z  b  at  all.  Without  going  into  detail  as  to  the  intensity  of  the 
refracted  rays,  it  is  evident  that  the  totality  of  light  so  thrown  into  the 
shadow  is  to  that  which  the  earth  intercepts,  as  the  area  of  a  circular 
section  of  the  atmosphere  to  that  of  a  diametrical  section  of  the  earth 
itself,  and,  therefore,  at  all  events  but  feeble.  And  it  is  still  further 
enfeebled  by  actual  clouds  suspended  in  that  portion  of  the  air  v/hich 
forms  the  visible  border  of  the  earth's  disc  as  seen  from  the  moon,  as 
well  as  by  the  general  want  of  transparency  caused  by  invisible  vapour, 
which  is  especially  efiFcctive  in  the  lowermost  strata,  within  three  or  four 
miles  of  the  surface,  and  which  will  impart  to  all  the  rays  they  transmit, 
the  ruddy  hue  of  sunset,  only  of  double  the  depth  of  tint  which  we 
admire  in  our  glowing  sunsets,  by  reason  of  the  rays  having  to  traverse 
twice  as  great  a  thickness  of  atmosphere.  This  redness  will  be  most 
intense  at  the  points  x,  y,  of  the  moon's  path  through  the  umbra,  and 
will  thence  degrade  very  rapidly  outwardly,  over  the  spaces  x  c,  i/  G,  less 
so  inwardly,  over  x  y.  And  at  C,  c,  its  hue  will  be  mingled  with  the 
bluish  or  greenish  light  which  the  atmosphere  scatters  by  irregular  dis- 
persion, or  in  other  words  by  our  twilight  (art.  44).  Nor  will  the  phe- 
nomenon be  uniformly  conspicuous  at  all  times.  Supposing  a  generally 
and  deeply  clouded  state  of  the  atmosphere  around  the  edge  of  the  earth's 
disc  visible  from  the  moon  {i.  e.  around  that  great  circle  of  the  earth,  in 
which,  at  the  moment  the  sun  is  in  the  horizon,)  little  or  no  refracted 
light  may  reach  the  moon.'  Supposing  that  circle  partly  clouded  and 
partly  clear,  patches  of  red  light  corresponding  to  the  clear  portions  will 
be  thrown  into  the  umbra,  and  may  give  rise  to  various  and  changeable 
distributions  of  light  on  the  eclipsed  disc ;  *  while,  if  entirely  clear,  the 
eclipse  will  be  remarkable  for  the  conspicuousness  of  the  moon  during 
the  whole  or  a  part  of  its  immersion  in  the  umbra.' 

'  As  in  the  eclipses  of  June  5,  1620,  April  25,  1642.    Lalande,  Ast.  1769. 

*  As  in  the  eclipse  of  Oct.  13,  1837,  observed  by  the  author. 

"  As  in  that  of  March  19,  1848,  when  the  moon  is  described  as  giving  "  good  light" 
during  more  than  an  hour  after  its  total  immersion,  and  some  persons  even  doubted 
i*B  being  eclipsed.    (Notices  of  R.  Ast.  Soc.  viii.  p.  132.) 


LUNAR   ECLIPTIC   LIMITS. 


227 


(425.)  Owing  to  the  great  size  of  the  earth,  the  cone  of  its  umbra 
always  projects  far  beyond  the  moon ;  so  that,  if,  at  the  time  of  a  lunar 
eclipse,  the  moon's  path  be  properly  directed,  it  is  sure  to  pass  through 
the  umbra.  This  is  not,  however,  the  case  in  solar  eclipses.  It  so 
happens,  from  the  adjustment  of  the  size  and  distance  of  the  moon,  that 
the  extremity  of  her  umbra  always  falls  near  the  earth,  but  sometimes 
attains  and  sometimes  falls  short  of  its  surface.  In  the  former  case 
(represented  in  the  lower  figure  art.  420)  a  black  spot,  surrounded  by  a 
fainter  shadow,  is  formed,  beyond  which  there  is  no  eclipse  on  any  part 
of  the  earth,  but  within  which  there  may  be  either  a  total  or  partial  one, 
as  the  spectator  is  within  the  umbra  or  penumbra.  When  the  apex  of 
the  umbra  falls  oji  the  surface,  the  moon  at  that  point  will  appear,  for  an 
instant,  to  just  cover  the  sun ;  but,  when  it  falls  short,  there  will  be  no 
total  eclipse  on  any  part  of  the  earth ;  but  a  spectator,  situated  in  or  near 
the  prolongation  of  the  axis  of  the  cone,  will  see  the  whole  of  the  moon 
on  the  sun,  although  not  large  enough  to  cover  it,  i.  e.  he  will  witness  an 
annular  eclipse. 

(426.)  Owing  to  a  remarkable  enough  adjustment  of  the  periods  in 
which  the  moon's  si/nodical  revolution,  and  that  of  her  nodes,  are  per- 
formed, eclipses  return  after  a  certain  period,  very  nearly  in  the  same 
order  and  of  the  same  magnitude.  For  223  of  the  moon's  mean  synodi- 
cal  revolutions,  or  lunations,  as  they  are  called,  will  be  found  to  occupy 
6585-32  days,  and  nineteen  complete  synodical  revolutions  of  the  node  to 
occupy  6585*78.  The  difference  in  the  mean  position  of  the  node,  then, 
at  the  beginning  and  end  of  223  lunations,  is  nearly  insensible ;  so  that 
a  recurrence  of  all  eclipses  within  that  interval  must  take  place.  Accord- 
ingly, this  period  f  223  lunations,  or  eighteen  years  and  ten  days,  is  a 
very  important  one  in  the  calculation  of  eclipses.  It  is  supposed  to  have 
been  known  to  the  Chaldeans,  the  earliest  astronomers,  the  regular  return 
of  eclipses  having  been  known  as  a  physical  fact  for  ages  before  their 
exact  theory  was  understood.  In  this  period  there  occur  ordinarily  70 
eclipses,  29  of  the  moon  and  41  of  the  sun,  visible  in  some  part  of  the 
earth.  Seven  eclipses  of  either  sun  or  moon  at  most,  and  two  at  least 
(both  of  the  sun,)  may  occur  in  a  year. 

(427.)  The  commencement,  duration,  and  magnitude  of  a  lunar  eclipse 
are  much  mo'*e  easily  calculated  than  those  of  a  solar,  being  independent 
of  the  position  of  the  spectator  on  the  earth's  surface,  and  the  same  as  if 
viewed  from  its  centre.  The  common  centre  of  the  umbra  and  penu  nbra 
lies  always  in  the  ecliptic,  at  a  point  opposite  to  the  sun,  and  the  path 
described  by  the  moon  in  passing  through  it  is  its  true  orbit  as  it  stands 
at  the  moment  of  the  full  moon.     In  this  orbit,  its  position,  at  every 


S^ 


m 


•^"s-'l 


228 


OUTLINES   OP  ASTRONOMY. 


instant,  is  known  from  the  lunar  tables  and  cpliemeris ;  and  all  wo  have, 
therefore,  to  ascertain,  is,  the  moment  when  the  distance  between  the 
moon's  centre  and  the  centre  of  the  shadow  is  exactly  equal  to  the  sun 
of  the  senndianicters  of  the  moon  and  jyenumbra,  or  of  the  moon  and 
umbra,  to  know  when  it  enters  upon  and  leaves  them  respectively.  No 
lunar  eclipse  can  take  place,  if,  at  the  moment  of  the  full  moon,  the  sun 
be  at  a  greater  angular  distance  from  the  node  of  the  moon's  orbit  than 
11°  21',  meaning  by  an  eclipse  the  inraersion  of  any  part  of  the  moon  in 
the  umbra,  as  its  contact  with  the  penumbra  cannot  bo  observed  (see  note 
■to  art.  421). 

(428.)  The  dimensions  of  the  shadow,  at  the  place  where  it  crosses  the 
moon's  path,  require  us  to  know  the  distances  of  the  sun  and  moon  at  the 
time.  These  are  variable ;  but  are  calculated  and  set  down,  as  well  as 
their  semidiameters,  for  every  day,  in  the  ephemeris,  so  that  none  of  the 
data  are  wanting.  The  sun's  distance  is  easily  calculated  from  its  elliptic 
orbit ;  but  the  moon's  is  a  matter  of  more  difficulty,  by  reason  of  the  pro- 
gressive motion  of  the  axis  of  the  lunar  orbit.  (Art.  409.) 

(429.)  The  physical  constitution  of  the  moon  is  better  known  to  us 
than  that  of  any  other  heavenly  body.  By  the  aid  of  telescopes,  we 
discern  inequalities  in  its  surface  which  can  be  no  other  than  mountains 
and  valleys, — for  this  plain  reason,  we  see  the  shadows  cast  by  the  former 
in  the  exact  proportion  as  to  len4;th  which  they  ought  to  have,  when  we 
take  into  account  the  inclination  oi  the  sun's  rays  to  that  part  of  the 
moon's  surface  on  which  they  stand.  The  convex  outline  of  the  limb 
turned  towards  the  sun  is  always  circular,  and  very  nearly  smooth ;  but 
the  opposite  border  of  the  enlightened  part,  which  (were  th«i  moon  a  per- 
fect sphere)  ought  to  be  an  exact  and  sharply  defined  ellipse,  is  always 
observed  to  be  extremely  ragged,  and  indented  with  deep  recesses  and  pro- 
minent points.  The  mountains  near  this  edge  cast  long  black  shadows, 
as  they  should  evidently  do,  when  we  consider  that  the  sun  is  in  the  act 
of  rising  or  setting  to  the  parts  of  the  moon  so  circumstanced.  But  as 
the  enlightened  edge  advances  beyond  them,  i.  e.  as  the  sun  to  them  gains 
altitude,  their  shadows  shorten ;  and  at  the  full  moon,  when  all  the  light 
falls  in  our  line  of  sight,  no  shadows  nre  seen  on  any  part  of  her  surface. 
From  micrometrical  measures  of  the  lengths  of  the  shadows  of  the  more 
conspicuous  mountains,  taken  under  the  most  favourable  circumstances, 
the  heights  of  many  of  them  have  been  calculated.  Messrs.  Beer  and 
Maedler  in  their  elaborate  work,  entitled  "  Der  Mond,"  have  given  a  list 
of  heights  resulting  from  such  measurements,  for  no  less  than  1095  lunar 
mountains,  among  which  occur  all  degrees  of  elevation  up  to  8569  toiscs, 
(22823  British  feet),  or  about  1400  feet  higher  than  Chimborazo  in  the 


PHYSICAL  CONSTITUTION   OP  THE   MOON. 


229 


Ancles.  The  existence  of  such  inountnins  is  further  corroborated  by  their 
appearance,  as  small  points  or  islands  of  light  beyond  the  extreme  edge 
of  the  enlightened  part,  which  are  their  tops  catching  the  sun-beams 
before  the  intermediate  plain,  and  which,  as  the  light  advances,  at  length 
connect  themselves  with  it,  and  appear  as  prominences  from  the  general 
edge. 

(430.)  The  generality  of  the  lunar  mountains  present  a  striking  uni- 
formity and  singularity  of  aspect.  Thc^  are  wonderfully  numerous, 
especially  towards  the  Southern  portion  of  the  disc,  occupying  by  far  the 
larger  portion  of  the  surface,  and  almost  universally  of  an  exactly  circu- 
lar or  cup-shaped  form,  foreshortened,  however,  into  ellipses  towards  the 
limb ;  but  the  large;!*  have  for  the  most  part  flat  bottoms  within,  from 
which  rises  centrally  a  small,  steep,  conical  hill.  They  offer,  in  short,  in 
its  highest  perfection,  the  true  volcanic  character,  as  it  may  be  seen  in  the 
crater  of  Vesuvius,  and  in  a  map  of  the  volcanic  districts  of  fhe  Campi 
Phlegraei'  or  the  Puy  de  Dome,  but  with  this  remarkable  peculiarity, 
viz. :  that  the  bottoms  of  many  of  the  craters  are  very  deeply  depressed 
below  the  general  surface  of  the  moon,  the  internal  depth  being  often 
twice  or  three  times  the  external  height.  In  some  of  the  principal  ones, 
decisive  marks  of  volcanic  stratification,  arising  from  successive  deposits 
of  ejected  matter,  and  evident  indications  of  lava  currents  streaming 
outwards  in  all  directions,  may  be  clearly  traced  with  powerful  telescopes. 
(See  PI.  V.  fig.  2.*)  In  Lord  Rosse's  magnificent  reflector,  the  flat 
bottom  of  the  crater  called  Albategnius  is  seen  to  be  strewed  with  blocks 
not  visible  in  inferior  telescopes,  while  the  exterior  of  another  (Aristillus) 
is  all  hatched  over  with  deep  gullies  radiating  towards  its  centre.  What  is, 
moreover,  extremely  singular  in  the  geology  of  the  moon  is,  that,  although 
nothing  having  the  character  of  seas  can  be  traced,  (for  the  dusky  spots, 
which  are  commonly  called  seas,  when  closely  examined,  present  appear- 
aiiccs  incompatible  with  the  supposition  of  deep  water,)  yet  there  are 
large  regions  perfectly  level,  and  apparently  of  a  decided  alluvial  cha- 
racter. 

(431.)  The  moon  has  no  clouds,  nor  any  other  decisive  indications  of 
an  atmosphere.  Were  there  any,  it  could  not  fail  to  be  perceived  in  the 
occultations  of  stars  and  the  phaenomena  of  solar  eclipses,  as  well  as  in 
a  great  variety  of  other  phaenomena.  The  moon's  diameter,  for  example, 
as  measured  micromctrically,  and  as  estimated  by  the  interval  between 
the  disappearance  and  reappearance  of  a  star  in  an  occultation,  ought  to 
differ  by  twice  the  horizontal  refraction  at  the  moon's  surface.     No  appre- 

'  See  Breislak's  map  of  the  environs  of  Naples,  and  Dcsmarest's  of  Auvcrgne. 
*  From  a  drawing  taken  with  a  reflector  of  twenty  feet  focal  length  (A.) 


"5i*» 


*fl10 


01**^* 


230 


OUTLINES   OF  ASTRONOMY. 


ciablo  difference  being  perceived,  we  are  entitled  to  conclude  the  non- 
existence of  nny  atmosphere  dense  enough  to  cause  a  refraction  <»f  1"  i.  e. 
having  one  1080th  part  of  the  density  of  the  earth's  atmosphere.  Tn  a 
solar  eolipso,  the  existence  of  any  sensible  refracting  atmosphere  in  the 
moon,  would  enable  us  to  trace  the  limb  of  the  latter  beyond  the  cusps, 
externally  to  the  sun's  disc,  by  a  narrow,  hut  hrilliant  line  of  light, 
extending  to  some  distance  along  its  edge.  No  such  phaenomenon  is 
seen.  Veri/  faint  stars  ought  to  be  extinguished  before  occultation,  were 
i»ny  appreciable  amount  of  vapour  suspended  near  the  surface  of  the  moon. 
But  such  is  not  the  case ;  when  occulted  at  the  bright  edge,  indeed,  the 
light  of  the  moon  extinguishes  small  stars,  and  even  at  the  dark  limb, 
the  glare  in  the  sky  caused  by  the  near  presence  of  the  moon,  renders 
the  occultation  of  very  minute  stars  unobservable.  But  during  the  con- 
tinuance of  a  total  lunar  eclipse,  stars  of  the  tenth  and  eleventh  magni- 
tude are  seen  to  come  up  to  the  limb,  and  undergo  sudden  extinction  as 
well  as  those  of  greater  brightness.'  Hence,  the  climate  of  the  moon 
must  be  vory  extraordinary;  the  alternation  being  that  of  unmitigated 
and  burning  sunshine  fiercer  than  an  equatorial  noon,  continued  for  a 
whole  fortnight,  and  the  keenest  severity  of  frost,  far  exceeding  that  of 
our  polar  winters,  for  an  equal  time.  Such  a  disposition  of  things  must 
produce  a  constant  transfer  of  whatever  moisture  may  exist  on  its  surface, 
from  the  point  beneath  the  sun  to  that  opposite,  by  distillation  in  vacuo 
after  the  manner  of  the  little  instrument  called  a  cri/ophorus.  The  con- 
sequence must  be  absolute  aridity  below  the  vertical  sun,  constant  accre- 
tion of  hoar  frost  in  the  opposite  region,  and,  perhaps,  a  narrow  zone  of 
running  water  at  the  borders  of  the  enlightenc  hemisphere.'  It  is 
possible,  then,  that  evaporation  on  the  one  hand,  and  condensation  on  the 
other,  may  to  a  certain  extent  preserve  an  equilibrium  of  temperature, 
and  mitigate  the  extreme  severity  of  both  climates;  but  this  process, 
which  would  imply  the  continual  generation  and  destruction  of  an  atmo- 
sphere of  aqueous  vapour,  must,  in  conformity  with  what  has  been  said 
above  of  a  lunar  atmosphere,  be  confined  within  very  narrow  limits. 

(432.)  Though  the  surface  of  the  full  moon  exposed  to  us,  must  neces- 
sarily be  very  much  heated, — possibly  to  a  degree  much  exceeding  that  of 
boiling  water, —  yet  we  feel  no  heat  from  it,  and  even  in  the  focus  of  large 
reflectors,  it  fails  to  aflFect  the  thermometer.  No  doubt,  therefore,  its  heat 
(conformably  to  what  has  been  observed  of  that  of  bodies  heated  below 
the  point  of  luminosity)  is  much  more  readily  absorbed  in  traversing 
transparent  media  than  direct  solar  heat,  and  is  extinguished  in  the  upper 


'  As  observed  by  myself  in  the  eclipse  of  Oct.  13,  1837. 
«  So  in  ed.  of  1833. 


CLIMATE  AND   HEAT   OP  THE   MOON. 


231 


the  non- 
of  1"  I  e. 
ire.     Tu  a 
re  in  the 
;hc  cusps, 
of  liglit, 
)menon   is 
ition,  were 
the  moon, 
indeed,  the 
dark  limb, 
on,  renders 
ig  the  con- 
nth  magni- 
:tinction  as 
f  the  moon 
anmitigated 
inued  for  a 
ling  that  of 
things  must 
its  surface, 
)n  in  vacuo 
The  con- 
istant  accre- 
row  zone  of 
ero.'     It  is 
ation  on  the 
emperature, 
his  process, 
of  an  atrao- 
s  been  said 
limits, 
must  neces- 
ding  that  of 
)cus  of  large 
"ore,  its  heat 
eated  below 
traversing 
in  the  upper 


regions  of  our  atraosphorc,  never  reaching  the  surface  of  the  earth  at  all. 
Some  probability  is  given  to  this  by  the  trin/enn/  to  dmipjwantncc 
of  cloiuh  under  the  fall  moon,  a  meteorological  fitct,  (for  as  such  we 
think  it  fully  entitled  to  rank')  for  which  it  is  necessary  to  seek  a  cause, 
and  for  which  no  other  rational  explanation  seems  to  offer.  As  for  any 
other  influence  of  the  moon  on  the  weather,  we  have  no  decisive  evidence 
in  its  favour. 

(43iJ.)  A  circle  of  one  second  in  diameter,  as  seen  from  the  earth,  on 
the  surface  of  the  moon,  contains  about  a  square  mile.  Telescopes,  there- 
fore, must  yet  be  greatly  improved,  before  we  could  expect  to  see  signs  of 
inhabitants,  as  manifested  by  edifices  or  by  changes  on  the  surface  of  the 
soil.  It  should,  however,  be  observed,  that,  owing  to  the  small  density 
of  the  materials  of  the  moon,  and  the  comparatively  feeble  gravitation  of 
bodies  on  her  surface,  muscular  force  would  there  go  six  times  as  far  in 
overcoming  the  weight  of  materials  as  on  the  earth.  Owing  to  the  want 
of  air,  however,  it  seems  impossible  that  any  form  of  life,  analogous  to 
those  on  earth,  can  subsist  there.  No  appearance  indicating  vegetation, 
or  the  slightest  variation  of  surface,  which  can,  in  our  opinion,  fairly  be 
ascribed  to  change  of  season,  can  any  where  be  discerned. 

(434,)  The  lunar  summer  and  winter  arise,  in  fact,  from  the  rotation 
of  the  moon  on  its  own  axis,  the  period  of  which  rotation  is  exactly/  equal 
to  its  sidereal  revolution  about  the  earth,  and  is  performed  in  a  plane  1° 
"3^'  11"  inclined  to  the  ecliptic,  whose  ascending/  node  is  always  precisely 
coincident  with  the  descending  node  of  the  lunar  orbit.  So  that  the  axis 
of  rotation  describes  a  conical  surface  about  the  pole  of  the  ecliptic  in 
one  revolirfion  of  the  node.  The  remarkable  coincidence  of  the  two  rota- 
tions, that  about  the  axis  and  that  about  the  earth,  which  at  first  sight 
would  seem  perfectly  distinct,  has  been  asserted  (but  we  think  somewhat 
too  hastily*)  to  be  a  consequence  of  the  general  laws  to  be  explained  here- 
after. Be  that  as  it  may,  it  is  the  cause  why  we  always  see  the  sane  face 
of  the  moon,  and  have  no  knowledge  of  the  other  side. 

(435.)  The  moon's  rotation  on  her  axis  is  uniform;  but  since  her 
motion  in  her  orbit  (like  that  of  the  sun)  is  not  so,  we  are  enabled  to 
look  a  few  degrees  ro^nd  the  equatorial  parts  of  h  ix  visible  border,  on  the 
eastern  or  western  side,  according  to  circumstances ;  or,  in  other  words, 
the  line  joining  the  centres  of  the  earth  and  moon  fluctuates  a  little  in  its 
position,  from  its  mean  or  average  inte?  ^ction  with  her  surface,  to  the 

'  From  my  own  observation,  mode  quite  iiK  jjendently  of  any  knowledge  of  such 
a  tendency  having  been  observed  by  others.  Humboldt,  however,  in  his  personal  nar- 
rative, speaks  of  it  as  well  known  to  the  pilots  and  seamen  of  Spanish  America :  see 
note  at  the  end  of  the  chapter  (A.) 

»  See  Edinburgh  Review,  No.  175,  p.  192. 


%mwm 


r 


.SO 


^ 


282 


OUTLINES  OF  ASTRONOMY. 


if 


W'^ 


w^ 


east  or  westward.  And,  moreover,  Bince  the  axis  a^  'it  which  she  revolves 
is  neither  exactly  perpendicular  to  her  orbit,  nor  holds  an  invariable  direc- 
tion in  space,  her  poles  come  alternately  into  view  for  a  small  space  at  the 
edges  of  her  disc.  These  phenomena  are  known  by  the  name  of  lihratiom 
In  consequence  of  these  two  distinct  kinds  of  libration,  the  same  identi- 
cal point  of  the  moon's  surface  is  not  always  the  centre  of  her  disc,  and 
wo  therefore  got  sight  of  a  zone  of  a  few  degrees  in  breadth  on  all  sides 
of  the  border,  beyond  an  exact  hemisphere. 

(436.)  If  there  be  inhabitants  in  the  moon,  the  earth  must  present  to 
them  the  extraordinary  appearance  of  a  moon  of  nearly  2°  degrees  in 
diameter,  exhibiting  phases  complementary  to  those  which  wo  see  the 
moon  to  do,  but  ivimoveably  fixed  in  their  sky,  (or,  at  least,  changing  its 
apparent  place  only  by  the  small  amount  of  the  libration,)  while  the  stars 
must  seem  to  pass  slowly  beside  and  behind  it.  It  will  appear  clouded 
with  variable  spots,  and  belted  with  equatorial  and  tropical  zones  corres- 
ponding to  our  trade-winds ;  and  it  may  be  doubted  whether,  in  their  per- 
petual change,  the  outlines  of  our  continents  and  seas  can  ever  bo  clearly 
discerned.  During  a  solar  eclipse,  the  ecrth's  atmosphere  will  bcoome 
visible  as  a  narrow,  but  bright  luminous  rr  g  of  a  ruddy  colour,  where  it 
rests  on  the  earth,  gradually  passing  into  I'liot  blue,  encircling  the  whole 
or  part  of  the  dark  disc  of  the  earth,  the  remainder  being  dark  and  rugged 
with  clouds. 

(437.)  The  best  charts  of  the  lunar  surface  are  those  of  Cassini,  of 
Russel  (engraved  from  drawings,  made  by  the  aid  of  a  seven  feet  reflect- 
ing telescope,)  the  seleno-topographical  charts  of  Lohrmann,  and  the  very 
elaborate  projection  of  Beer  and  Maedler  accompanying  Iheir  work 
already  cited.'  Madame  Witte,  a  Hanoverian  lady,  has  recently  suc- 
ceeded in  producing  from  her  own  observations,  aided  by  Maedlar's 
charts,  more  than  one  complete  model  of  the  whole  visible  lunar  hemi- 
sphere, of  the  most  perfect  kind,  the  result  of  incredible  diligence  and 
assiduity.  Single  craters  have  also  been  modelled  on  a  large  scale,  both 
by  her  and  Mr.  Nasmyth.  [Still  more  recently  (1851)  photography  has 
been  successfully  applied  to  the  exact  delineation  of  the  lunar  surface  by 
Mr.  Whipple,  using  for  the  purpose  the  great  Fraunhofer  equatorial  of 
the  Observatory  at  Cambridge,  U.  S.]  >• 

'  Tho  representations  of  Heveliiis  in  his  Selenographia,  though  not  without  great 
merit  at  the  time,  and  fine  specimens  of  his  own  engraving,  are  now  become  antiquated. 

Additional  Note  on  Art.  432. 
M.  Arago  has  shown,  from  a  comparison  of  rain,  registered  as  having  fallen  during 
a  long  period,  that  a  slight  preponderance  in  respect  of  quantity  falls  near  the  new 
Moon  over  that  which  falls  near  the  full.  This  would  be  a  natural  and  necessary  con- 
sequence of  a  preponderance  of  a  cloudless  sky  about  the  full,  and  forms,  therefore, 
part  and  parcel  of  the  same  meteorological  fact. 


OF  TERRESTIAL  ORAVITT. 


238 


CHAPTER  VIII. 


OP  TERRESTRIAL  GRAVITY. — OP  THE  LAW  OP  UNIVERSAL  GRAVITA- 
TION.—  PATHS  OP  PROJECTILES;  APPARENT  —  REAL  —  THE  MOON 
RETAINED  IN  HER  ORBIT  BY  GRAVITY. — ITS  LAW  OP  DIMINUTION. — 
LAWS  OP  ELLIPTIC  MOTION.  —  ORBIT  OP  THE  EARTH  ROUND  THE  SUN 
IN  ACCORDANCE  WITH  THESE  LAWS.  —  MASSES  OP  THE  EARTH  AND 
SUN  COMPARED. — DENSITY  OP  THE  SUN. — PORCE  OP  GRAVITY  AT  ITS 
SURPACE. — DISTURBING  EPPEOT  OP  THE  SUN  ON  THE  MOON '  8  MOTION. 

(438.)  The  reader  has  now  been  made  acquainted  with  the  chief  phe- 
nomena of  the  motions  of  the  earth  in  its  orbit  round  the  sun,  and  of  the 
moon  about  the  earth. — We  come  next  to  speak  of  the  physical  caisc 
which  maintains  and  perpetuates  these  motions,  and  ccu^cs  the  massive 
bodies  so  revolving  to  deviate  continually  from  the  directions  they  would 
naturally  seek  to  follow,  in  pursuance  of  the  first  law  of  motion,'  and 
bend  their  courses  into  curves  concave  to  their  centres. 

(439.)  "Whatever  attempts  may  have  been  made  by  metaphysical 
writers  to  reason  away  the  connection  of  cause  and  effect,  and  fritter  it 
down  into  the  unsatisfactory  relation  of  habitual  sequence,'  it  is  certain 
that  the  conception  of  some  more  real  and  intimate  connection  is  quite  as 
strongly  impressed  upon  the  human  mind  as  that  of  the  existence  of  an 
external  world,  —  the  vindication  of  whose  reality  has  (strange  to  say) 
been  regarded  as  an  achievement  of  no  common  merit  in  the  annuls  uf 
this  branch  of  philosophy.  It  is  our  own  immediate  consciousness  of 
effort,  when  we  exert  force  to  put  matter  in  motion,  or  to  oppose  and  neu- 
tralize force,  which  gives  us  this  internal  conviction  oi  power  and  causa- 

'  Princip.  Lex.  i. 

»  See  Brown  '•  On  Cause  and  Effect,"  —  a  work  of  great  acuteness  and  subtlety  of 
reasoning  on  some  points,  but  in  which  the  whole  train  of  argument  is  vitiated  by  one 
enormous  oversight ;  the  omission,  namely,  of  a  dittinct  and  immediate  personal  con- 
tciousnets  of  cautation  in  his  enumeration  of  that  sequence  of  events,  by  which  the 
volition  of  the  mind  is  made  to  terminate  in  the  motion  of  material  objects.  I  mean 
the  conscionsiiesa  of  effort,  accompanied  with  intention  thereby  to  accomplish  an  end, 
as  a  thing  cniin.-ly  distinct  from  mere  desire  or  volition  on  the  one  hand,  and  from  mere 
spasmodic  contraction  of  muscles  on  the  other.  Brown,  3d  edit.  Edin.  1818,  p.  47. 
(Note  to  edition  of  1833.) 


^J»» 


r.HI 


•Mi-*' I 


%-^'iYi 


234 


OUTLINES  OP  ASTRONOMY. 


ifj? 


tion  so  fur  ns  it  refers  to  tho  matcriul  world,  and  compels  us  to  bclicvo 
that  whenever  we  see  niateriul  objects  put  iu  motion  from  a  state  of  rest, 
or  deflected  from  their  rectilinear  paths  and  changed  in  their  velocities  if 
already  in  motion,  it  is  in  consequence  of  such  an  effort  nomihow 
exerted,  though  not  accompanied  with  mir  consciousness.  That  such  an 
effort  should  bo  exerted  with  success  through  an  interposed  space,  is  no 
more  ditHeult  to  conceive,  than  that  our  hand  should  communicate  motiou 
to  a  stone,  with  which  it  is  iJnnomtmhli/  not  in  contact, 

(440.)  All  bodies  with  which  we  are  acquainted,  when  raised  into  tho 
air  and  quietly  abandoned,  descend  to  the  earth's  surface  iu  lines  perpen- 
dicular to  it.  They  are  therefore  urged  thereto  by  a  force  or  effort,  which 
it  is  but  reasonable  to  regard  as  tho  direct  or  indirect  result  of  a  conxcious' 
ness  and  a  tcill  existiu'r  sometchcre,  though  beyond  our  power  to  trace, 
which  force  wo  term  yraviti/,  and  whose  tendency  or  direction,  as  uni- 
versal experience  teaches,  is  towards  tho  earth's  centre;  or  rather,  to 
speak  strictly,  with  reference  to  its  spheroidal  figure,  perpendicular  to  the 
surface  of  still  water.  But  if  wo  cast  a  body  obliquely  into  the  air,  this 
tendency,  though  not  extinguished  or  diminished,  is  materially  modified 
in  its  ultimate  effect.  Tho  upward  impetus  we  give  the  stone  is,  it  is 
true,  after  a  time  destroyed,  and  a  downward  one  communicated  to  it, 
which  ultimately  brings  it  to  tho  surface,  where  it  is  opposed  in  its  fur- 
ther progress,  and  brought  to  rest.  But  all  tho  while  it  has  been  conti- 
nually deflected  or  bent  aside  from  its  rectilinear  progress,  and  made  to 
describe  a  curved  line  concave  to  the  earth's  centre;  and  having  a  highest 
jjoiiif,  vertex,  or  apoyee,  ju.st  as  tho  moon  has  in  its  orbit,  where  the  direc- 
tion of  its  motion  is  perpendieulur  to  the  radius. 

(441.)  When  tho  stone  which  we  fling  obliquely  upwards  meets  and  is 
stopped  in  its  descent  by  the  earth's  surface,  its  motion  is  not  toxoards  the 
centre,  but  inclined  to  the  earth's  radius  at  the  same  angle  as  when  it 
quitted  our  hand.  As  we  are  sure  that,  if  not  stopped  by  the  resistance 
of  the  earth,  it  would  continue  to  descend,  and  that  ohliquelt/,  what  pre- 
sumption, we  may  ask,  is  there  that  it  would  ever  roach  the  centre  towards 
which  its  motion,  in  no  part  of  its  visible  course,  was  ever  directed? 
What  reason  have  we  to  believe  that  it  might  not  rather  circulate  round 
it,  ns  the  moon  does  round  tho  earth,  returning  again  to  the  point  it  set 
out  from,  after  completing  an  elliptic  orbit  of  which  the  earth's  centre 
occupies  the  lower  focus  ?  And  if  so,  is  it  not  reasonable  to  imagine  that 
the  same  force  of  gravity  may  (since  wo  know  that  it  is  exerted  at  all 
accessible  heights  above  the  surface,  and  even  in  the  highest  regions  of 
the  atmosphere)  extend  as  far  as  60  radii  of  the  earth,  or  to  the  moon  ? 
and  may  not  this  be  the  power, — for  some  power  there  must  be, — which 


fu^Tfll  foi 


3f"(1U' 


GRAVITATION   OF  THE    MOON   TO   THE   EARTH. 


235 


to  bclicvo 
to  of  rest, 
ilocitics  if 
gomrhoio 
i  such  aa 
pace,  19  no 
ato  motiou 

cd  into  tho 
les  pcrpen- 
ffort,  which 
a  consvioua- 
)r  to  trace, 
ion,  as  uni- 
•  rather,  to 
cular  to  the 
iho  air,  this 
Uy  niodifiod 
ono  irt,  it  is 
icatcd  to  it, 
id  in  its  fur- 
been  coiiti- 
nd  made  to 
ug  tt  hiijhest 
re  the  direc- 

iicets  and  is 
towards  the 
as  when  it 
e  resistance 
',  what  pre- 
itre  towards 
er  directed? 
iulato  round 
point  it  set 
Tth's  centre 
magino  that 
:erted  at  all 
regions  of 
the  moon? 
be, — which 


deflects  her  at  every  instant  from  tho  tangent  of  her  orbit,  and  keeps  her 
ill  the  elliptic  path  which  oxperiuncu  teaches  us  she  actually  pursues? 

(44'2.)  If  a  .stone  be  whirled  round  lit  tho  end  of  a  string  it  will  stretch 
the  string  by  a  n-ntri/iKjal  force,  which,  if  tho  speed  of  rotation  be  sufli- 
cicntly  increased,  will  at  length  break  tho  string,  and  lot  tho  stone  escape. 
However  strong  tho  string,  it  may,  by  a  sufficient  rotary  velocity  of  tho 
stone,  bo  brought  to  the  utmost  tension  it  will  bear  without  breaking ;  and 
if  wo  know  what  weight  it  is  capable  of  carrying,  tho  velocity  necessary 
for  this  i)urposo  is  easily  calculated.  Suppose,  now,  a  string  to  connect 
tho  earth's  centre  with  a  weight  at  its  surface,  whose  strength  should  bo 
just  sufficient  to  sustain  that  weight  suspended  from  it.  lict  us,  however, 
for  a  moment  imagine  gravity  to  have  no  existence,  and  that  tho  weight 
is  made  to  revolve  with  the  limltitiy  veloviti/  which  that  string  can  barely 
counteract:  then  will  its  tension  bo  just  eijual  to  the  weight  of  tlu'  re- 
volving body;  and  any  power  which  should  continually  urge  the  body 
towards  tho  centre  with  a  force  equal  to  its  weight  would  perform  tho 
office,  and  might  supply  tho  place  of  the  string,  if  divided.  Divide  it 
then,  and  in  its  place  let  gravity  act,  and  tho  body  will  circulate  as  before ; 
its  tendency  to  the  centre,  or  its  wei(jht,  being  just  balanced  by  its  centri- 
fu^Tfll  force.  Knowing  the  radius  of  tho  earth,  wo  can  calculate  by  tho 
principles  of  mechanics  the  periodical  time  in  which  a  body  so  balanced 
must  circulate  to  keep  it  up;  and  this  appears  to  bo  1"  23"  ii2*. 

(448.)  If  we  make  the  same  calculation  for  a  body  at  tho  distance  of 
the  moon,  supposini/  itn  uri't/ht  or  yraviti/  the  same  as  at  the  earth's 
surface,  wo  shall  find  the  period  required  to  be  lO**  45""  30*.  The  actual 
period  of  tho  moon's  revolution,  however,  is  27''  7"  43" ;  and  hence  it  is 
clear  that  the  moon's  velocity  is  not  nearly  sufficient  to  sustain  it  against 
siivh  a  power,  supposing  it  to  revolve  in  a  circle,  or  neglecting  (for  the 
present)  the  slight  ellipticity  of  its  orbit.  In  order  that  a  body  at  the 
distance  of  the  moon  (or  the  moon  itself)  should  be  capable  of  keeping 
its  distil  nee  from  the  earth  by  tho  outward  effort  of  its  centrifugal  force, 
while  yet  its  timo  of  revolution  should  be  what  the  moon's  actually  is, 
it  will  appear'  that  yravift/,  instead  of  being  as  intense  as  at  the  surface, 
would  require  to  be  very  nearly  8600  times  less  energetic;  or,  in  other 
woi*ds,  that  its  intensity  is  so  enfeebled  by  the  remoteness  of  the  body  on 
which  it  acts,  as  to  be  capable  of  producing  in  it,  in  the  same  time,  only 
if'qq^^  part  of  the  motion  which  it  would  impart  to  the  same  mass  of 
matter  at  the  earth's  surface. 

(444.)  The  distance  of  tho  moon  from  the  earth's  centre  is  a  very  little 
less  than  sixty  times  the  distance  from  the  centre  to  the  surface,  and 

'  Newton,  Prinoip.  b.  i.,  Prop.  4.,  Cor.  2. 


n^ 


'n 


'"''"'•'-"Sll 

•WW-"! 


1^— 


236 


OUTLINES  OF  ASTRONOMY. 


3600  : 1  :  :  60^ :  1' ;  so  that  the  proportion  in  which  we  must  admit  the 
earth's  gravity  to  be  enfeebled  at  the  moon's  distance,  if  it  be  really  the 
force  which  retains  the  moon  in  her  orbit,  must  be  (at  least  in  this  par- 
ticular instance)  that  of  the  squares  of  the  distances  at  which  it  is  com- 
pared. Now,  in  such  a  diminution  of  energy  with  increase  of  distance, 
there  is  nothing  prima  facie  inadmissible.  Emanations  from  a  centre, 
such  as  light  and  heat,  do  really  diminish  in  intensity  by  increase  of  dis- 
tance, and  in  this  identical  proportion ;  and  though  we  cannot  certainly 
argue  much  from  this  analogy,  yet  we  do  see  that  the  power  of  magnetic 
and  electric  attractions  and  repulsions  is  actually  enfeebled  by  distance, 
and  much  more  rapidly  than  in  the  simple  proportion  of  the  increased 
distances.  The  argument,  therefore,  stands  thus  :  —  On  the  one  hand, 
Gravity  is  a  real  power,  of  whose  agency  we  have  daily  experience.  We 
know  that  it  extends  to  the  greatest  accessible  heights,  and  far  beyond ; 
and  we  sec  no  reason  for  drawing  a  line  at  any  particular  height,  and 
there  asserting  that  it  must  cease  entirely ;  though  we  have  analogies  to 
lead  us  to  suppose  its  energy  may  diminish  as  we  ascend  to  great  heights 
from  the  surface,  such  as  that  of  the  moon.  On  the  other  hand  we  are 
sure  the  moon  is  urged  towards  the  earth  by  some  power  which  retains 
her  in  her  orbit,  and  that  the  intensity  of  this  power  is  such  as  would 
correspond  to  a  gravity,  diminished  in  the  proportion  —  otherwise  not 
improbable  —  of  the  squares  of  the  distances.  If  gi^avity  be  not  that 
power,  there  must  exist  some  other;  and,  besides  this,  gravity  must 
cease  at  some  inferior  level,  or  the  nature  of  the  moon  must  be  different 
from  that  of  ponderable  matter ;  —  for  if  not,  it  would  be  urged  by  both 
powers,  and  therefore  too  much  urged  and  forced  inwards  from  her  path. 

(445.)  It  is  on  such  an  argument  that  Newton  is  understood  to  have 
rested,  in  the  first  instance,  and  provisionally,  his  law  of  universal  gravi- 
tation, which  may  be  thus  abstractly  stated : — "  Every  particle  of  matt<>r 
in  the  universe  attracts  every  other  particle,  with  a  force  directly  propor- 
tioned to  the  mass  of  the  attracting  particle,  and  inversely  to  the  square 
of  the  distance  between  them."  In  this  abstract  and  general  form, 
however,  the  proposition  is  not  applicable  to  the  case  before  us.  The 
earth  and  moon  are  not  mere  particles,  but  great  spherical  bodies,  and  to 
such  the  general  law  docs  not  immediately  apply;  and,  before  we  can 
make  it  applicable,  it  becomes  necessary  to  inquire  what  will  be  the  force 
with  which  a  congeries  of  particles,  constituting  a  solid  mass  of  any 
assigned  figure,  will  attract  another  such  collection  of  material  atoms. 
This  problem  is  one  purely  dynamical,  and,  in  this  its  general  form,  is 
of  extreme  difficulty.  Fortunately  however,  for  human  knowledge,  when 
the  attracting  and  attracted  bodies  are  spheres,  it  admits  of  an  easy  and 


GENERAL  LAW  OF  GRAVITATION. 


23T 


idmit  the 
really  the 
this  par- 
it  is  corn- 
distance, 
I  a  centre, 
ise  of  dis- 
;  certainly 
'  magnetic 
J  distance, 
1  increased 
one  hand, 
ence.    We 
ir  beyond; 
leight,  and 
inalogies  to 
reat  heights 
land  we  are 
lich  retains 
h  as  would 
icrwise  not 
not  that 
ivity  must 
be  different 
'ed  by  both 
her  path, 
lod  to  have 
-ersal  gravi- 
|e  of  matter 
ictly  propor- 
the  square 
neral  form, 
■e  us.    The 
lies,  and  to 
fore  we  can 
be  the  force 
lass  of  any 
Icrial  atoms, 
iral  form,  is 
|ledge,  when 
an  easy  and 


direct  solution.  Newton  himself  has  shown  (Princip.  b.  i.  prop.  75) 
that,  in  that  case,  the  attraction  is  precisely  the  same  as  if  the  whole 
matter  of  each  sphere  were  collected  into  its  centre,  and  the  spheres  were 
single  particles  there  placed ;  so  that,  in  this  case,  the  general  law  applies 
in  its  strict  wording.  The  effect  of  the  trifling  deviation  of  the  earth 
from  a  spherical  form  is  of  too  minute  an  order  to  need  attention  at  pre- 
sent.    It  is,  however,  perceptible,  and  may  be  hereafter  noticed. 

(446.)  The  next  step  in  the  Newtonian  argument  is  one  which  divests 
the  law  of  gravitation  of  its  provisional  character,  as  derived  from  a  loose 
and  superficial  consideration  of  the  lunar  orbit  as  a  circle  described  with  an 
average  or  mean  velocity,  and  elevates  it  to  the  rank  of  a  general  and  pri- 
mordial relation  by  proving  its  applicability  to  the  state  of  existing  nature 
in  all  its  circumstances.  This  step  consists  in  demonstrating,  as  he  has 
done '  (Princip.  i.  17.  i.  75.),  that,  under  the  influence  of  such  an  attract- 
ive force  mutually  urging  two  spherical  gravitating  bodies  towards  each 
other,  they  will  each,  when  moving  in  each  other's  neighbourhood,  be 
deflected  into  an  orbit  concave  towards  the  other,  and  describe,  one  about 
the  other  regarded  as  fixed,  or  both  round  their  common  centre  of  gravity, 
curves  whose  forms  are  limited  to  those  figures  known  in  geometry  by  the 
general  name  of  conic  sections.  It  will  depend,  he  shows,  in  any  assigned 
case,  upon  the  particular  circumstances  or  velocity,  distance,  and  direction, 
which  of  these  curves  shall  be  described,  — whether  an  ellipse,  a  circle,  a 
parabola,  or  an  hyperbola ;  but  one  or  other  it  must  be ;  and  any  one  of 
any  degree  of  excentricity  it  maf/  be,  according  to  the  circumstances  of 
the  case;  and,  in  all  cases,  the  point  to  which  the  motion  is  referred, 
whether  it  be  the  centre  of  one  of  the  spheres,  or  their  common  centre  of 
gravity,  will  of  necessity  be  the  focus  of  the  conic  section  described.  He 
shows,  furthermore  {Prhicip.  i.  1.),  that,  in  every  case,  the  angular  velo- 
city with  which  the  line  joining  their  centres  moves,  must  be  inversely 
proportional  to  the  square  of  their  mutual  distance,  and  that  equal  areas 
of  the  curves  described  will  be  swept  over  by  their  line  of  junction  in 
equal  times. 

(447.)  All  this  is  in  conformity  with  what  we  have  stated  of  the  solar 

'  We  refer  for  these  fundamental  propositions,  as  a  point  of  duty,  to  the  immortal 
work  in  which  they  were  first  propounded.  It  is  impossible  for  us,  in  this  volume,  to 
go  into  these  investigations :  even  did  our  limits  permit,  it  would  be  utterly  inconsist- 
ent  with  our  plan  :  a  general  idea,  however,  of  their  conduct  will  be  given  in  the  next 
chapter.  We  trust  that  the  careful  and  attentive  study  of  the  Principia  in  t(s  original 
form  will  never  be  laid  aside,  whatever  be  the  improvements  of  the  modern  analysis 
as  respects  facility  of  calculation  and  expression.  From  no  other  quarter  can  a  thorough 
"nd'complete  comprehension  of  the  mechanism  of  our  system,  (so  far  as  the  immedi- 
ate scope  of  that  work^)  be  anything  like  so  well,  and  we  may  add,  so  easily  obtained. 


»^V1 


wf 


238 


OUTLINES   OP  ASTRONOMY. 


1^ 


and  lunar  movements.  Their  orbits  are  ellipses,  but  of  different  degrees 
of  exccntricity ;  and  this  circurastar?')  already  indicates  the  general  appli- 
cability of  the  principles  in  question. 

(448.)  But  here  we  have  already,  by  a  natural  and  ready  implication 
(such  is  always  the  progress  of  generalization),  taken  a  further  and  most 
important  step,  almost  unperceived.  We  have  extended  the  action  of 
gravity  to  the  case  of  the  earth  and  sun,  to  a  distance  immensely  greater 
than  that  of  the  moon,  and  to  a  body  apparently  quite  of  a  different 
nature  from  either.  Are  we  justified  in  this  ?  or,  at  all  events,  are  there 
no  modifications  introduced  by  the  change  of  data,  if  not  into  the  general 
expression,  at  least  into  the  particular  interpretation,  of  the  law  of  gravi- 
tation ?  Now,  the  moment  we  come  to  numbers,  an  obvious  incongruity 
strikes  us.  When  we  calculate,  as  above,  from  the  known  distance  of  the 
sun  (art.  357),  and  from  the  period  in  which  the  earth  circulates  about  it 
(art.  305),  what  must  be  the  centrifugal  force  of  the  latter  by  which  the 
sun's  attraction  is  balanced,  (and  which,  therefore,  becomes  an  exact  mea- 
sure of  the  sun's  attractive  energy  as  ot>  in  the  earth,)  we  find  it  to 
be  immensely  greater  than  would  suffice  !  ;  ■<-•  mteract  the  earth'' s  attrac- 
tion on  an  equal  body  at  that  distance — greater  in  the  high  proportion  of 
354936  to  1.  It  is  clear,  then,  that  if  tlic  earth  be  retained  in  its  orbit 
about  the  sun  by  solar  attraction,  conformable  in  its  rate  of  diminution 
with  the  general  law,  this  force  must  be  no  less  than  354936  times  more 
intense  than  what  the  earth  would  be  capable  of  exerting,  cseteris  paribus, 
at  an  equal  distance. 

(449.)  What,  then,  are  we  to  understand  from  this  result  ?  Simply 
this, —  that  the  sun  attracts  as  a  collection  of  354936  earths  occupying 
its  place  would  do,  or,  in  other  words,  that  the  sun  contains  354936  times 
the  mass  or  quantity  of  ponderable  matter  that  the  earth  consists  of.  Nor 
let  this  conclusion  startle  us.  We  have  only  to  recall  what  has  been 
already  shown  (in  art.  358)  of  the  gigantic  dimensions  of  this  magnifi- 
cent body,  to  perceive  that,  in  assigning  to  it  so  vast  a  mass,  we  are  not 
outstepping  a  reasonable  proportion.  In  fact,  when  we  come  to  compare 
its  mass  with  its  bulk,  we  find  its  density'  to  be  less  than  that  of  the  earth, 
being  no  more  than  0-2543.  So  that  it  must  consist,  in  reality,  of  far 
lighter  materials,  especially  when  we  consider  the  force  under  which  its 
central  parts  must  be  condensed.  This  consideration  renders  it  highly 
probable  that  an  intense  heat  prevails  in  its  interior  by  which  its  elasticity 


*  The  density  of  a  material  body  is  as  the  ma$a  directly,  and  the  volume  inversely : 
hence  density  of  O :  density  of  ® : :  ^^m :  1  :  0-2543  :  1. 


GRAVITATION  AND   MASS   OF  THE   PUN. 


239 


it  degrees 
iral  appli- 

nplication 
and  most 
action  of 
jly  greater 
%  different 
J  are  there 
ihe  general 
^  of  gravi- 
incongraity 
,ance  of  the 
tes  about  it 
r  -which  the 
I  exact  mea- 
re  find  it  to 
.rill's  attrac- 
roportion  of 

in  its  orbit 
'  diminution 

times  more 
eris  paribus, 

\i  ?     Simply 
IS  occupying 
(54936  times 
lists  of.    Nor 
>at  has  been 
this  magnifi- 
},  we  are  not 
|e  to  compare 
lof  the  earth, 
(cality,  of  far 
ler  which  its 
srs  it  highly 
its  elasticity 

ime  inversely : 


is  reinforcecl,  and  rendered  capable  of  resisting  this  almost  inconceivable 
pressure  without  collapsing  into  smaller  dimensions. 

(450.)  This  will  be  more  distinctly  appreciated,  if  we  estimate,  as  wo 
are  now  prepared  to  do,  the  intensity  of  gravity  at  the  sun's  surface. 

The  attraction  of  a  sphere  being  the  same  (art.  445)  as  if  its  whole 
mass  were  collected  in  its  centre,  will,  of  course,  be  proportional  to  the 
mass  directly,  and  the  square  of  the  distance  inversely ;  and,  in  this  case, 
the  distance  is  the  radius  of  the  sphere.  Hence  we  conclude',  that  the 
intensities  of  solar  and  terrestrial  gravity  at  the  surfaces  of  the  two  globes 
are  in  the  proportions  of  27 -9  to  1.  A  pound  of  terrestrial  matter  at  the 
sun's  surface,  then,  would  exert  a  pressure  equal  to  what  27*9  such  pounds 
would  do  at  the  earth's.  The  efficacy  of  muscular  power  to  overcome 
weight  is  therefore  proportionally  nearly  28  times  less  on  the  sun  than  on 
the  earth.  An  ordinary  man,  for  example,  would  not  only  be  unable  to 
sustain  his  own  weight  on  the  sun,  but  would  be  lite:'  illy  crushed  to  atoms 
under  the  load.' 

(451.)  Henceforward,  then,  we  must  co  ^nt  to  dismiss  all  idea  of  the 
earth's  immobility,  and  transfer  that  attribui  0  the  sun,  whose  ponderous 
mass  is  calculated  to  exhaust  tha  feeble  attractions  of  such  comparative 
atoms  as  the  earth  and  moon,  without  being  perceptibly  dragged  from  its 
place.  Their  centre  of  gravity  lies,  as  we  have  already  hinted,  almost 
close  to  the  centre  of  the  solar  globe,  at  an  interval  quite  imperceptible 
from  our  distance ;  and  whether  we  regard  the  earth's  orbit  as  being  per- 
formed about  the  one  or  tho  other  centre  makes  no  appreciable  diflFerence 
iu  any  one  phenomenon  of  astronomy. 

(452.)  It  is  in  conseqienee  of  the  mutual  gravitation  of  all  the  several 
parts  of  matter,  which  the  Newtonian  law  supposes,  that  the  earth  and 
moon,  while  in  the  act  of  revolving,  monthly,  in  their  mutual  orbits  about 
their  common  centre  of  gravity,  yet  continue  to  circulate,  without  parting 
company,  in  a  greater  annual  orbit  round  the  sun.  We  may  conceive  this 
motion  by  connecting  two  unequal  balls  by  a  stick,  which,  at  their  centre 
of  gravity,  is  tied  by  a  long  string,  and  whirled  round.  Their  joint  si/s- 
tern  will  circulate  as  one  body  about  the  common  cen^^e  to  which  the 
string  is  attached,  while  yet  they  may  go  on  circulating  round  each  other  in 
subordinate  gyrations,  as  if  the  stick  were  quite  free  from  any  such  tie, 
and  merely  hurled  through  the  air.  If  the  earth  alone,  and  not  the 
moon,  gravitated  to  the  sun,  it  would  be  dragged  away,  and  leave  the  moon 


r.'«.irt«« 


•l-l 


27'9  :  1 ;  the  respective  radii 


'riolar  gravity:  terrestrial  . .  (Tfiro»5)3  •  (xhtst!) 
of  the  sun  and  earth  being  440000,  and  4000  miles. 

*A  mass  weighing  12  stone  or  I68Ibs.  on  the  earth,  would  produce  a  pressure  of 
4687  lbs.  on  tho  sun. 


'  i 


240 


OUTLINES   OF  ASTRONOMY. 


behind — and  vice  versd;  but,  acting  on  both,  they  continue  together 
under  its  attraction,  just  as  the  loose  parts  of  the  earth's  surface  continue 
to  rest  upon  it.  It  is,  then,  in  strictness,  not  the  earth  or  the  moon 
which  describes  an  ellipse  around  the  sun,  but  their  common  centre  of 
gravity.  The  effect  is  to  produce  a  small,  but  very  perceptible,  monthly 
equation  in  the  sun's  apparent  motion  as  seen  from  the  earth,  which  is 
always  taken  into  account  in  calculating  the  sun's  place.  The  moon's 
actual  path  in  its  compound  oibit  round  the  earth  and  sun  is  an  epicycloi- 
dal  curve  intersecting  the  orbit  of  the  earth  twice  in  every  lunar  month, 
and  alternately  within  and  without  it.  But  as  there  are  not  more  than 
twelve  such  months  in  the  yet  r,  and  as  the  total  departure  of  the  moon 
from  it  either  way  does  not  exceed  one  400th  part  of  the  radius,  this 
amounts  only  to  a  slight  undulation  upon  the  earth's  ellipse,  so  slight, 
indeed,  that  if  dra<vn  in  true  proportion  on  a  large  sheet  of  paper,  no  eye 
unaided  by  measurement  with  compasses  would  detect  it.  The  real  orbit 
of  the  moon  is  everywhere  concave  towards  the  sun. 

(453.)  Here  moreover,  i.  e.  in  the  attraction  of  the  sun,  we  have  the 
key  to  all  those  differences  from  an  exact  elliptic  movement  of  the  moon 
in  her  monthly  orbit,  which  we  have  already  noticed  (arts.  407,  409),  viz. 
to  the  retrograde  revolution  of  her  nodes ;  to  the  direct  circulation  of  the 
axis  of  her  ellipse ;  and  to  all  the  other  deviations  from  the  laws  of  elliptic 
motion  at  which  wc  have  further  hinted.  If  the  moon  simply  revolved 
about  the  earth  under  the  influence  of  its  gravity,  none  of  these  pheno- 
mena would  take  place.  Its  orbit  would  ha  a  perfect  ellipse,  returning 
into  itself,  and  always  lying  in  one  and  the  same  plane.  That  it  is  not  so, 
is  a  proof  that  some  cause  didurhs  it,  and  interferes  with  the  earth's 
attraction ;  and  this  cause  is  no  other  than  the  sun's  attraction — or  rather, 
that  part  of  it  which  is  not  equally  exerted  on  the  earth. 

(454.)  Suppose  two  stones,  side  by  side,  or  otherwise  situated  with  re- 
spect to  each  other,  to  be  let  fall  together ;  then,  as  gravity  accelerates 
them  equally,  they  will  retain  their  relative  positions,  and  fall  together  as 
if  they  formed  one  mass.  But  suppose  gravity  to  be  rather  more  intensely 
exerted  on  one  than  on  the  ocher;  then  would  that  one  be  rather  more 
accelerated  in  its  fall,  and  would  gradually  leave  the  Oiher ;  and  thus  a 
relative  motion  between  them  would  arise  from  the  difference  of  action, 
however  slight. 

(455.)  The  sun  is  about  400  times  more  remote  than  the  moon;  and, 
in  consequence,  while  the  moon  describes  her  monthly  orbit  round  the 
earth,  her  distance  from  the  sun  is  alternately  ^  J^th  part  greater  and  as 
much  less  than  the  earth's.  Small  as  this  is,  it  is  yet  sufficient  to  produce 
a  perceptible  excess  of  attractive  tendency  of  the  moon  towards  the  sun, 


SOLAR  DTSTCBANGE  OF  THE  MOON'S  SURFACE. 


241 


e  together 
e  contiDuo 

the  moon 
a  ceotre  of 
le,  monthly 
h,  iiyhich  is 
The  moon's 
in  epicycloi- 
mar  month, 
b  more  than 
)f  the  moon 

radius,  this 
se,  80  slight, 
)aper,  no  eye 
he  real  orhit 

we  have  the 
of  the  moon 
07, 409),  viz. 
Illation  of  the 
iws  of  elliptic 
nply  revolved 
these  pheno- 
(se,  returning 
\,t  it  is  not  sOf 
[h  the  earth's 
in — or  rather, 

^ated  with  re- 
ty  accelerates 


Fig.  62. 


NqM. 


K 


S 


above  that  of  the  earth  when  in  the  nearer  point  of  her  orbit,  M,  and  a 
corresponding  defect  on  the  opposite  part,  N :  and,  in  the  intermediate 
positions,  not  only  will  a  difference  of  forcef  h  Tcdist,  but  a  difference  of 
directions  also ;  since  however  small  the  lunar  orbit  M  N,  it  is  not  a  pointy 
and,  therefore,  the  lines  drawn  from  the  sun  S  to  its  several  parts  cannot 
be  regarded  as  strictly  parallel.  If,  as  we  have  already  seen,  the  force  of 
the  sun  were  equally  exerted,  and  in  parallel  directions  on  both,  no  disturb- 
ance of  their  relative  situations  would  take  place ;  but  from  the  non-veri- 
fication of  these  conditions  arises  a  disturbing  force,  oblique  to  the  line 
joining  the  moon  and  earth,  which  in  some  situations  acts  to  accelerate,  in 
others  to  retard,  her  elliptic  orbitual  motion ;  in  some  to  draw  the  earth 
from  the  moon,  in  others  the  moon  from  the  earth.  Again,  the  lunar 
orbit,  though  very  nearly,  is  yet  not  quite  coincident  with  the  plane  of  the 
ecliptic ;  and  hence  the  action  of  the  sun,  which  is  v  ery  nearly  parallel  to 
the  last-mentioned  plane,  tends  to  draw  her  somewhat  out  of  the  plane  of 
her  orbit,  and  does  act'ially  do  so — producing  the  revolution  of  her  nodes, 
and  other  phenomena  iess  striking.  We  are  not  yet  prepared  to  go  into 
the  subject  of  these  perturbations,  as  they  are  called ;  but  they  are  intro- 
duced to  the  reader's  notice  as  early  as  possible,  for  the  purpose  of  re- 
assuring his  mind,  should  doubts  have  arisen  as  to  the  logical  correctness 
of  our  argument,  in  consequence  of  our  temporary  neglect  of  them  while 
working  our  way  upward  to  the  law  of  gravity  from  a  general  considera- 
tion of  the  moon's  orbit. 


16 


»  ..    ».       .     .  ....  J 


"•''sn-.v,.. 


t 


■!    \> 


242 


OUTLINES   OF  ASTRONOMY. 


CHAPTER  IX. 
OF    THE    SOLAR    SYSTEM. 

APPARENT   MOTIONS    OF  THE    PLANETS. — THEIR   STATIONS    AND    RE- 
TROORADATIONS.  —  THE   SUN   THEIR   NATURAL   CENTRE   OP   MOTION. 

—  INFERIOR    PLANETS.  —  THEIR    PHASES,   PERIODS,    ETC.  —  DIMEN- 
SIONS AND  FORM   OF  THEIR  ORBITS.  —  TRANSITS  ACROSS   THE   SUN. 

—  SUPERIOR  PLANiSTS.  —  THEIR  DISTANCES,  PERIODS,  ETC.  —  KEP- 
LER's  laws  and  their  INTERPRETATION. — ELLIPTIC  ELEMENTS 
OP  A  planet's  orbit. — ITS  HELIOCENTRIC  AND  GEOCENTRtq 
PLACE. —  EMPIRICAL  LAW  OF  PLANETARY  DISTANCES; — VIOLATE. 
IN  THE  CASE  OF  NEPTUNE. — THE  ULTRA-ZODIACAL  PLANETS. — 
PHYSICAL  PECULIARITIES   OBSERVABLE  IN   EACH  OP  THE  PLANETS. 


I'' 


(456.)  The  sun  and  moon  are  not  the  only  celestial  objects  which 
appear  to  have  a  motion  independent  of  that  by  which  the  great  con- 
stellation of  the  heavens  is  daily  carried  round  the  earth.  Among  the 
stars  there  are  several,  —  and  those  among  the  brightest  and  most  con- 
spicuous,—  which,  when  Jittentively  watched  from  night  to  night,  are 
found  to  change  their  relative  situations  among  the  rest ;  some  rapidly, 
others  much  more  slowly.  These  are  called  planets.  Four  of  them  — 
Venus,  Mars,  Jupiter,  and  Saturn  —  are  remarkably  large  and  brilliant; 
another.  Mercury,  is  also  visible  to  the  naked  eye  as  a  large  star,  but,  for 
a  reason  which  will  presently  appear,  is  seldom  conspicuous;  a  sixth, 
Uranus,  is  barely  discernible  without  a  telescope ;  and  nine  others — Nep- 
tune, Ceres,  Pallas,  Vesta,  Juno,  Astraea,  Hebe,  Iris,  Flora  —  are  never 
visible  to  the  naked  eye.  Besides  these  fifteen,  others  yet  undiscovered 
may  exist;'  and  it  is  extremely  probable  that  such  is  the  case, — the  mul- 
titude of  telescopic  stars  being  so  great  that  only  a  small  fraction  of  their 
number  has  been  suflSciently  noticed  to  ascertain  whether  they  retain  the 
same  places  or  not,  and  the  ten  last-mentioned  planets  having  all  been 
discovered  within  little  more  than  half  a  century  from  the  present  time. 

'  While  this  sheet  is  passing  through  the  press,  a  sixteenth,  not  yet  named,  has 
been  added  to  the  list,  by  the  observations  of  Mr.  Graham,  astronomical  assistant  to 
E.  Cooper,  Esq.  at  hia  observatory  at  Markree,  Sligo,  Ireland. 


APPARENT  MOTIONS  OF  THE  PLANETS. 


248 


(457.)  The  apparent  motions  of  the  planets  are  much  more  irregular 
than  those  of  the  sun  or  moon.  Generally  speaking,  and  comparing  their 
places  at  distant  times,  they  all  advance,  though  with  very  different  ave- 
rage or  mean  velocities,  in  the  same  direction  as  those  luminaries,  i.  e.  in 
opposition  to  the  apparent  diurual  motion,  or  from  west  to  east :  all  of 
them  make  the  entire  tour  of  the  heavens,  though  under  very  differc 
circumstances;  and  all  of  them,  with  the  exception  of  the  eight  teles- 
copic planets, — Ceres,  Pallas,  Juno,  Vesta,  Astraoa,  Hebe,  Iris,  and  Flora 
(which  may  therefore  be  termed  ultra-zodiacal,^  —  are  confined  in  their 
visible  paths  within  very  narrow  limits  on  either  side  the  ecliptic,  and 
perform  their  movements  within  that  zone  of  th(  avens  we  have  called, 
above,  the  Zodiac  (art.  308.) 

(458.)  The  obvic",8  conclusion  from  this  is,  that  whatever  be^  other- 
wise, the  nature  and  law  of  their  motions,  they  are  performed  nearly/  in 
the  plane  of  the  ecliptic  —  that  plane,  namely,  in  which  our  own  motion 
about  the  sun  is  performed.  Hence  it  follows,  that  we  see  their  evolu- 
tions, not  in  plan,  but  in  section;  their  real  angular  movements  and 
lineal  distances  being  &\\  foresJwrtened  and  confounded  undistinguishably, 
while  only  their  deviations  from  the  ecliptic  appear  of  their  natural  mag- 
nitude, unr^'.minished  by  the  effect  of  perspective. 

(459.)  The  apparent  motions  of  the  sun  and  moon,  though  not  uni- 
form, do  not  deviate  very  greatly  from  uniformity ;  a  moderate  accelera- 
tion and  retardation,  accour  table  for  by  the  ellipticity  of  their  orbits, 
being  all  that  is  remarked.  But  the  case  is  widely  different  with  the 
planets :  sometimes  they  advance  rapidly ;  then  relax  in  their  apparent 
speed  —  come  to  a  momentary  stop;  and  then  actually  reverse  their 
motion,  and  run  back  upon  their  former  course,  with  a  rapidity  at  first 
increasing,  then  diminishing,  till  the  reversed  or  retrograde  motion  ceases 
altogether.  Another  stationf  or  moment  of  apparent  rest  or  indecision, 
now  takes  place;  after  which  the  movement  is  again  reversed,  and 
resumes  its  original  direct  character.  On  the  whole,  however,  the  amount 
of  direct  motion  more  than  compensates  the  retrograde;  and  by  the 


Fig.  68. 


!    i. 


;'  .1 


excess  of  the  former  over  the  latter,  the  gradual  advance  of  the  planet 
from  west  to  east  is  maintained.  Thus,  supposing  the  Zodiac  to  be 
unfolded  into  a  plane  surface,  (or  represented  as  in  Mercator's  projection, 


K.tcy, 


'>«:« 


Ki.V*1 


244 


OUTLINES   OF  ASTRONOMY. 


art.  283,  taking  the  ecliptic  E  C  for  its  ground  line,)  the  track  of  a  planet 
when  mapped  down  by  observation  from  day  to  day,  will  offer  the  appear- 
ance P  Q  R  S,  &c. ;  the  motion  from  P  to  Q  being  direct,  at  Q  stationary, 
from  Q  to  K  retrograde,  at  E  again  stationary,  from  R  to  S  direct,  and 
so  on. 

(460.)  In  the  midst  of  the  irregularity  and  fluctuation  of  this  motion, 
one  remarkable  feature  of  uniformity  is  observed.  Whenever  the  planet 
crosses  the  ecliptic,  as  at  N  in  the  figure,  it  is  said  (like  the  moon)  to  be 
in  its  node ;  and  as  the  earth  necessarily  lies  in  the  plane  of  the  ecliptic, 
the  planet  cannot  be  ajijmrentfi/  or  uranographicalli/  situated  in  the 
celestial  circle  so  called,  without  being  really  and  locally  situated  in  that 
plane.  The  visible  passage  of  a  planet  through  its  node,  then,  is  a  phe- 
nomenon indicative  of  a  circumstance  in  its  real  motion  quite  independent 
of  the  station  from  which  we  view  it.  Now,  it  is  easy  to  ascertain,  by 
observation,  when  a  planet  passes  from  the  north  to  the  south  side  of  the 
ecliptic :  we  have  only  to  convert  its  right  ascensions  and  declinations  into 
longitudes  and  latitudes,  and  the  change  from  north  to  south  latitude  on 
two  successive  days  will  advertise  us  on  what  day  the  transition  took 
place ;  while  a  simple  proportion,  grounded  on  the  observed  state  of  its 
motion  in  latitude  in  the  interval,  will  suflicc  to  fix  the  precise  hour  and 
minute  of  its  arrival  on  the  ecliptic.  Now,  this  being  done  for  several 
transitions  from  side  to  side  of  the  ecliptic,  and  their  dates  thereby  fixed, 
we  find,  universally,  that  the  interval  of  time  elapsing  between  the  suc- 
cessive passages  of  each  planet  through  the  same  node  (whether  it  be  the 
ascending  or  the  descending)  is  always  alike,  whether  the  planet  at  the 
moment  of  such  passage  be  direct  or  retrograde,  swift  or  slow,  in  its 
apparent  movement. 

(461.)  Here,  then,  we  have  a  circumstance  which,  while  it  shows  that 
the  motions  of  the  planets  are  in  fact  subject  to  certain  laws  and  fixed 
periods,  may  lead  us  very  naturally  to  suspect  that  the  apparent  irregu- 
larities and  complexities  of  their  movements  may  be  owing  to  our  not 
seeing  them  from  their  natural  centre  (art.  338, 371),  and  from  our  mixing 
up  with  their  own  proper  motions  movements  of  a  parallactic  kind,  due  to 
our  own  change  of  place,  in  virtue  of  the  orbitual  motion  of  the  earth 
about  the  sun. 

(462.)  If  we  abandon  the  earth  a?  a  centre  of  the  planetary  motions,  it 
cannot  admit  of  a  moment's  hesitation  where  we  should  place  that  centre 
with  the  greatest  probability  of  truth.  It  must  surelybe  the  sun  which 
is  entitled  to  the  first  trial,  as  a  station  to  which  to  refer  to  them.  If  it 
be  not  connected  with  them  by  any  physical  relation,  it  at  least  possesses 
the  advantage,  which  the  earth  does  not,  of  comparative  inmobility.    But 


THE   SUN   THE   CENTRE   OP   OUR   SYSTEM. 


245 


after  what  has  been  shown  in  art.  440,  of  the  immeuse  mass  of  that  lumi- 
nary, and  of  the  office  it  perforins  to  us  as  u  quiescent  centre  of  our  orbi- 
tual  motion,  nothing  can  bo  more  natural  than  to  suppose  it  may  perform 
the  same  to  other  globes  which,  like  the  earth,  may  be  revolving  round  it; 
and  these  globes  may  be  visible  to  us  by  its  light  reflected  from  them,  as 
the  moon  is.  Now  there  are  many  facts  which  give  a  strong  support  to 
the  idea  that  the  planets  are  in  this  predicament. 

(463.)  In  the  first  place,  the  planets  really  are  great  globes,  of  a  size 
commensurate  with  the  earth,  and  several  of  them  much  greater.  When 
examined  through  powerful  telescopes,  they  are  seen  to  be  round  bodies, 
of  sensible  and  even  of  considerable  apparent  diameter,  and  offering  dis- 
tinct and  characteristic  peculiarities,  which  show  them  to  be  solid  masses, 
each  possessing  its  individual  structure  and  mechanism ;  and  that,-  in  one 
instance  at  least,  an  exceedingly  artificial  and  complex  one.  (See  the 
representations  of  Mars,  Jupiter,  and  Saturn,  in  Plate  III.)  That  their 
distances  from  us  are  great,  much  greater  than  that  of  the  moon,  and  some 
of  them  even  greater  than  that  of  the  sun,  we  infer,  1st,  from  their  being 
occulted  by  the  moon,  and  2dly,  from  the  smallness  of  their  diurnal 
parallax,  which,  even  for  the  nearest  of  them,  when  most  favourably 
situated,  does  not  exceed  a  few  seconds,  and  for  the  remote  ones  is  almost 
imperceptible.  From  the  comparison  of  the  diurnal  parallax  of  a  celestial 
lody,  with  its  apparent  semidiameter,  we  can  at  once  estimate  its  real  size. 
For  the  parallax  is,  in  fact,  nothing  else  than  the  apparent  semidiameter 
of  the  earth  as  seen  'rom  the  body  in  question  (art.  339  et  seq.) ;  and,  the 
intervening  distance  being  the  same,  the  real  diameters  must  be  to  each 
other  in  the  pi'oportion  of  the  apparent  ones.  Without  going  into  parti- 
culars, it  will  suffice  to  state  it  as  a  general  result  of  that  comparison,  that 
the  planets  arc  all  of  them  incomparably  smaller  than  the  sun,  but  some 
of  them  as  large  as  the  earth,  and  others  much  greater. 

(464.)  The  next  fact  respecting  them  is,  that  their  distances  from  us, 
as  estimated  from  the  measurement  of  their  angular  diameters,  are  in  a 
continual  state  of  change,  periodically  increasing  and  decreasing  within 
certain  limits,  but  by  no  means  corresponding  with  the  supposition  of 
regular  circular  or  elliptic  orbits  described  by  them  about  the  earth  as  a 
centr''  '>r  focus,  but  maintaining  a  constant  and  obvious  relation  to  their 
apparent  angular  distances  or  elongations  from  the  sun.  For  example ; 
the  apparent  diameter  of  Mars  is  greatest  when  in  opposition  (as  it  is 
called)  to  the  sun,  i.  e.  when  in  the  opposite  part  of  the  ecliptic,  or  when 
it  comes  on  the  meridian  at  midnight,  —  being  then  about  18",  —  but 
diminishes  rapidly  from  that  to  about  4",  which  is  its  apparent  diameter 
when  in  conjunction^  or  when  seen  in  nearly  the  same  direction  os  that 


«•/ 


m^«:f. 


i^J* 


»''V] 


I? 


246 


OUTLINES  OF  ASTRONOMY. 


luminary.  This,  and  facts  of  a  similar  character,  observed  with  respect 
to  the  apparent  diameters  of  the  other  planets,  clearly  point  out  the  sun 
as  having  more  than  an  accidental  relation  to  their  movements. 

(465.)  Lastly,  certain  of  the  planets,  (Mercury,  Venus,  and  Mars,) 
when  viewed  through  telescopes,  exhibit  the  appearance  of  phases  like 
those  of  the  moon.  This  proves  that  they  are  opaque  bodies,  shining 
only  by  reflected  light,  which  can  be  no  other  than  that  of  the  sun's; 
not  only  because  there  is  no  other  source  of  light  external  to  them  suffi- 
ciently powerful,  but  because  the  appearance  and  succession  of  the  phases 
themselves  are  (like  their  visible  diameters)  intimately  connected  with 
their  elongations  from  the  sun,  as  will  presently  be  shown. 

(466.)  Accordingly  it  is  found,  that,  when  we  refer  the  planetary  move- 
ments to  the  sun  as  a  centre,  all  that  apparent  irregularity  which  they 
offer  when  viewed  from  the  earth  disappears  at  once,  and  resolves  itself 
into  one  simple  and  general  law,  of  which  the  earth's  motion,  as  ex- 
plained in  a  former  chapter,  is  only  a  particular  case.  In  order  to  show 
how  this  happens,  let  us  take  the  case  of  a  single  planet,  which  we  will 
suppose  to  revolve  round  the  sun,  in  a  plane  nearly,  but  not  quite,  coin- 
cident with  the  ecliptic,  but  passing  through  the  sun,  and  of  course  inter- 
secting the  ecliptic  in  a  fixed  line,  which  is  the  line  of  the  planet's  nodes. 
This  line  must  of  course  divide  its  orbit  into  two  segments  j  and  it  ii 
evident  that,  so  long  as  the  circumstances  of  the  planet's  motion  remain 
otherwise  unchanged,  the  times  of  describing  these  segments  must  remain 
the  same.  The  interval,  then,  between  the  planet's  quitting  either  node, 
and  returning  to  tlie  same  node  again,  must  be  that  in  which  it  describes 
one  complete  revolution  round  the  sun,  or  its  periodic  time ',  and  thus  we 
are  furnished  with  a  direct  method  of  ascertaining  the  periodic  time  of 
each  planet.  ,    1^ 

(467.)  "We  have  said  (art.  457)  that  the  planets  make  the  entire  tour 
of  the  heavens  under  very  different  circumstances.  This  must  be  ex- 
plained. Two  of  them  —  Mercury  and  Venus  —  perform  this  circuit 
evidently  as  attendants  upon  the  sun,  from  whose  vicinity  they  never 
depart  beyond  a  certain  limit.  They  are  seen  sometimes  to  the  east, 
sometimes  to  the  west  of  it.  In  the  former  case  they  appear  conspicuous 
over  the  western  horizon,  just  after  sunset,  and  are  called  evening  stars : 
Venus,  especially,  appears  occasionally  in  this  situation  with  a  dazzling 
lustre ;  and  in  favourable  circumstances  may  be  observed  to  cast  a  pretty 
strong  shadow.'     When  they  happen  to  be  to  the  west  of  the  sun,  they 

'  It  must  be  thrown  upon  a  white  ground.  An  open  window  in  a  white-washed  room 
is  the  best  exposure.  In  this  situation  I  have  observed  not  only  the  shadow,  but  the 
diffracted  fringes  edging  its  outline.  —  H.  Note  to  the  edition  of  1833.  Venus  may 
often  be  seen  with  the  naked  eye  in  the  daytime. 


INFERIOR   PLANETS. 


247 


rise  before  that  luminary  in  the  morning,  and  appear  over  the  eastern 
horizon  as  morning  stars :  tliey  do  not,  however,  attain  the  same  elomja- 
tiun  from  the  sun.  Mercury  never  attains  a  greater  angular  distance  from 
it  than  about  29**,  while  Venus  extends  her  excursions  on  either  side  to 
about  47°.  When  they  have  receded  from  the  sun,  emtwanl,  to  their 
respective  distances,  they  remain  for  a  time,  as  it  were,  immoveable  iclth 
respect  to  it,  and  are  carried  along  with  it  in  the  ecliptic  with  a  motion 
equal  to  its  own  j  but  presently  they  begin  to  approach  it,  or,  which  comes 
to  the  same,  their  motion  in  longitude  diminishes,  and  the  sun  gains  upon 
them.  As  this  approach  goes  on,  their  continuance  above  the  horizon 
after  sunset  becomes  daily  shorter,  till  at  length  they  set  before  the  dark- 
ness has  become  sufficient  to  allow  of  their  being  seen.  For  a  time,  then, 
they  are  not  seen  at  all,  unless  on  very  rare  occasions,  when  they  are  to 
be  observed  passing  across  the  sun's  disc  as  small,  round,  wclUdeJined 
Hack  spots,  totally  different  in  appearance  from  the  solar  spots  (art.  386.) 
These  phenomena  are  emphatically  called  transits  of  the  respective 
planets  across  the  sun,  and  take  place  when  the  earth  happens  to  be 
passing  the  line  of  their  nodes  while  they  are  in  that  part  of  their  orbits, 
just  as  in  the  account  we  have  given  (art.  412)  of  a  solar  eclipse.  After 
having  thus  continued  invisible  for  a  time,  however,  they  begin  to  appear 
on  the  other  side  of  the  sun,  at  first  showing  themselves  only  for  a  few 
minutes  before  sunrise,  and  gradually  longer  and  longer  as  they  recede 
from  him.  At  this  time  their  motion  in  longitude  is  rapidly  retrograde. 
Before  they  attain  their  greatest  elongation,  however,  they  become  station- 
ary in  the  heavens ;  but  their  recess  from  the  sun  is '  still  maintained  by 
the  advance  of  that  luminary  along  the  ecliptic,  which  continues  to  leave 
them  behind,  until,  having  reversed  their  motion,  and  become  again 
direct,  they  acquire  sufficient  speed  to  commence  overtaking  him — at 
which  moment  they  have  their  greatest  western  elongation  :  and  thus  is  a 
kind  of  oscillatory  movement  kept  up,  while  the  general  advance  along 
the  ecliptic  goes  on. 

(468.)  Suppose  P  Q  to  be  the  ecliptic,  and  A  B  D  the  orbit  of  one  of 
these  planets,  (for  instance.  Mercury,)  seen  almost  edgewise  by  an  eye 
situated  very  nearly  in  its  plane ;  S,  the  sun,  its  centre  j  and  A,  B,  D,  S, 
successive  positions  of  the  planet,  of  which  B  and  S  are  in  the  nodes. 
If,  then,  the  sun  S  stood  apparently  still  in  the  ecliptic,*  the  planets  would 
simply  appear  to  oscillate  backwards  and  forwards  from  A  to  D,  alter- 
nately passing  before  and  behind  the  sun ;  and,  if  the  eye  happened  to 
lie  exactly  in  the  plane  of  the  orbit,  transiting  his  disc  in  the  former 
case,  and  being  covered  by  it  in  the  latter.  But  as  the  sun  is  not  so 
stationary,  but  apparently  carried  along  the  ecliptic  P  Q,  let  it  be  supposed 


-rflpfl' 


r 

If 


248 


OUTLINES   OF  ASTRONOMT. 


Fig.  64. 


to  move  over  the  spaces  S  T,  T  U,  U  V,  \yhilo  the  planet  in  each  case  exe- 
cutes one  quarter  of  its  period.  Then  will  its  orbit  be  apparently  carried 
along  with  the  sun,  into  tho  successive  positions  represented  in  the  figure; 
and  while  its  real  motion  round  the  sun  brings  it  into  the  respective  points, 
B,  D,  S,  A,  its  apparent  movement  in  the  heavens  will  seem  to  have  been 
along  tho  wavy  or  zigzag  line  A  N  H  K.  In  this,  its  motion  in  longitude 
will  have  been  direct  in  tho  parts  AN,  N  H,  and  retrograde  in  the  parts 
H  n  K ;  while  at  the  turns  of  tho  zigzag,  as  at  H,  it  will  have  been  sta- 
tionary. 

(469.)  The  only  two  planets  —  Mercury  and  Venus  —  whose  evolu- 
tions are  such  as  above  described,  are  called  inferior  planets ;  their  points 
of  farthest  recess  from  the  sun  are  called  (as  above)  their  greatest  eastern 
and  western  elongations  ;  and  their  points  of  nearest  approach  to  it,  their 
inferior  and  superior  conjunctions, — tho  former  when  the  planet  passes 
between  the  earth  and  the  sun,  the  latter  wher  behind  the  sun. 

(470.)  In  art.  467  we  have  traced  tho  apparent  path  of  an  inferior 
planet,  by  considering  its  orbit  in  seciion,  or  as  viewed  from  a  point  in 
the  plane  of  tho  ecliptic.  Let  us  now  contemplate  it  in  plan,  or  as  viewed 
from  a  station  above  that  plane,  and  projected  on  it.  Suppose  then,  S  to 
represent  the  sun,  abed  the  orbit  of  Mercury,  and  A B  C D  a  part  of 
that  of  the  earth  —  the  direction  of  the  cu'culation  being  the  same  in 

F'g-  65. 


both,  viz.  that  of  the  arrow.  When  the  planet  stands  at  a,  let  the  earth 
be  sif/uated  at  A,  in  the  direction  of  a  tangent,  a  A,  to  its  orbit ;  then  it 
is  eviaent  that  it  will  appear  at  its  greatest  elongation  from  the  sun, — 


INFERIOR   PLANETS. 


249 


the  anglo  a  AS,  which  measures  thoir  apparent  interval  as  seen  from  A, 
being  then  greater  than  in  any  other  situation  of  a  upon  its  own  cirolo. 

(471.)  Now,  this  ouglo  being  known  by  observation,  wo  uro  hereby 
furnished  with  a  ready  means  of  ascertaining,  at  least  approximately,  tho 
distance  of  the  planet  from  the  sun,  or  the  radius  of  its  orbit,  supposed  a 
circle.  For  the  triangle  S  A  a  is  right-angled  at  a,  and  consequently  wo 
have  8a:  S  A  :  :  sin.  S  >  • :  radius,  by  which  proportion  tho  radii  S  a, 
S A  of  the  two  orbits  ai-  .irectiy  compared.  If  the  orbits  were  both 
exact  circles,  this  would  of  course  be  a  perfectly  rigorous  mode  of  proceed- 
ing :  but  (as  is  proved  by  the  iuoquulity  of  the  resulting  values  of  8  a 
obtair  d  at  different  times)  this  is  not  tho  case  ;  and  it  becomes  necessary 
to  admit  an  excentricity  of  position,  and  a  deviation  from  the  exact  circu- 
lar form  in  loth  oibits,  to  account  for  this  difference.  Neglecting,  how- 
ever, at  present  I'ais  inequ,vlity,  a  mean  or  average  value  of  S  a  may,  at 
least,  be  obtained  from  tl  ;  frequent  repetition  of  this  process  in  all  vari- 
eties of  situation  of  the  Ufo  bodies.  The  calculations  being  performed, 
it  is  conclude'!  that  the  mean  ii.tance  of  Mercury  from  tho  sun  is 
about  860000!>0  :niles;  and  that  of  Venus,  similarly  derived,  about 
68000000;  tho  radius  of  the  earth's  orbit  being  95000000. 

(472.)  The  sidereal  periods  of  tho  planets  may  be  obtained  (as  before 
observed),  with  a  considerable  approach  to  accuracy,  by  observing  their 
passages  through  tho  nodes  of  their  orbits;  and  indeed,  when  a  certain 
very  minute  motion  of  these  nodes  and  the  apsides  of  their  orbits  (similar 
to  that  of  the  moon's  nodes  and  apsides,  but  incomparably  slower)  is 
allowed  for,  with  a  precision  only  limited  by  tho  imperfection  of  the 
appropriate  observations.  By  such  observations,  so  corrected,  it  appears 
that  the  sidereal  period  of  Mercury  is  87*  SS**  15™  43-9' ;  and  that  of 
Vv  o-"».  224*  16"  49"  80v  These  periods,  however,  are  widely  different 
Uhiv.  the  intervals  at  which  the  successive  appearances  of  the  two  planets 
at  their  eastern  and  western  elongations  from  tho  sun  are  observed  to 
happen.  Mercury  is  seen  at  its  greatest  splendour  as  an  evening  star,  at 
average  intervals  of  about  116,  and  Venus  at  intervals  of  about  584  days. 
The  difference  between  the  sidereal  and  si/nodical  revolution's  (art.  418) 
accounts  for  this.  Referring  again  to  the  figure  of  art.  470,  if  the  sun 
stood  still  at  A,  while  the  planet  advanced  in  its  orbit,  the  lapse  of  a 
sidereal  period,  which  should  bring  it  round  again  to  a,  would  also  produce 
a  similar  elongation  from  the  sun.  But,  meanwhile,  the  earth  has 
advanced  in  its  orbit  in  the  same  direction  towards  E,  and  therefore  the 
next  greatest  elongation  on  the  same  side  of  the  sun  will  happen  —  not 
in  the  position  a  A  of  the  two  bodies,  but  in  some  more  advanced  posi- 
tion, e  £.    The  determination  of  this  position  depends  on  a  calculation 


Ik?*  ■»<• 


—.••■■in*!* 


K>< 


tTi^ 


250 


OUTLINES   OF  ASTRONOMY. 


m 


,i( 


exactly  similar  to  what  has  been  explained  in  the  article  referred  to ;  and 
we  need,  therefore,  only  state  the  resulting  synodical  revolutions  of  the 
two  planets,  which  come  out  respectively  115-877*,  and  583-920''. 

(478.)  In  this  interval,  the  planet  will  have  described  a  whole  revolu- 
tion plus  the  arc  ace,  and  the  earth  only  the  arc  ACE  of  its  orbit. 
During  its  lapse,  the  inferior  conjunction  will  happen  when  the  earth  has 
a  certain  intermediate  situation,  B,  and  the  planet  has  reached  b,  a  point 
between  the  sun  and  earth.  The  greatest  elongation  on  the  opposite  side 
of  the  sun  will  happen  when  the  earth  has  come  to  C,  and  the  planet  to 
c,  where  the  line  of  junction  C  c  is  a  tangent  to  the  interior  circle  on  the 
opposite  side  from  M.  Lastly,  the  superior  conjunction  will  happen 
when  the  earth  arrives  at  D,  and  the  planet  at  d  in  the  same  line  pro- 
longed on  the  other  side  of  the  sun.  The  intervals  at  which  these  phe- 
nomena happen  may  easily  be  computed  from  a  knowledge  of  the  synodi- 
cal periods  and  the  radii  of  the  orbits. 

(474.)  The  circumferences  of  circles  are  in  the  proportion  of  their 
radii.  If,  then,  we  calculate  the  circumferences  of  the  orbits  of  Mercury 
and  Venus,  and  the  earth,  and  compare  them  with  the  times  in  which 
their  revolutions  are  performed,  we  shall  find  that  the  actual  velocities 
with  which  they  move  in  their  orbits  differ  greatly;  that  of  Mercury 
being  about  109360  miles  per  hour,  of  Venus  80000,  and  of  the  earth 
68040.  From  this  it  follows,  that  at  the  inferior  conjunction,  or  at  b, 
either  planet  is  moving  in  the  same  direction  as  the  earth,  but  with  a 
greater  velocity;  it  will,  therefore,  leave  the  earth  behind  it;  and  the 
apparent  motion  of  the  planet  viewed  from  the  earth,  will  be  as  if  the 
planet  stood  still,  and  the  earth  moved  in  a  contrary  direction  from  what 
it  really  does.  In  this  situation,  then,  the  apparent  motion  of  the  planet 
must  be  contrary  to  the  apparent  motion  of  the  sun;  and,  therefore, 
retrograde.  On  the  other  hand,  at  the  superior  conjunction,  the  real 
motion  of  the  planet  being  in  the  opposite  direction  to  that  of  the  earth, 
the  relative  motion  will  be  the  same  as  if  the  planet  stood  still,  and  the 
earth  ad'/anced  with  their  united  velocities  in  its  own  proper  direction. 
In  this  situation,  then,  the  apparent  motion  will  be  direct.  Both  these 
results  are  in  accordance  with  observed  fact. 

(475.)  The  stationary  points  may  be  determined  by  the  following  con- 
sideration. At  a  or  c,  the  points  of  greatest  elongation,  the  motion  of 
the  planet  is  directly  to  or  from  the  earth,  or  along  their  line  of  junction, 
while  that  of  the  earth  is  nearly  perpendicular  to  it.  Here,  then,  the 
apparent  motion  must  be  direct.  At  b,  the  inferior  conjunction,  we  have 
seen  that  it  must  be  retrograde,  owing  to  the  planet's  motion  (which  is 
there,  as  well  as  the  earth's,  perpendicular  to  the  line  of  junction)  sur- 


INFERIOR  PLANETS. 


251 


i to;  and 

ins  of  the 
0*. 

3le  revolu- 
:  its  orbit. 
5  earth  has 
i  b,  a  point 
)posite  side 
le  planet  to 
pcle  on  the 
rill  happen 
ne  line  pro- 
these  phe- 
the  synodi- 

ion  of  their 
of  Mercury 
les  in  which 
lal  velocities 
of  Mercury 
of  the  earth 
ion,  or  at  6, 

but  with  a 
it;  and  the 
be  as  if  the 
)n  from  what 
of  the  planet 
id,  therefore, 
ion,  the  real 
of  the  earth, 
still,  and  the 
per  direction. 

Both  these 

bllowing  con- 
le  motion  of 
e  of  junction, 
ere,  then,  the 
;tion,  we  have 
tion  (which  is 
junction)  sur- 


passing the  earth's.  Hence,  the  stationary  points  ought  to  lie,  as  it  is 
found  by  observation  they  do,  between  a  and  6,  or  c  and  6,  viz.  in  such  a 
position  that  the  obliquity  of  the  planet's  motion  with  respect  to  the  line 
of  junction  shall  just  compensate  for  the  excess  of  its  velocity,  and  cause 
an  equal  advance  of  each  extremity  of  that  line,  by  the  motion  of  the 
planet  at  one  end,  and  of  the  earth  at  the  other :  so  that,  for  an  instant 
of  time,  the  whole  line  shall  move  parallel  to  itself.  The  question  thus 
proposed  is  purely  geometrical,  and  its  solution  on  the  supposition  of 
circular  orbits  is  easy.     Let  E  e  and  P  p  represent  small  arcs  of  the 


orbits  of  the  earth  and  planet  described  contemporaneously,  at  the  moment 
when  the  latter  appears  stationary,  about  S,  the  sun.  Produce  />  V  and 
c  E,  tangents  at  P  and  E,  to  meet  at  E,  and  prolong  E  P  backwards  to 
Q,  join  ep.  Then  since  VE,pe  are  parallel,  we  have  by  similar  ti  i;m- 
gles  Pjp:Ec::PR:KE,  and  since,  putting  v  and  V  for  the  respec- 
tive velocities  of  the  planet  and  the  earth,  P  j^ :  E  c  : :  t;  :  V  j  therefore 

t; :  V  : :  P  R  :  R  E  : :  sin.  P  E  R  :  sin.  E  P  R 
: :  cos.  SEP:  cos.  S  P  Q 
: :  COS.  S  E  P  :  cos.  (S  E  P+E  S  P) 

because  the  angles  S  E  R  and  S  P  R  are  right  angles.  Moreover,  if  r 
and  R  be  the  radii  of  the  respective  orbits,  we  have  also 

r  :  R  : :  sin.  S  E  P  :  sin.  (S  E  P+E  S  P) 

from  which  two  relations  it  is  easy  to  deduce  the  values  of  the  two  angles 
SEP  and  ESP;  the  former  of  which  is  the  apparent  elongation  of  the 


»■ 


252 


OUTLINES  OF  ASTRONOMY. 


planet  from  the  sun,'  the  latter  the  difference  of  heliocentrio  loogitudes 
of  the  earth  and  planet. 

(476.)  When  we  regard  the  orbits  as  other  than  circles  (which  they 
really  are),  the  problem  becomes  somewhat  complex  —  too  much  so  to  be 
here  entered  upon.  It  will  suffice  to  state  the  results  which  experience 
verifies,  and  which  assigns  the  stationary  points  of  Mercury  at  from  15° 
to  20°  of  elongation  from  the  sun,  according  to  circumstances ;  and  of 
Venus,  at  an  elongation  never  varying  much  from  29°.  The  former  con- 
tinues to  retrograde  during  about  22  days ;  the  latter,  about  42. 

(477.)  We  have  said  that  some  of  the  planets  exhibit  phases  like  the 
moon.  This  is  the  case  with  both  Mercury  and  Venus ;  and  is  readily 
explained  by  a  consideration  of  their  orbits,  such  as  we  have  above  sup- 
posed them.  In  fact,  it  requires  little  more  than  mere  inspection  of  the 
figure  annexed,  to  show,  that  to  a  spectator  situated  on  the  earth  E,  an 


III 


inferior  planet,  illuminated  by  the  sun,  and  therefore  bright  on  the  side 
next  to  him,  and  dark  on  that  turned  from  him,  will  appear /u?^  at  the 
superior  conjunction  A;  gibbous  (i.  e.  more  than  half  full,  like  the  moon 
between  the  first  and  second  quarter)  between  that  point  and  the  points 
BC  of  its  greatest  elongation;  half-mooned  at  these  points;  and  crescent- 
shaped,  or  homed,  between  these  and  the  inferior  conjunction  D.  As  it 
approaches  this  point,  the  crescent  ought  to  thin  off  till  it  vanishes  alto- 
gether, rendering  the  planet  invisible,  unless  in  those  cases  where  it 
transits  the  sun's  disc,  and  appears  on  it  as  a  black  spot.  All  these  phe- 
nomena are  exactly  conformable  to  observation. 

(478.)  The  variation  in  brightness  of  Venus  in  different  parts  of  its 
apparent  orbit  is  very  remarkable.    This  arises  from  two  causes :  1st,  the 

R  V 

•If— =m  and— =«,  SEP=#,  ESP=i/',  the  equations  to  be  resolved  are  tin, 

14-fn  n 
{>p+ip)=m  sin.  ^,  and  co$.  (#+</')=«  eos, «/»,  which  give  co$.  V'—— r — . 

fllTfl 


TRANSITS  OF  VENUS  AND  MERCURY. 


258 


longitudes 

^hich  tboy 
sh  80  to  be 
experience 
from  15° 
38 ;  and  of 
former  con- 
2. 

ics  like  the 
d  is  readily 
above  sup- 
ction  of  tbo 
eartb  E,  an 


on  tbe  8ide 
IV  full  at  tbe 
Ike  tbe  moon 

id  tbe  points 
land  crescent- 
In  D.  As  it 
janisbcs  alto- 
Ises  wbere  it 

.11  tbcse  pbe- 

parts  of  its 
Isos :  1st,  tbe 

9lved  are  sin. 


varying  proportion  of  its  visible  illuminated  area  to  its  whole  disc ;  and, 
2dly,  tbe  vai-ying  angular  diameter,  or  whole  apparent  magnitude  of  the 
disc  itself.  As  it  approaches  its  inferior  conjunction  from  its  greater 
elongation,  the  half-moon  becomes  a  crescent,  which  thins  off;  bat  this  is 
more  than  compensated,  for  some  time,  by  tbe  increasing  apparent  magni- 
tude, in  consequence  of  its  diminishing  distance.  Thus  the  total  light 
r'^ceived  from  it  goes  on  increasing,  till  at  length  it  attains  a  maximum, 
which  takes  place  when  the  planet's  elongation  is  about  40°. 

(479.)  The  transits  of  Venus  are  of  very  rare  Occurrence,  taking  place 
alternately  at  the  very  unequal  but  regularly  recurring  intervals  of  8, 122, 
8, 105,  8,  122,  &c.,  years  in  succession,  and  always  in  June  or  December. 
As  astronomical  pbsenomena,  they  are  extremely  important ;  since  they 
afford  the  best  and  most  exact  means  we  possess  of  ascertaining  tbe  sun'c 
distance,  or  its  parallax.  Without  going  into  the  niceties  of  calculation 
of  this  problem,  which,  owing  to  the  great  multitude  of  circumstances  to 
be  attended  to,  are  extremely  intricate,  we  shall  here  explain  its  principle, 
which,  in  the  abstract,  is  very  simple  and  obvious.  Let  E  be  tbe  earth, 
V  Venus,  and  S  the  sun,  and  C  D  tbe  portion  of  Venus's  relative  orbit 
which  she  describes  while  in  the  act  of  transiting  the  sun's  disc.  Suppose 
A  B  two  spectators  at  opposite  extremities  of  that  diameter  of  the  earth 


'';j 


Fig.  67. 


which  is  perpendicular  to  the  ecliptic,  and,  to  avoid  complicating  tbe  case, 
let  us  lay  out  of  consideration  the  earth's  rotation,  and  suppose  A,  B,  to 
retain  that  situation  during  the  whole  time  of  the  transit.  Then,  at  any 
moment  when  tbe  spectator  at  A  sees  the  centre  of  Venus  projected  at  a 
on  tbe  sun's  disc,  he  at  B  will  see  it  projected  at  6.  If  then  one  or  other 
spectator  could  suddenly  transport  himself  from  A  to  B,  be  would  see 
Venus  suddenly  displaced  on  tbe  disc  from  a  to  6 ;  and  if  he  had  any 
means  of  noting  accurately  the  place  of  the  points  on  the  disc,  either  by 
micrometrical  measures  from  its  edge,  or  by  other  means,  he  might  ascer- 
tain the  angular  measure  of  a  6  as  seen  from  the  earth.  Now,  since 
A  V  a,  B  V  J,  are  straight  lines,  and  therefore  make  equal  angles  on  each 
side  V,  a  6  will  be  to  A  B  as  tbe  distance  of  Venus  from  the  sun  is  to  its 
distance  from  the  earth,  or  as  68  to  27,  or  nearly  as  2}  to  1 ;  a  2*  there- 


■>!«:;'£ 


'■«c» 


pa 


H 


254 


OUTLINES  OP  ASTRONOMY. 


foro  occupies  on  the  sun's  disc  a  space  2i  times  as  great  as  the  earth's 
diameter ;  and  its  angular  measure  is  therefore  equal  to  about  2^  times 
the  earth's  apparent  diameter  at  the  distance  of  the  sun,  or  (which  is  the 
same  thing)  to  five  times  the  sun's  horizontal  parallax  (art.  339).  Any 
error,  therefore,  which  may  be  committed  in  measuring  a  b,  will  entail 
only  one  fifth  of  that  error  on  the  horizontal  parallax  concluded  from  it. 

("480. )  The  thing  to  be  ascertained,  therefore,  is,  in  fact,  neither  more 
Lor  less  than  the  breadth  of  the  zone  P  Q  R  S,^  jrs,  included  between 
the  extreme  apparent  paths  of  the  centro  of  Venus  across  the  sun's  disc, 
from  its  entry  on  one  side  to  its  quitting  it  on  the  other.  The  whole 
business  of  the  observers  at  A,  B,  therefore,  resolves  itself  into  this ; — to 
ascertain,  with  all  possible  care  and  precision,  each  at  his  own  station,  this 
path, — where  it  enters,  where  it  quits,  and  what  segment  of  the  sun's  disc 
it  cuts  off.  Now,  one  of  the  most  exact  ways  in  which  (conjoined  with 
careful  micrometric  measures)  this  can  be  done,  is  by  noting  the  time  occu- 
pied in  the  whole  transit ;  for  the  relative  angular  motion  of  Venus  being, 
in  fact,  very  *)recisely  known  from  the  tables  of  her  motion,  and  the  appa* 
rent  pach  being  very  nea^-ly  a  straight  line,  these  times  give  us  a  measure 
(on  a  very  enlarged  scale)  of  the  lengths  of  the  chords  of  the  segments 
cut  off;  and  the  sun's  diameter  being  known  also  with  great  precision, 
their  versed  sines,  and  therefore  their  difference,  or  the  breadth  of  the 
zone  required,  becomes  known.  To  obtain  these  times  correctly,  each 
observer  must  ascertain  the  instants  of  ingress  and  egress  of  the  centre. 
To  do  this,  he  must  note,  1st,  the  instant  when  the  first  visible  impression 
or  notch  on  the  edge  of  the  disc  at  P  is  produced,  or  the  first  external 
contact;  2dly,  when  the  planet  is  just  wholly  immersed,  and  the  broken 
edge  of  the  dise  just  closes  again  at  Q,  or  the  first  internal  contact;  and, 
lastly,  he  must  make  the  same  observations  at  the  egress  at  K,  S.  The 
mean  of  the  internal  end  external  contacts,  corrected  for,  the  curvature  of 
the  sun's  limb  in  the  intervals  of  the  respective  points  of  contract,  internal 
and  external,  gives  the  entry  and  egress  of  the  planet's  centre. 

(481.)  The  modifications  introduced  into  this  process  by  the  earth's 
rotation  on  its  axis,  and  by  other  geographical  stations  of  the  observers 
thereon  than  here  supposed,  are  similar  in  their  principles  to  those  which 
enter  into  the  ialculation  of  a  solar  eclipse,  or  the  occultation  of  a  star  by 
the  moon,  only  more  refined.  Any  consideration  of  them,  however,  here, 
would  lead  us  too  far;  bat  in  the  view  we  have  taken  of  the  subject,  it 
affords  an  admirable  example  of  the  way  in  which  minutu  elements  in 
astronomy  may  become  magnified  in  their  effects,  and,  by  being  made  sub- 
ject to  measurement  on  a  greatly  enlarged  scale,  or  by  substituting  the 
measure  of  time  for  space,  may  be  ascertained  with  a  degree  of  precision 


adequ 

taking 

portan 

of  Vet 

by  the 

corner! 

brated 

ral  resi 

8"677f 

this  ph 

(482 

nearly  ( 

of  the 

and  whi 

measure 

Venus 

describe 

(483. 


IL^ 


SUPERIOR   PLANETS. 


255 


le  earth's 
2i  times 
lich  is  the 
9).    Any 
iviU  entul 
from  it. 
ither  more 
d  between 
sun's  disc, 
The  whole 
0  this ; — to 
)tation,  this 
e  sun's  disc 
joined  with 
B  time  occu- 
enus  being, 
id  the  appa- 
B  a  measure 
be  segments 
at  precision, 
jadth  of  the 
rrectly,  each 
the  centre. 
le  impression 
rst  external 
the  broken 
[ontact;  and, 
R,  S.    The 
Icurvature  of 
raot,  internal 


adequate  to  every  purpose,  by  only  watching  favourable  opportunities,  and 
taking  advantage  of  nicely  adjusted  combinations  of  circumstance.  So  im- 
portant has  this  observation  appeared  to  astronomers,  that  at  the  last  transit 
of  Venus,  in  1769,  expeditions  were  fitted  out,  on  the  most  extensive  scale, 
by  the  British,  French,  Russian,  and  other  governments,  to  the  remotest 
corners  of  the  globe,  for  the  express  purpose  of  performing  it.  The  cele- 
brated expedition  of  Captain  Cook  to  Otaheite  was  one  of  them.  The  gene- 
ral result  of  all  the  observations  made  on  this  most  memorable  occasion  gives 
8"5776  for  the  sun's  horizontal  parallax.  The  two  next  occurrences  of 
this  phaenomenon  will  happen  on  Dec.  8,  1874,  and  Dec.  6,  1882. 

(482.)  The  orbit  of  Mercury  is  V3ry  elliptical,  the  exccntricity  being 
nearly  one  fourth  of  the  mean  distance.  This  appears  from  the  inequality 
of  the  greatest  elongations  from  the  sun,  as  observed  at  different  times, 
and  which  vary  between  the  limits  16°  12'  and  28"  48',  and,  from  exact 
measures  of  such  elongations,  it  is  not  difficult  to  show  that  the  orbit  of 
Venus  also  is  slightly  excentric,  and  that  both  these  planets,  in  fact, 
describe  ellipses,  having  the  sun  in  their  common  focus. 

(483.)  Transits  of  Mercury  over  the  sun's  disc  occasionally  occur,  as 
in  the  case  of  Venus,  but  more  frequently;  those  at  the  ascendine  node 
in  November,  at  the  descending  in  May.  The  intervals  (considering 
each  node  separatvjiy)  are  usualltf  either  13  or  7  years,  and  in  the  order 
13,  13,  13,  7,  &c. ;  but  owing  to  the  considerable  inclination  of  the  oroit 
of  Mercury  to  the  ecliptic,  this  cannot  be  taken  as  an  exact  expression 
of  the  said  recurrence,  and  it  requires  a  period  of  at  least  217  years  to 
bring  round  the  transits  in  regular  order.  One  will  occur  in  the  present 
year  (1848,)  the  next  in  1861.  They  are  of  much  less  astronomical 
importance  than  that  of  Venns,  on  account  of  the  proximity  of  Mercury 
to  the  sun,  which  affords  a  much  less  favourable  combination  for  the 
determination  of  the  sun's  parallax. 

(484.)  Let  us  now  consider  the  superior  planets,  or  those  whose  orbits 
enclose  on  all  sides  that  of  the  earth.  That  they  do  so  is  proved  by 
several  cureumstances :  —  1st,  They  are  not,  like  the  inferior  planets,  con- 
fined to  certain  limits  of  elongation  from  the  sun,  but  appear  at  all  dis- 
tances from  it,  even  in  the  opposite  quarter  of  the  heavens,  or,  as  it  is 
called,  in  oj^odtion;  which  could  not  happen,  did  not  the  earth  at  such 
times  place  itself  between  them  and  the  sun :  2dly,  They  never  appear 
horned,  like  Venus  or  Mercury,  nor  even  semilunar.  Those,  on  the 
contrary,  which,  frojn  the  minuteness  of  their  parallax,  we  conclude  to  be 
tb<)  most  distant  from  us,  viz.  Jupiter,  Saturn,  Uranus,  and  Neptune, 
never  appear  otherwise  than  round ;  a  sufficient  proof,  of  itself,  that  we 
see  them  always  in  a  durection  not  very  remote  from  Uiat  in  which  the 


n 


»u^ 


^»«  few.* 


0""   , 


t 


>.#.  m 


256 


OUTLINES   OF  ASTRONOMY. 


i^ 


i  fPS; 


sun's  rays  illuminato  them ;  and  that,  therefore,  we  occupy  a  station  which 
is  never  very  widely  removed  from  the  centre  of  their  orbits,  or,  in  other 
words,  that  the  earth's  orbit  is  entirely  enclosed  within  theirs,  and  of 
companitivelj  small  diameter.  Only  one  of  them,  Mars,  exhibits  any 
peicfptiMe  jvAas;,  and  in  its  deficiency  from  a  circular  outline,  never 
sur|iassoH  &  moderately '/'''AoMs  appearance,  —  the  enlightened  portion  of 
the  uisc  he'r..^  nc  •.  jr  loss  tl.an  seven-eighths  of  the  whole.  To  understand 
this,  ve  need  only  ca.st  our  eyes  on  the  annexed  figure,  in  which  E  is  the 
earth,  tit  its  apparent  greatest  elongation  from  the  sun  S,  ««  seen  from 
In  this  position,  the  angle  S  M  E,  included  between  the  lines 


Mais,  M 


Fig.  69. 


E    . 


S  M  and  E  M,  is  at  its  maximum ;  and  therefore,  in  this  state  of  things, 
a  spectator  on  the  earth  is  enabled  to  see  a  greater  portion  of  the  dark 
hemisphere  of  Mars  than  in  any  other  situation.  The  extent  of  the 
phase,  then,  or  greatest  observable  degree  of  gibbosity,  affords  a  measure 
—  a  sure,  although  a  coarse  and  rude  one  —  of  the  angle  S  M  E,  and 
therefore  of  the  proportion  of  the  distance  S  M,  of  Mars,  to  S  E,  that  of 
the  earth  from  the  sun,  by  which  it  appears  that  the  diameter  of  the 
orbit  of  Mars  cannot  be  less  than  1^  times  that  of  the  earth's.  The 
phases  of  Jupiter,  Saturn,  Uranus,  and  Neptune,  being  imperceptible,  it 
follows  that  their  orbits  must  include  not  only  that  of  the  earth,  but  of 
Mars  also. 

(485.)  All  the  superior  planets  are  retrograde  in  their  apparent 
motions  when  in  opposition^  and  for  some  time  before  and  after  j  but  they 
differ  greatly  from  each  other,  both  in  the  extent  of  their  arc  of  retrogra- 
dation,  in  the  duration  of  their  retrograde  movement,  and  in  its  rapidity 
when  swiftest.    It  is  more  extensive  and  rapid  in  the  case  of  Mars  tlian 


SUPERIOR  PLANETS. 


257 


ion  which 
r,  in  other 
8,  and  of 
dibits  any 
ine,  never 
portion  of 
understand 
ih  E  is  the 
seen  from 
n  the  lines 


«  of  things, 
of  the  dark 
iteni  of  the 
jg  a  measure 
S  M  E,  and 
S  E,  that  of 
meter  of  the 
arth's.     The 
)erceptible,  it 
earth,  but  of 

icir  apparent 
"ter;  but  they 
of  retrogra- 
in  its  rapidity 
jf  Mars  than 


of  Jupiter,  of  Tupiter  than  of  Saturn,  of  that  planet  than  of  Uranus, 
and  of  Uranus  again  than  Neptune.  The  angular  velocity  with  which  a 
planet  appears  to  retrograde  is  easily  vscertaincd  by  '>V^serving  its  apparent 
place  in  the  heavens  from  day  to  day ;  and  from  such  c^bservations,  made 
about  the  time  of  opposition,  it  is  easy  to  conclude  the  relative  magni- 
tudes of  their  orbits,  as  compared  with  the  earth's,  supposing  their 
periodical  times  known.  For,  from  these,  their  mean  angular  velocities 
are  known  also,  being  inversely  as  the  times.     Suppose,  then,  £  e  to  be  a 

Fig.  70. 


very  small  portion  of  the  earth's  orbit,  and  M  m  a  corresponding  portion 
of  that  of  a  superior  planet,  described  on  the  day  of  Opposition,-  about 
the  sun  S,  on  which  day  the  three  bodies  He  in  one  straight  line  S  E  M  X. 
Then  the  angles  E  S  e  and  M  S  m  are  given.  Now,  if  e  m  be  joined  and 
prolonged  to  meet  S  M  continued  in  X,  the  angle  e  X  E,  which  is  equal 
to  the  alternate  angle  X  e  Y,  is  evidently  the  retrogradation  of  Mars  on 
that  day,  and  is,  therefore,  also  given.  E  e,  therefore,  and  the  angle 
E  X  <?,  being  given  in  the  right-angled  triangle  E  e  X,  the  side  E  X  is 
easily  calculated,  and  thus  S  X  becomes  known.  Consequently,  in  the 
triangle  S  m  X,  we  have  given  the  side  S  X  and  the  two  angles  m  S  X, 
and  m  X  S,  whence  the  other  sides,  S  wi,  m  X,  are  easily  determined. 
Now,  S  m  is  no  other  than  the  radius  of  the  orbit  of  the  superior  planet 
required,  which  in  this  calculation  is  supposed  circular,  as  well  as  that  of 
the  earth ;  a  supposition  not  exact,  but  sufficiently  so  to  afford  a  satisfac- 
tory approximation  to  the  dimensions  of  its  orbit,  and  which,  if  the 
process  be  often  repeated,  in  every  variety  of  situation  at  which  the 
opposition  can  occur,  will  ultimately  afford  an  average  or  mean  value  of 
its  diameter  fully  to  be  depended  upon. 

(486.)  To  apply  this  principle,  however,  to  practice,  it  is  necessary  to 
know  the  periodic  times  of  the  several  planets.  These  may  be  obtained 
directly,  as  has  been  already  stated,  by  observing  the  intervals  of  their 
passages  through  the  ecliptic ;  but,  owing  to  the  very  small  inclination  of 
the  orbits  of  some  of  them  to  its  plane,  they  cross  it  so  obliquely  that 
the  precise  moment  of  their  arrival  on  it  is  not  ascertainable,  unless  by 
very  nice  observations.  A  better  method  consists  in  determining,  from 
the  observations  of  several  successive  days,  the  exact  moments  of  their 
arriving  in  opposition  with  the  sun,  the  criterion  of  which  is  a  difference 
of  longitudes  between  the  sun  and  planet  of  exactly  180°.  "The  interval 
17 


€ 


J.HOm 


kwMumw 
toiiwur 


258 


OUTLINES   OF  ASTRONOMY. 


between  suycessive  oppositions  thus  obtained  is  nearly  one  nynodical  pe- 
riod ;  and  would  be  exactly  so,  were  the  planet's  orbit  and  that  of  the 
earth  both  circles,  and  uniformly  described ;  but  as  that  is  found  not  to 
bo  the  case  (and  the  criterion  is,  the  inequalitj/  of  successive  synodical 
revolutions  so  observed),  the  average  of  a  great  number,  taken  in  all  va- 
rieties of  situation  in  which  the  oppositiond  occur,  will  bo  freed  from  the 
elliptic  inequality,  and  may  bo  taken  as  a  mean  s^/nodical  period.  From 
this,  by  the  considerations  and  by  the  process  of  calculation,  indicated 
(art.  418)  the  sidereal  periods  are  readily  obtained.  The  accuracy  of  this 
determination  will,  of  course,  be  greatly  increased  by  embracing  a  long 
interval  between  the  extreme  observations  employed.  In  point  of  fact, 
that  interval  extends  to  nearly  2000  years  in  the  cases  of  the  planets 
known  to  the  ancients,  who  have  recorded  their  observations  of  them  in 
a  manner  suflBciently  careful  to  be  made  use  of.  Their  periods  may,  there- 
fore, be  regarded  as  ascertained  with  the  utmost  exactness.  Their  nume- 
rical values  will  be  found  stated,  as  well  as  the  mean  distances,  and  all 
the  other  elements  of  the  planetary  orbits,  in  the  synoptic  table  at  the 
end  of  the  volume,  to  which  (to  avoid  repetition)  the  reader  is  once  for 
all  referred. 

(487.)  In  casting  our  eyes  down  the  list  »f  the  planetary  distances,  and 
comparing  them  with  the  periodic  times,  we  cannot  but  be  struck  with  a 
certain  correspondence.  The  greater  the  distance,  or  the  larger  the  orbit, 
evidently  the  longer  the  period.  The  order  of  the  planets,  beginning 
from  the  sun,  is  th;;  same,  whether  we  arrange  them  according  to  their 
distances,  or  to  the  time  they  occupy  in  completing  their  revolutions ;  and 
is  as  follows :  —  Mercury,  Venus,  Earth,  Mars, —  the  ultra-zodiacal  pla- 
nets, or,  as  they  are  sometimes  also  called.  Asteroids, — Jupiter,  Saturn,  Ura- 
nus, and  Neptune.  Nevertheless,  when  we  come  to  examine  the  numbers 
expressing  them,  we  find  that  the  relation  between  the  two  series  is  not 
that  of  simple  proportional  increase.  The  periods  increase  more  than  in 
proportion  to  the  distances.  Thus,  the  period  of  Mercury  is  about  88  days, 
and  that  of  the  earth  365  —  being  in  proportion  as  1  to  4*15,  while  their 
distances  are  in  the  less  proportion  of  1  to  2-56;  and  a  similar  remark 
holds  good  in  every  instance.  Still,  the  ratio  of  increase  of  the  times  is 
not  so  rapid  as  that  of  the  squares  of  the  distances.  The  square  of  2*56 
is  ^'5536,  which  is  considerably  greater  than  4*15.  An  intermediate 
rate  of  increase,  between  the  simple  proportion  of  the  distances  and  that 
of  their  squares  is  therefore  clearly  pointed  out  by  the  sequence  of  the 
numbers ;  but  it  required  no  ordinary  penetration  in  the  illustrious  Kep- 
ler, backed  by  uncommon  perseverance  and  industry,  at  a  period  when 
the  data  themselves  were  involved  in  obscurity,  and  when  the  pro> 


KEPLER  S  THIRD   LAW. 


259 


cesses  of  trigonometry  and  of  numerical  calculation  wero  encumbered 
with  difficulties,  of  which  the  more  recent  invention  of  logarithmic  tables 
has  happily  left  us  no  conception,  to  perceive  and  demonstrate  the  real 
law  of  their  connection.  This  connection  is  expressed  in  the  following 
proposition  :  — "  The  squares  of  the  periodic  times  of  any  two  planets  are 
to  each  other,  in  the  same  proportion  as  the  cubes  of  their  mean  distances 
from  tho  sun."  Take,  for  example,  the  Earth  and  Mars,'  whose  periods 
are  in  the  proportion  of  3052564  to  6860796,  and  whose  distance  from 
the  sun  is  that  of  100000  to  152369 ;  and  it  will  be  found,  by  any  one 
who  will  take  the  trouble  to  go  through  the  calculation,  that  — 

(8652564)' :  (6869796)' : :  (100000)" :  (152360)". 

(488.)  Of  all  the  laws  to  which  induction  from  pure  observation  has 
ever  conducted  man,  this  third  Imo  (as  it  is  called)  of  Kepler  may  justly 
be  regarded  as  the  most  remarkable,  and  the  most  pregnant  with 
important  consequences.  When  we  contemplate  the  constituents'  of  the 
planetary  system  from  tho  point  of  view  which  this  relation  affords  us,  it 
is  no  longer  mere  analogy  which  strikes  us  —  no  longer  a  general  resem- 
blance among  them,  as  individuals  independent  of  each  other,  and  circula- 
ting about  the  sun,  each  according  to  its  own  peculiar  nature,  and  con- 
nected with  it  by  its  own  peculiar  tie.  The  resemblance  is  now  perceived 
to  be  a  true  family  likeness  j  they  are  bound  up  in  one  chain  —  in  "^r- 
woven  in  one  web  of  mutual  relation  and  harmonious  agreement  —  ob- 
jected to  one  pervading  influence^  which  extends  from  the  centre  to  the 
farthest  limits  of  that  great  system,  of  which  all  of  them,  the  earth 
included,  must  henceforth  be  regarded  as  members. 

(489.)  The  laws  of  elliptic  motion  about  the  sun  as  a  focus,  and  of  the 
equable  description  of  areas  by  lines  joining  the  sun  and  planets,  were 
originally  established  by  Kepler,  from  a  consideration  of  the  observed 
motions  of  Mars ;  and  were  by  him  extended,  analogically,  to  all  the  other 
planets.  However  precarious  such  an  extension  might  then  have  ap- 
peared, modern  astronomy  has  completely  verified  it  as  a  matter  of  fact, 
by  the  general  coincidence  of  its  results  with  entire  series  of  observations 
of  the  apparent  places  of  the  planets.  These  arc  found  to  accord  satis- 
factorily with  the  assumption  of  a  particular  ellipse  for  each  planet,  whose 
magnitude,  degree  of  cxccntricity,  and  situation  in  space,  are  numerically 
assigned  in  the  synoptic  table  before  referred  to.  It  is  true,  that  when 
observations  are  carried  to  a  high  degree  of  precision,  and  when  each 
planet  is  traced  through  many  successive  revolutions,  and  its  history  car- 

'  The  expression  of  this  law  of  Kcplcr  requires  a  slight  modification  when  we  come 
to  the  extreme  nicety  of  numerical  calculation,  ior  the  greater  planets,  due  to  the 
influence  of  their  masses.    This  correction  is  imperceptible  for  the  Earth  and  Mars. 


'Wiat«Hi 


€J% 


r.ni»  ■.•.v<l 


260 


OUTLINES  OP  ASTRONOMY. 


a  ■ 


ried  back,  by  the  aid  of  calculations  founJud  on  those  data,  for  many  cen- 
turies, wo  learn  to  regard  tlio  laws  of  Kepler  as  on\y  Ji ml  approxunatmn 
to  the  much  more  complicated  ones  which  actually  prevail ;  and  that  to 
bring  remote  observations  into  rigorous  and  niatlieuiatical  accordance 
with  each  other,  and  at  the  same  time  to  retain  the  extremely  convenient 
nomenclature  and  relations  of  the  elliptic  system,  it  becomes  necessary 
to  modify,  to  a  certain  extent,  our  verbal  expression  of  the  laws,  and  to 
regard  the  numerical  data  or  elliptic  elements  of  the  planetary  orbits  as 
not  absolutely  permanent,  but  subject  to  a  series  of  extremely  slow  and 
almost  imperceptible  changes.  These  changes  may  be  neglected  when  we 
consider  only  a  few  revolutions;  but  going  on  from  century  to  century, 
and  continually  accumulating,  they  at  length  produce  material  departures 
in  the  orbits  from  their  original  state.  Their  explanation  will  form  tlm 
subject  of  a  subsequent  chapter ;  but  for  the  present  we  must  lay  them 
out  of  consideration,  as  of  an  order  too  minute  to  affect  the  general  con- 
elusions  with  which  we  are  now  concerned.  By  what  means  astronomers 
are  enabled  to  compare  the  results  of  the  elliptic  theory  with  observatidn, 
and  thus  satisfy  themselves  of  its  accordance  with  nature,  will  be  ex- 
•plained  presently. 

(490.)  It  will  first,  however,  bo  proper  to  point  out  what  particular 
theoretical  conclusion  is  involved  in  each  of  the  three  laws  of  Kepler, 
considered  as  satisfactorily  established, — what  indication  each  of  them, 
separately,  affords  of  the  mechanical  forces  prevalent  in  our  system,  and 
the  mode  in  which  its  parts  are  connected, — and  how,  when  thus  con- 
sidered, they  constitute  the  basis  on  which  the  Newtonian  explanation  of 
the  mechanism  of  the  heavens  is  mainly  supported.  To  begin  with  the 
first  law,  that  of  the  equable  description  of  areas. — Since  the  planets  move 
in  curvilinear  paths,  they  must  (if  they  be  bodies  obeying  the  laws  of 
dynamics)  be  deflected  from  their  otherwise  natural  rectilinear  progress 
hy  force.  And  from  this  law,  taken  as  a  matter  of  observed  fact,  it  fol- 
lows, that  the  direction  of  such  force,  at  every  point  of  the  orbit  of  each 
planet,  always  passes  though  the  sun.  No  matter  from  what  ultimate 
cause  the  power  which  is  called  gravitation  originates, — be  it  a  virtue 
lodged  in  the  sun  as  its  receptacle,  or  be  it  pressure  from  without,  or  the 
resultant  of  many  pressures  or  solicitations  of  unknown  fluids,  magnetic 
or  electric  ethers,  or  impulses, — still,  when  finally  brought  under  our  con- 
templation, and  summed  up  into  a  single  resultant  energy — its  direction 
js,  from  every  point  on  all  sides,  toioards  the  sun's  centre.  As  an  abstract 
dynamical  proposition,  the  reader  will  find  it  demonstrated  by  Newton,  in 
the  first  proposition  of  the  Principin,  with  an  elementary  simplicity  to 
which  we  really  could  add  nothing  but  obscurity  by  amplification,  that 


INTERPRETATION   OF   KEPLER's   LAWS. 


261 


any  body,  urged  towuni.s  n  certain  ccntml  point  by  a  force  contioually 
Jircctetl  thereto,  und  tlieroby  deflected  into  a  curvilinear  patb,  will  describe 
about  that  centre  equal  areas  in  equal  times;  and  vice  versd,  that  such 
e([Uublo  description  of  areas  is  itself  the  essential  criterion  of  a  continual 
ilirection  of  the  acting  force  towards  the  centre  to  which  this  character 
bclitngs.  The  tirst  law  of  Kepler,  then,  gives  us  no  information  as  to  the 
iiiture  or  intensity  of  the  force  urging  the  planets  to  the  sun ;  the  only 
conclusion  it  involves  is,  that  it  does  so  urge  them.  It  is  a  property  of 
orbitual  rotation  under  the  influence  of  central  forces  generalfi/,  and,  as 
iuch,  we  daily  see  it  oxeniplifljd  in  a  thousand  familiar  instances.  A 
simple  experimental  illustration  of  it  is  to  tie  a  bullet  to  a  thin  string, 
ami,  having  whirled  it  round  with  a  moderate  velocity  in  a  vertical  plane, 
to  draw  the  end  of  the  string  through  a  small  ring,  or  allow  it  to  coil 
itself  round  the  linger,  or  round  a  cylindrical  rod  held  very  flrmly  in  a 
horizontal  position.  The  bullet  will  then  approach  the  centre  of  piotion 
in  a  spiral  line ;  and  the  incrense  not  only  of  its  angular  but  of  its  linear 
velocity,  and  the  rapid  dinjinution  of  its  penodio  time  when  near  the 
centre,  will  express,  more  clearly  than  any  words,  the  compensation  by 
which  its  uniform  description  of  areas  is  maintained  under  a  constantly 
diminishing  distance.  If  the  motion  be  reversed,  and  the  thread  allowed 
to  uncoil,  beginning  with  a  rapid  impulse,  the  velocity  will  diminish  by 
the  same  degrees  as  it  before  increased.  The  increasing  rapidity  of  a 
imccr' a  j>iruuc((c,  as  he  draws  in  his  limbs  and  straightens  bis  whole  per- 
son, so  as  to  bring  every  part  of  his  frame  as  near  as  possible  to  the  axis 
of  his  motion,  is  another  instance  where  the  connection  of  the  observed 
effect  with  the  central  force  exerted,  though  equally  real,  is  mucb  less 
obvious. 

(491.)  The  second  law  of  Kepler,  or  that  which  asserts  that  the  planets 
describe  ellipses  about  the  sun  as  their  focus,  involves,  as  a  consequence, 
the  laio  of  solar  gravitation  (so  be  it  allowed  to  call  the  force,  whatever  it 
be,  which  urges  them  towards  the  sun)  as  exerted  on  each  individual 
planet,  apart  froip  all  connection  with  the  rest.  A  straight  line,  dynamic- 
ally speakiiiff,  is  tue  only  path  which  can  be  pursued  by  a  body  ahsolutdy 
/fi'c,  and  Jindi.r  the  action  of  no  external  force.  All  drjiection  into  a 
curve  is  evidence  of  the  exertion  of  a  force  ;  and  the  greater  the  deflection 
in  equal  times,  the  more  intense  the  force.  Deflection  from  a  straight 
line  is  only  another  word  for  curvature  of  path ;  and  as  a  circle  is  char- 
acterized by  the  uniformity  of  its  curvatures  in  all  its  parts — so  is  every 
other  curve  (as  an  ellipse)  characterized  by  the  particular  Into  which  regu- 
lates the  increase  and  diminution  of  its  curvature  as  we  advance  along  its 
circumference.    The  deflecting  force,  then,  which  coutiDually  bends  a 


'A   ■n.r 


V'.. .  -MrtJ  » 

*  uriiimit* 


262 


OUTLINES  OF  ASTRONOMY. 


i:  t 


movin*^  oouy  into  a  curve,  may  be  ascertained,  provided  its  direction,  in 
the  first  place,  and,  secondly,  the  law  of  curvature  of  the  curvo  itself,  bo 
known.  Both  tbeao  enter  as  elements  into  the  expression  of  tbo  force. 
A  body  may  describe,  for  instance,  an  ellipse,  under  u  great  variety  of 
dispositions  of  the  acting  forces :  it  may  glide  along  it,  for  example,  as  a 
bead  upon  a  polished  wire,  bent  into  an  elliptic  form ;  in  which  case  the 
acting  force  is  always  perpendicular  to  the  wire,  and  the  velocity  is  uni- 
form. In  this  case  the  force  is  directed  to  no  fixed  centre,  and  there  is 
no  equable  description  of  areas  at  all.  Or  it  may  describe  it  as  we  may 
see  done,  if  we  suspend  a  ball  by  a  very  long  string,  and,  drawing  it  a 
little  aside  from  the  perpendicular,  throw  it  round  with  a  gentle  impulse. 
In  this  case  the  acting  force  is  directed  to  the  centre  of  the  ellipse,  about 
which  areas  are  described  equally,  and  to  which  a  force  proportional  to 
the  distance  (the  decomposed  result  of  terrestrial  gravity)  perpetually 
urges  it.*  This  is  ut  once  a  very  easy  experiment,  and  a  very  instructive 
one,  and  we  shall  again  refer  to  it.  In  the  case  before  us,  of  an  ellipse 
described  by  the  action  of  a  force  directed  to  the  fociix,  the  steps  of  the 
investigation  of  the  law  of  force  are  these :  1st,  The  law  of  tho  areas  de- 
termines the  actual  velocity  of  tho  revolving  body  at  every  point,  or  the 
space  really  run  over  by  it  in  a  given  minute  portion  of  time  j  2dly,  The 
law  of  curvature  of  the  ellipse  determines  the  linear  amount  of  deflection 
from  tiie  tangent  in  the  direction  of  the  focus,  which  corresponds  to  that 
space  so  run  over ;  3dly,  and  lastly,  Tho  laws  of  accelerated  motion  de- 
clare that  the  intensity  of  tho  acting  force  causing  such  deflection  in  its 
own  direction,  is  mea.sured  by  or  proportional  to  tho  amount  of  that  de- 
flection, and  may  therefore  be  calculated  in  any  particular  position,  or 
generally  expressed  by  geometrical  or  algebraic  symbols,  as  a  law  inde- 
pendent of  particular  positions,  when  that  deflection  is  so  calculated  or 
expressed.  We  have  here  the  spirit  of  the  process  by  which  Newton  has 
resolved  this  interesting  problem.  For  its  geometrical  detail,  we  must 
refer  to  tho  3d  section  of  his  Principia.  We  know  of  no  artificial  mode 
of  imitating  this  species  of  elliptic  motion ;  though  a  rude  approximation 
to  it — enough,  however,  to  give  a  conception  of  tho  alternate  approach 
and  recess  of  the  revolving  body  to  and  from  the  focus,  and  the  variation 
of  its  velocity — may  be  had  by  suspending  a  small  steel  bead  to  a  fine  and 
very  long  silk  fibre,  and  setting  it  to  revolve  in  a  small  orbit  round  the 
pole  of  a  powerful  cylindrical  magnet,  held  upright,  and  vertically  under 
the  point  of  suspension. 

*  If  the  suspended  body  be  a  vessel  full  of  fine  sand,  having  a  small  hole  at  its  bottom, 
the  elliptic  trace  of  its  orbit  will  be  left  in  n  sand  streak  on  a  table  placed  below  it. 
This  neat  illustration  is  due,  to  the  best  of  my  knowledge,  to  Mr.  Babbage. 


INTERPRETATION   OF   KEPLER'S  LAWS. 


268 


(402.)  The  third  law  of  Keplor,  which  conuccts  the  distances  and 
periods  of  the  planets  by  a  general  rule,  bears  with  it,  us  its  theoretical 
interpretation,  this  important  consequence,  viz.  that  it  is  one  and  the  same 
force,  modified  only  by  distance  from  the  sun,  which  retains  all  the  planets 
in  their  orbits  about  it.  That  the  attraction  of  the  sun  (if  such  it  be) 
i?  exerted  upon  all  the  bodies  of  our  system  indifferently,  without  regard 
to  the  peculiar  materials  of  which  they  may  consist,  in  the  exact  pro* 
portion  of  their  inertieo,  or  quantities  of  mutter ;  that  it  is  not,  therefore, 
of  the  nuturo  of  the  elective  uitructions  of  chemistry  or  of  nmgnotio 
action,  which  is  powerless  on  other  mbstanccs  than  iron  and  some  one  or 
two  more,  but  is  of  a  more  universal  character,  and  extends  equally  to  all 
the  material  constituents  of  our  sytitcm,  and  (us  we  shall  hereafter  see 
abundant  reason  to  admit)  to  those  of  other  systems  than  our  own.  This 
law,  important  and  general  us  it  is,  results,  us  the  simplest  of  corollaries, 
from  the  relutions  established  by  Newton  in  the  section  of  the  Priiirt'itki 
ret'urred  to  (Prop,  xv.),  from  which  propo»itiun  it  results,  that  if  the  earth 
were  taken  from  its  actual  orbit,  and  launched  anew  in  space  at  the  place, 
in  the  direction,  and  with  the  velocity  of  any  of  the  other  plunets,  it 
would  describe  the  very  same  orbit,  and  in  the  same  period,  which  that 
planet  actually  does,  a  minute  correction  of  the  period  only  excepted, 
arising  from  the  difference  between  the  mass  of  the  earth  and  that  of  the 
planet.  Small  as  the  planets  are  compared  to  the  sun,  some  of  them  are 
not,  us  the  earth  is,  mere  atoms  in  the  comparison.  The  strict  wording 
of  Kepler's  law,  as  Newton  has  proved  in  his  fifty-ninth  proposition,  is 
applicable  only  to  the  case  of  planets  whose  proportion  to  the  central 
body  is  absolutely  inappreciable.  When  this  is  not  the  case,  the  periodic 
time  is  shortened  in  the  proportion  of  the  square  root  of  the  number  ex- 
pressing the  sun's  mass  or  inertias,  to  that  of  the  sum  of  the  numbers 
expressing  the  masses  of  the  sun  and  planet ;  and  in  general,  whatever 
be  the  masses  of  two  bodies  revolving  round  each  other  under  the  influ- 
ence of  the  Newtonian  law  of  gravity,  the  square  of  their  periodic  time 
will  be  expressed  by  a  fraction  ^hose  numerator  is  the  cube  of  their  mean 
distance,  i.  e.  the  greater  semi-axis  of  their  elliptic  orbit,  and  whose  de- 
nominator is  the  sum  of  their  masses.  When  one  of  the  masses  is  in- 
comparably greater  than  the  other,  this  resolves  into  Kepler's  law ;  but 
when  this  is  not  the  case,  the  proposition  thus  generalized  stands  in  lieu 
of  that  law.  In  the  system  of  the  sun  and  planets,  however,  the  numerical 
correction  thus  introduced  into  the  results  of  Kepler's  law  is  too  small  to 
be  of  any  importance,  the  mass  of  the  largest  of  the  planets  (Jupiter) 
being  much  less  than  a  thousandth  part  of  that  of  the  sun.     We  shall 


CZ 


•»''.'ffi 


..»• 


irrs 


8— 


i 


264 


OUTLINES   OP  ASTEONOMT. 


presently,  however,  perceive  all  the  importance  of  this  generalization, 
when  we  come  to  speak  of  the  satellites. 

(493.)  It  will  first,  however,  be  proper  to  explain  by  what  process  of 
calculation  the  expression  of  a  planet's  elliptic  orbit  by  its  elements  can  be 
compared  with  observation,  and  how  we  can  satisfy  ourselves  tbat  the 
numerical  data  contained  in  a  table  of  such  elements  for  the  whole  system 
does  really  exhibit  a  true  picture  of  it,  and  afford  the  means  of  deter- 
mining its  state  at  every  instant  of  time,  by  the  mere  application  of  Kep- 
ler's laws.  Now,  for  eai  h  planet,  it  is  necessary  for  this  purpose  to  know, 
1st,  the  magnitude  and  form  of  its  ellipse;  2dly,  the  situation  of  this 
ellipse  in  space,  with  respect  to  the  ecliptic,  and  to  a  fixed  line  drawn 
therein ;  3dly,  the  local  situation  of  the  planet  in  its  ellipse  at  some  known 
epoch,  and  its  periodic  time  or  mean  angular  velocity,  or,  as  it  is  called, 
its  mean  motion. 

(494.)  The  magnitude  and  form  of  an  ellipse  are  determined  by  its 
greatest  length  and  least  breadth,  or  its  two  principal  axes;  but  for  astro- 
nomical uses  it  is  preferable  to  use  the  semi-axis  major  (or  half  the  greatest 
length),  and  the  excentricity  or  distance  of  the  focus  from  the  centre, 
which  last  is  usually  estimated  in  parts  of  the  former.  Thus,  an  ellipse, 
whose  length  is  10  and  breadth  8  parts  of  any  scale,  has  for  its  major 
semi-axis  5,  and  for  its  excentricity  3  such  parts ;  but  when  estimated  in 
parts  of  the  semi-axis,  regarded  as  a  unit,  the  excentricity  is  expressed  by 
the  fraction  |. 

(495.)  The  ecliptic  is  the  plane  to  which  an  inhabitant  of  the  earth 
most  naturally  refers  the  rest  of  the  solar  system,  as  a  soit  of  ground- 
plane  ;  and  the  axis  of  its  orbit  might  be  taken  for  a  line  of  departure  in 
that  plane  or  origin  of  angular  reckoning.  Were  the  axis  fixed,  this 
would  be  the  best  possible  origin  of  longitudes ;  but  as  it  has  a  motion 
(though  an  excessively  slow  one),  there  is,  in  fact,  no  advantage  in  reck- 
oning from  the  axis  more  than  from  the  line  of  the  equinoxes,  and  astro- 
nomers therefore  prefer  the  latter,  taking  account  of  its  variation  by 
the  effect  of  precession,  and  restoring  it,  by  calculation  at  every  in- 
stant, to  a  fixed  position.  Now,  to  determine  the  situation  of  the  ellipse 
described  by  a  planet  with  respect  to  this  plane,  three  elementa  require 
to  be  known:  —  Ist,  the  inclination  of  the  plane  of  the  planet's  orbit 
to  the  plane  of  the  ecliptic;  2dly,  the  line  in  which  these  two  planes 
intersect  each  other,  which  of  necessity  passes  through  the  sun,  and 
whose  position  with  respect  to  the  line  of  the  equinoxes  is  therefore 
given  by  stating  its  longitude.  This  line  is  called  the  line  of  the 
nodes.  When  the  planet  is  in  this  line,  in  the  act  of  passing  from  the 
south  to  the  north  side  of  the  ecliptic,  it  is  in  its  ascending  node,  and 


ELEMENTS   OF  A   PLANET  S   OllBIT. 


265 


its  longitude  at  that  moment  is  the  element  called  the  longitude  of  the 
node.  These  two  data  determine  the  situation  of  the  plane  of  tht  orbit; 
and  there  only  remains,  for  the  complete  determination  of  the  situation 
of  the  planet's  ellipse,  to  know  how  it  ia  placed  in  that  plane,  which 
(since  its  focus  is  necessarily  in  the  sun)  is  ascertained  by  stating  the 
lo)>(/iftide  of  its  perihelion,  or  the  place  which  the  extremity  of  the  axis 
nearest  the  sun  occupies,  when  orthographically  projected  on  the  ecliptic. 

(490.)  The  dimensions  and  situation  of  the  planet's  orbit  thus  deter- 
mined, it  only  remains,  for  a  complete  acquaintance  with  its  history,  to 
determine  the  circumstances  of  its  motion  in  the  orbit  so  precisely  fixed. 
Now,  for  this  purpose,  all  that  is  needed  is  to  know  the  moment  of  time 
when  it  is  either  at  the  perihelion,  or  at  any  other  precisely  determined 
point  of  its  orbit,  and  its  whole  period ;  for  these  being  known,  the  law 
of  the  areas  determines  the  place  at  every  other  instant.  This  moment  is 
called  (when  the  perihelion  is  the  point  chosen)  the  perihelion  pdssaye, 
or,  when  some  point  of  the  orbit  is  fixed  upon,  without  special  reference 
to  the  perihelion,  the  epoch. 

(497.)  Thus,  then,  we  have  seven  particulars  or  elements,  which  must 
be  numerically  stated,  before  we  can  reduce  to  calculation  the  state  of  the 
system  at  any  given  moment.  But,  these  known,  it  is  easy  to  ascertain 
the  apparent  positions  of  each  planet,  as  it  would  be  seen  from  the  sun,  or 
is  seen  from  the  earth  at  any  time.  The  former  is  called  the  heliocentric, 
the  latter  the  geocentric,  place  of  the  planet, 

(498.)  To  commence  with  the  heliocentric  places.  Let  S  represent 
the  sun ;  P  A  N  the  orbit  of  the  planet,  being  an  ellipse,  having  the  S  in 
its  focus,  and  A  for  its  perihelion ;  and  letp  a  N  T  represent  the  projection 
of  the  orbit  on  the  plane  of  the  ecliptic,  intersecting  the  line  of  ec^uinoxea 

Fig.  71. 


Sr  in  r,  which,  therefore,  is  the  origin  of  longitudes.  Then  will  S  N  be 
the  line  of  nodes;  and  if  we  suppose  13  to  lie  on  the  south,  and  A  on  tho 
north  side  of  the  ecliptic,  and  the  direction  of  the  planet's  motion  to  be 
from  B  to  A,  N  will  be  the  ascending  node,  and  the  angle  T  S  N  the  Ion- 
(jltude  of  the  node.  In  like  manner,  if  P  be  the  place  of  the  planet  at 
any  time,  and  if  it  and  the  perihelion  A  be  projected  on  the  ecliptic,  upon 
the  points  jp,  a,  the  angles  T  Qp,  r  S  a,  will  be  the  respective  heliocentrio 


ITS*" 


►■••^   'All 


•I 


-,=SP«- 


266 


OUTLINES   OF  ASTRONOMY. 


longitudes  of  the  planet  and  of  the  perihelion,  the  former  of  which  is  to 
be  determined,  and  the  latter  is  one  of  the  given  elements.  Lastly,  the 
angle  j?  S  P  is  the  heliocentric  latitude  of  the  planet,  which  is  also  required 
to  be  known. 

(499.)  Now,  the  time  being  given,  and  also  the  moment  of  the  planet's 
passing  th.;  perihelion,  the  interval,  or  the  time  of  describing  the  portion 
A  P  of  the  orbit,  is  given,  and  the  periodical  time,  and  the  whole  area  of 
the  ellipse  being  known,  the  law  of  proportionality  of  areas  to  the  times 
of  their  description  gives  the  magnitude  of  the  area  ASP.  From  this 
it  is  a  problem  of  pure  geometry  to  determine  the  corresponding  anyh 
ASP,  which  is  called  the  planet's  true  anomaly.  This  problem  is  of 
the  kind  called  transcendental,  and  has  been  resolved  by  a  great  variety 
of  processes,  some  more,  some  less  intricate.  It  offers,  however,  no 
peculiar  difficulty,  and  is  practically  resolved  with  great  facility  by  the 
help  of  tables  constructed  for  the  purpose,  adapted  to  the  case  of  each 
particular  planet,' 

(500.)  The  true  anomaly  thus  obtained,  the  planet's  angular  distance 
from  the  node,  or  the  angle  N  S  P,  is  to  be  found.  Now,  the  longitudes  of 
the  perihelion  and  node  being  respectively  T  a  and  t  N,  which  are  given, 
their  difference  «  N  is  also  given,  and  the  angle  N  of  the  spherical  right- 
angled  triangle  A  N  a,  being  the  inclination  of  the  plane  of  the  orbit  to 
the  ecliptic,  is  known.  Hence  we  calculate  the  arc  N  A,  or  the  angle 
N  8  A,  which,  added  to  ASP,  gives  the  angle  N  S  P  required.  And 
from  this,  regarded  aii  the  nieasaro.  of  the  arc  N  P,  forming  the  hypothe- 
nuse  of  the  right-angled  spherical  triangle  P  N  p,  whose  angle  N,  as 
before,  is  known,  it  is  easy  to  obtain  i;e  other  two  sides,  N^  and  P^. 
The  latter,  being  the  measure  of  the  angle  ^  S  P,  expresses  the  planet's 
heliocentric  latitude  .  the  former  measures  the  angle  N  Sp,  or  the  planet's 
distance  in  longitude  from  its  node,  which,  added  to  the  known  angle 
3C  S  N,  the  longitude  of  the  node,  igi»m  the  heliocentric  longitude.    This 


'  Tf  will  roadily  bo  under#«ood,  •*>"if  •ifiwpl  in  fti*  A«e  of  uniform  circular  motion, 
an  equable  <Uj«cription  of  arm**  abou'  ariy  centre  is  incomi»atible  with  an  equable  de- 
scription of  anf^,$.  Th*  oi*i|«ct  of  tke  pro*>lem  in  the  text  is  to  pass  from  the  area 
supposed  kiwwB,  t^  the  imgle,  suppos*  <•  inki^/mn  :  in  other  words,  to  derive  the  true 
amount  of  angular  Motion  from  the  jx^rih*-  K>n,  or  the  true  ancmmly  from  what  is  tech- 
nically called  th«  mean  anomwiy,  thM  w,  tW  mean  angular  motion  which  would  have 
been  per'  )i  incd  hn'i  the  moti^/fi  in  angle  be« »  <*riif<*'«  ntm  'ad  of  the  motion  in  area. 
It  happt  ria  forturtaiely,  xha*  this  is  ttw»  s\invU<i^  (A'  all  j>rot><«e«*«>  of  the  transcendental 
kind,  and  can  be  resolved,  in  the  twml  tMt^.mi  ram  bf  ih»  r>ii«  of  "  false  position," 
or  trial  and  error,  in  a  very  few  rninule*  ^»y,  *>  mf  «ven  be  resolved  insiantly  on 
inspection  t>y  u  simple  arid  eantly  c.w\Hiriu:te4  piec*  of  m-yhanttirrt ,  of  which  the  reader 
may  see  a  description  in  the  CambnrJjj/«  f  hilosophu  al  TrtMactions,  vol.  iv.  p.  425,  by 
the  author  of  this  work. 


GEOCENTRIO  PLACE  OF  A  PLANET. 


267 


vrbich  is  to 
Lastly,  the 
,so  required 

the  planet's 
the  portion 
lole  area  of 
to  the  times 
From  this 
tiding  angle 
oblera  is  of 
xreat  variety 
bowever,  no 
cility  by  the 
case  of  each 


process,  however  circuitous  it  may  appear,  when  once  well  understood  may 
be  gone  through  numerically  by  the  aid  of  the  usual  logarithmic  and  tri- 
gonometrical tables,  in  little  more  time  than  it  will  have  taken  the  reader 
to  peruse  its  description. 

(501.)  The  geocentric  differs  from  the  heliocentric  place  of  a  planet  by 
reason  of  that  parallactic  change  of  apparent  situation  which  arises  from 
the  earth's  motion  in  its  orbit.  Were  the  planet's  distances  as  vast  as 
those  of  the  stars,  the  earth's  orbitual  motion  would  be  insensible  wben 
viewed  from  them,  and  they  would  always  appear  to  us  to  hold  the  same 
relative  situations  among  the  fixed  stirs,  «  'f  viewed  from  the  sun,  i.  e. 
they  would  then  be  seen  in  their  heIio<  '•  pJi'oes.  The  difference,  then, 
between  the  heliocentric  and  gcocentrii  ;>iuce3  of  a  planet  is,  in  fiict,  the 
same  thing  with  its  parallax,  arising  from  the  earth's  r  ^moval  from  the 
centre  of  the  system  and  its  annual  motion.  It  folb  ^  from  this,  that 
the  first  step  to^^ards  a  knowledge  of  its  amount,  and  the  consequent 
determination  of  the  apparent  place  of  each  planet,  as  referred  from  the 
earth  to  the  sphere  of  the  fixed  stars,  must  be  to  ascertain  the  proportion 
of  its  linear  distances  from  the  earth  and  from  the  sun,  as  compared  with 
the  earth's  distance  from  the  sun,  and  the  angular  positions  of  all  three 
with  respect  to  each  other. 

(502.)  Suppose,  therefore,  S  to  represent  the  sun,  E  the  earth,  and  P 
the  planet  j  S  r  the  line  of  equinoxes,  T  E  the  earth's  orbit,  and  P  p 
a  perpendicular  let  fall  from  the  planet  on  the  ecliptic.  Then  will  the 
angle  S.P  E  (according  to  the  general  notion  of  parallax  conveyed  in  art. 
69)  represent  the  parallax  of  the  planet  arising  from  the  change  of  station 

Fig.  72. 


from  S  to  E ;  E  P  will  be  the  apparent  direction  of  the  planet  seen  from 
E;  ar  i  if  S  Q  be  drawn  parallel  to  E^,  the  angle  T  S  Q  will  be  the  geo- 
centric longitude  of  the  planet,  while  T  S  E  represents  the  heliocentric 
longitude  of  the  earth,  T  S  j>  that  of  the  planet.  The  former  of  these, 
T  S  E,  is  given  by  the  solar  table ;  the  latter,  T  S  p,  is  found  by  the  pro- 
cess above  described  (art.  5(^0).  Moreover,  S  P  is  the  radius  vector  of 
the  planet's  orbit,  and  S  E  that  of  the  earth's,  both  of  which  are  determined 


c:3 


•'■■'■10    ■»:! 


|{     tt    si 


Sacr 


268 


OUTLINES   OP  ASTRONOMY. 


from  thft  known  dimensions  of  their  respective  ellipses,  and  lae  places  of 
the  bodies  in  thctn  at  the  assigned  time.  Lastly,  the  angle  P  S  j>  is  the 
planet's  heliocentric  latitude. 

(503.)  Our  objoct,  then,  is,  from  all  these  data,  to  determine  the  angle 
T  S  Q,  and  P  E  p,  which  is  the  geocentric  latitude.  The  process,  then, 
will  stand  as  follows  : — lst,-In  the  triangle  S  Pjo,  right-angled  nip,  given 
S  P,  and  the  angle  P  S/>  (the  planet's  radius  vector  and  heliocentric  lati- 
tude), find  Sjt)  and  V p;  2dly,  In  the  trianglo  SE^^,  given  ^p  (just 
found),  S  E  (the  earth's  radius  vector),  and  the  angle  E  S  p  (the  diflFerence 
of  heliocentric  longitudes  of  the  earth  and  planet),  find  the  angle  S  p  E, 
and  the  side  E  j).  The  former  being  equal  to  the  alternate  angle  p  S  Q, 
is  the  parallactic  removal  of  the  planet  in  longitude,  which,  added  to  Y  S^>, 
gives  its  geocentric  longitude.  The  latter,  V^p  (which  is  called  the  curtate 
distance  of  the  planet  from  the  earth),  ^'ives  at  once  the  geocentric  lati- 
tude, by  means  of  the  right-angled  trian^-le  P  E/),  of  which  E^^  and  Vp 
are  known  sides,  and  the  angle  P  E  p  is  the  geocentric  latitude  .sought. 

(504.)  The  calculations  required  for  these  purposes  are  nothing  but 
the  most  ordinary  processes  of  plane  trigonometry  ;  and,  though  some- 
what tedious,  are  neither  intricate  nor  difficult.  When  executed,  how- 
ever, they  afford  us  the  means  of  comparing  the  places  of  the  planets 
actually  observed  with  the  elliptic  theory,  with  the  utmost  exactness,  and 
thus  putting  it  to  the  severest  trial ;  and  it  is  upon  the  testimony  of  such 
computations,  so  brought  into  comparison  with  observed  facts,  that  we 
declare  that  theory  to  be  a  true  representation  of  nature. 

(505.)  The  planets  Mercury,  Venus,  Mars,  Jupiter,  and  Saturn,  have 
been  known  from  the  earliest  ages  in  which  astronomy  ha.s  been  culti- 
vated. Uranus  was  discovered  by  Sir  W.  Herschel  in  1781,  March  13th, 
in  the  course  of  a  review  of  the  heavens,  in  which  every  star  visible  in  a 
telescope  of  a  certain  power  was  brought  under  close  examination,  when 
the  new  planet  was  immediately  detected  by  its  disc,  under  a  high  magni- 
fying power.  It  has  since  been  ascertained  to  have  been  observed  on 
many  previous  occasions,  with  telescopes  of  insufficient  power  to  show  its 
disc,  and  even  entered  in  catalogues  as  a  star ;  and  some  of  the  observa- 
tions which  have  been  so  recorded  have  been  used  to  improve  and  extend 
our  knowledge  of  its  orbit.  The  discovery  of  the  ultra-zodiacal  planets 
dates  from  the  first  day  of  1801,  when  Ceres  was  discovered  by  Piazzi,  at 
Palermo;  a  discovery  speedily  followed  by  those  of  Juno  by  professor 
Harding,  of  Giittingen,  iu  1804  ;  and  of  Pallas  and  Vesta,  by  Dr.  Olbers, 
of  Bremen,  in  1802  and  1 607  respectively.  It  is  extremely  remarkable 
that  this  important  additk/n  to  our  system  had  been  in  some  sort  surmised 
as  a  thing  not  unlikely;  on  tikv  ground  that  the  interval  between  i.he  orbit 


ORDER   AND   DISCOVERY   OP  THE   TLANETS. 


269 


places  of 
S  j>  is  the 

!  the  augle 
icess,  theu, 
at  p,  given 
en  trie  lati- 
1  S  p  (just 
e  difFcrenee 
igle  S;)E, 
igle  p  8  Q, 
ed  to  Y  S  P) 

the  curtate 
centric  Uiti- 
*^p  and  Vj) 
G  sought, 
nothing  but 
lOUgh  sonic- 
icuted,  how- 

the  phinets 
:actness,  and 
lony  of  such 

ts,  that  we 

Saturn,  have 

been  culti- 
March  13th, 

visible  in  a 
lation,  when 
ligh  magni- 
observed  on 

to  show  its 
the  observa- 

and  extend 
iacal  planets 
by  Piazzi,  at 
by  professor 

Dr.  Olbers, 
remarkable 

ort  surmised 

len  the  orbit 


of  Mercury  and  the  other  planetary  orbits,  go  on  doubling  as  we  recede 
from  the  sun,  or  nearly  so.  Thus,  the  interval  between  the  orbits  of  the 
Earth  and  Mercury  is  nearly  twice  that  between  those  of  Venus  and  Mer- 
cury; that  between  the  orbits  of  Mars  and  Mercury  nearly  twice  that 
between  the  Earth  and  Mercury :  and  so  on.  The  interval  between  the 
orbits  of  Jupiter  and  Mercury,  however,  is  much  too  great,  and  would 
form  an  exception  to  this  law,  which  is,  however,  again  resumed  in  the 
case  of  the  three  planets  next  in  order  of  remoteness,  Jupiter,  Saturn,  and 
Uranus.  It  was  therefore  thrown  out,  by  the  late  professor  Bode,  of  Ber- 
lin,' fis  a  possible  surmise,  that  a  planet  not  then  yet  discovered  might 
exist  between  Mars  and  Jupiter:  and  it  may  easily  be  imagined  what 
was  the  astonishment  of  astronomers  on  finding  not  only  one,  but  four 
planets,  differing  greatly  in  all  the  other  elements  of  their  orbits,  but 
agreeing  very  nearly,  both  inter  se,  and  with  the  above  stated  empirical 
law,  in  respect  of  their  mean  distances  from  the  sun.  No  account,  A  pri- 
ori or  from  theory,  was  to  be  given  of  this  singular  progression,  which  is 
not,  like  Kepler's  laws,  strictly  exact  in  numerical  verification ;  but  the 
circumstances  we  have  just  mentioned  tended  to  create  a  strong  belief  that 
it  was  something  beyond  a  mere  accidental  coincidence,  and  bore  reference 
to  the  essential  structure  of  the  planetary  system.  It  was  even  conjec- 
tured that  the  ultra-zodiacal  planets  are  fragments  of  some  greater  planet 
which  formerly  circulated  in  that  intevvnl,  but  which  has  been  blown  to 
atoms  by  an  explosion  j  an  idea  countenanced  by  the  exceeding  minute- 
ness of  these  bodies  which  present  discs;  and  it  was  argued  that  in  that 
case  innumerable  more  such  fragments  must  exist  and  might  come  to  be 
hereafter  discovered.  Whatever  may  be  thought  of  such  a  speculation  as 
a  physical  hypothesis, -this  conclusion  has  been  verified  to  a  considerable 
extent  as  a  matter  of  fact  by  subsequent  discovery,  the  result  of  a  careful 
and  minute  examination  and  mapping  down  of  the  smaller  stars  in  and 
near  the  zodiac,  undertaken  with  that  express  object.  Zodiacal  charts  of 
this  kind,  the  product  of  the  zeal  and  industry  of  many  astronomers,  have 
been  constructed,  in  which  every  star  down  to  the  ninth  or  tenth  magni- 
tude is  inserted,  and  these  stars  being  compared  with  the  actual  stars  of 
the  heavens,  the  intrusion  of  any  stranger  within  their  limits  cannot  foil 
to  be  noticed  when  the  comparison  is  systematically  conducted.  The  dis- 
covery of  Astiaea,  and  that  of  Hebe  by  Professor  Ilenckc,  date  respec- 
tively from  December  8th,  1845,  and  July  1st,  1817;  those  of  Iris  and 

'  The  empirical  law  itself,  as  Wd  have  above  stated  it,  is  ascribed  by  Voiron,  not  to 
Bode  (who  would  appear,  however,  at  all  events,  to  liave  first  drawn  atcennoii  to  this 
interpretation  of  its  interruption),  but  to  Professor  Titius  of  Wittemberg.  (Voiron, 
Supplement  to  Bailly.) 


•■v-nsi  ■■.■\<l 


•     1  -y^^ 


Is 

•5' 


C=5. 


270 


OUTLINES   OF  ASTRONOMY. 


f 


[i 


Flora,  by  Mr.  Hind,  from  August  13th  and  October  18th,  1847;  of  Me- 
tis,  by  Mr.  Graham,  from  April  25,  1848;  and  of  Hygeia,  by  M.  De 
Gasparis,  April  12th,  1849. 

(50G.)  The  discovery  of  Neptune  marks  in  a  signal  manner  the  matu- 
rity of  astronomical  science.  The  proof,  or  at  least  the  urgent  presump- 
tion  of  the  existence  of  such  a  planet,  as  a  means  of  accounting  (by  ita 
attraction)  for  certain  .small  irregularities  observed  in  the  motions  of 
Uranus,  was  afforded  almost  simultaneously  by  the  independent  researches 
of  two  geometers,  Messrs.  Adams  of  Cambridge  and  Leverrier  of  Paris, 
who  were  enabled,  from  theory  ahne,  to  calculate  whereabouts  it  ought 
to  appear  in  the  heavens,  if  visible,  the  places  thus  independently  calcu- 
lated agreeing  surprisingly.  Within  a  single  degree  of  the  place  assigned 
by  M.  Leverrier's  calculations,  and  by  him  communicated  to  Dr.  Galle  of 
the  Royal  Observatory  at  Berlin,  it  was  actually  found  by  that  astronomer 
on  the  very  first  night  after  the  receipt  of  that  communication,  on  turning 
a  telt.scope  on  the  spot,  and  comparing  the  stars  in  its  immediate  neigh- 
bourhood with  those  previously  laid  down  in  one  of  the  zodiacal  charts 
already  alluded  to.'  This  remarkable  verification  of  an  indication  so 
extraordinary  took  place  on  the  23d  of  September,  1846." 

(507.)  The  mean  distance  of  Neptune  from  the  sun,  however,  so  far 
from  falling  in  with  the  supposed  law  of  planetary  distances  above  men- 
tioned, offers  a  decided  case  of  discordance.  The  interval  between  its 
orbit  and  that  of  Mercury,  instead  of  being  nearly  double  the  interral 
be. ween  those  of  Uranus  and  Mercury,  does  not,  in  fact,  exceed  the  latter 
interval  by  much  more  than  half  its  amount.  This  remarkable  exception 
may  serve  to  make  us  cautious  in  the  too  ready  admission  of  enipirical 
laws  of  this  nature  to  the  rank  of  fundamental  truths,  though,  as  in  the 
present  instance,  they  may  prove  useful  auxiliaries,  and  serve  as  stepping 
stones,  affording  a  temporary  footing  in  the  path  to  great  discoveries.  The 
force  of  this  remark  will  be  more  apparent  when  wo  come  to  explain  more 


'  Constructed  by  Dr.  Bremiker,  of  Berlin.  On  reading  the  history  of  this  noble 
discovery,  we  are  ready  fo  exclaim  with  Schiller — 

"  Mit  dem  Genius  steht  die  Natur  in  ewigem  Bunde, 
Was  der  Eine  verepricht  liestet  die  Andre  gewiss." 

'  Professor  Challis,  of  the  Cambridge  Observatory,  directing  the  Northiimberlaiid 
telescope  of  that  Institution  to  the  place  assigned  by  Mr.  Adams's  calculations  ami  i*-; 
vicinity,  on  the  4th  and  12th  of  August  1846,  saw  the  planet  on  both  those  days,  and 
noted  its  place  (among  those  of  other  stars)  for  re-observation.  He,  however,  post- 
poned the  comparifon  of  the  places  observed,  and,  not  possessing  Dr.  Bremiker's 
chart  (which  would  kave  at  once  indicated  the  presence  of  an  unmapped  star,) 
remained  in  ignorance  of  the  planet's  existence  as  a  visible  object  tiil  na  announce- 
ment as  such  by  Dr.  Galle. 


PHYSICAL  DESCRIPTION  OF  THE  PLANETS. 


271 


particularly  the  nature  of  the  theoretical  views  which  led  to  the  discovery 
of  Neptune  itself. 

(508.)  We  shall  devote  the  rest  of  this  chapter  to  an  account  of  the 
physical  peculiarities  and  probable  condition  of  the  several  planets,  so  far 
as  the  former  are  known  by  observation,  or  the  latter  rest  on  probable 
grounds  of  conjecture.  In  this,  three  features  principally  strike  us  as 
necessarily  productive  of  extraordinary  diversity  in  the  provisions  by 
which,  if  they  be,  like  our  earth,  inhabited,  animal  life  must  be  supported. 
These  are,  first,  the  difiFerence  in  their  respective  supplies  of  light  and 
heat  from  the  sun ;  secondly,  the  difference  in  the  intensities  of  the 
gravitating  forces  which  must  subsist  at  their  surfaces,  or  the  different 
ratios  which,  on  their  several  globes,  the  inertise  of  bodies  must  bear  to 
their  weights;  and,  thirdly,  the  difference  in  the  nature  of  the  materials 
of  which,  from  what  we  know  of  their  mean  density,  we  have  every 
reason  to  believe  they  consist.  The  intensity  of  solar  radiation  is  nearly 
seven  times  greater  on  Mercury  than  on  the  Earth,  and  on  Uranus  330 
times  less ;  the  proportion  between  the  two  extremes  being  that  of  upwards 
of  2000  to  1.  Let  any  one  figure  to  himself  the  condition  of  our  globe, 
were  the  sun  to  bo  septupled,  to  say  nothing  of  the  greater  ratio !  or  were 
it  diminished  to  a  seventh,  or  to  a  300th  of  its  actual  power !  Again, 
the  intensity  of  gravity,  or  its  efBcacy  in  counteracting  muscular  power 
and  repressing  animal  activity,  on  Jupiter,  is  nearly  two  and  a  half  times 
that  on  the  earth,  on  Mars  not  more  than  one-half,  on  the  Moon  one- 
sixth,  and  on  the  smaller  planets  probably  not  more  than  one-twentieth ; 
giving  a  scale  of  which  the  extremes  are  in  the  proportion  of  sixty  to  one. 
Lastly,  the  density  of  Saturn  hardly  exceeds  one-eighth  of  the  mean 
density  of  the  Earth,  so  that  it  must  consist  of  materials  not  much  heavier 
than  cork.  Now,  under  the  various  combinations  of  elements  so  important 
to  life  as  these,  what  immense  diversity  must  we  not  admit  in  the  condi- 
tions of  that  great  problem,  the  maintenance  of  animal  and  intellectual 
existence  and  happiness,  which  seems,  so  far  as  we  can  judge  by  what  we 
see  around  us  in  our  own  planet,  and  by  the  way  in  which  every  corner 
of  it  is  crowded  with  living  beings,  to  form  an  unceasing  and  worthy 
object  for  the  exercise  of  the  Benevolence  and  Wisdom  which  preside 
over  all ! 

(.'>()9.)  Quitting,  however,  the  region  of  mere  speculation,  we  will  now 
show  what  information  the  telescope  affords  us  of  the  actual  condition  of 
the  several  planets  within  its  reach.  Of  Mercury  we  can  see  little  more 
than  that  it  is  round,  and  exhibits  phases.  It  is  too  small,  and  too  much 
lost  in  the  constant  neighbourhood  of  the  Sun,  to  allow  us  to  make  out 


't.** 


272 


OUTLINES   OF  ASTRONOMY. 


m 


more  of  its  nature.  The  real  diameter  of  Mercury  is  about  3200  miles : 
its  apparent  diameter  varies  from  5"  to  12".  Nor  does  Venus  offer  any 
rcniurkuble  peculiarities :  although  its  real  diameter  is  7800  miles,  and 
although  it  occasionally  attains  the  considerable  apparent  diameter  of  61", 
which  is  larger  than  that  of  any  other  planet,  it  is  yet  the  most  difficult 
of  them  all  to  define  with  telescopes.  The  intense  lustre  of  its  illumin- 
ated part  dazzles  the  sight,  and  exaggerates  every  imperfection  of  the  tele- 
scope J  yet  we  see  clearly  that  its  surface  is  not  mottled  over  with  permanent 
spots  like  the  Moon ;  we  notice  in  it  neither  mountains  nor  shadows,  but 
a  uniform  brightness,  in  which  sometimes  we  may  indeed  fancy,  or  per- 
haps more  than  fancy,  brighter  or  obscurer  portions,  but  can  seldom  or 
never  rest  fully  satisfied  of  the  fact.  It  is  from  some  observations  of  this 
kind  that  both  Venus  and  Mercury  have  been  concluded  to  revolve  on 
their  axes  in  about  the  same  time  as  the  Earth,  though  in  the  case  of 
Venus,  Bianchini  and  other  more  recent  observers  have  contended  for  a 
period  of  twenty-four  times  that  length.  The  most  natural  conclusion, 
from  the  very  rare  appearance  and  want  of  permanence  in  the  spots,  ig, 
that  we  do  not  see,  as  in  the  Moon,  the  real  surface  of  these  planets,  but 
only  their  atmospheres,  much  loaded  with  clouds,  and  which  may  serve 
to  mitigate  the  otherwise  intense  glare  of  their  sunshine. 

(510.)  The  case  is  very  different  with  Mars.  In  this  planet  we  fre- 
quently discern,  with  perfect  distinctness,  the  outlines  of  ..Jat  may  be 
continents  and  seas.  (SeePlatelll.yJg'.l.,  which  represents  Mars  in  its 
gibbous  state,  as  seen  on  the  16th  of  August,  1830,  in  the  20-feet 
reflector  at  Slough.)  Of  these,  the  former  are  distinguished  by  that 
ruddy  colour  which  characterizes  the  light  of  this  planet  (which  always 
appears  red  and  fiery),  and  indicates,  no  doubt,  an  ochrey  tinge  in  the 
general  soil,  like  what  the  red  sandstone  districts  on  the  Earth  may  pos- 
sibly offer  to  the  inhabitants  of  Mars,  only  more  decided.  Contrasted 
with  this  (by  a  general  law  in  optics),  the  seas,  as  we  may  call  them, 
appear  greenish.'  These  spots,  however,  are  not  always  to  be  seen 
equally  distinct,  but,  when  seen,  they  offer  the  appearance  of  forms  con- 
siderably definite  and  highly  characteristic,^  brought  successively  into 
view  by  the  rotation  of  the  planet,  from  the  assiduous  observation  of 


'  I  have  noticed  the  phienoinena  described  in  the  text  on  many  occasions,  but  never 
more  distinct  than  on  the  occasion  when  the  drawing  was  made  from  which  the  figure 
in  Plate  III.  is  engraved.  —  Author. 

'  The  reader  will  find  many  of  these  forms  represented  in  Schumacher's  Astrono- 
misehe  yachriehten,  No.  191,  434,  and  in  the  chart  in  No.  349,  by  Messrs.  Beer  and 
Madler. 


JUPITER. 


278 


which  it  has  even  been  found  practicable  to  construct  a  rude  chart  of  the 
surface  of  the  planet.  The  variety  in  the  spots  may  arise  from  the  planet 
not  being  destitute  of  atmosphere  and  clouds  j  and  what  adds  greatly  to 
th<'  probability  of  this  is  the  appearance  of  brilliant  white  spots  at  its 
poles,  —  one  of  which  appears  in  our  figure,  —  which  have  been  conjec- 
tured, with  some  probability,  to  be  snow ;  as  they  disappear  when  they 
have  been  long  exposed  to  the  sun,  and  are  greatest  when  just  emerging 
from  the  long  night  of  their  polar  winter,  the  snow  lino  then  extending 
to  about  six  degrees  (reckoned  on  a  meridian  of  the  planet)  from  the  pole. 
By  watching  the  spots  during  a  whole  night,  and  on  successive  nights,  it 
is  found  that  Mars  has  a  rotation  on  an  axis  inclined  about  30°  18'  to  the 
ecliptic,  and  in  a  period  of  24'"  ST"  23*'  in  the  same  direction  as  the 
Earth's,  or  from  west  to  east.  The  greatest  and  least  apparent  diameters 
of  Mars  are  4"  and  18",  and  its  real  diameter  about  4100  miles. 

(511.)  Wo  now  come  to  a  much  more  magnificent  planet,  Jupiter,  the 
largest  of  them  all,  being  in  diameter  no  less  than  87,000  miles,  and  in 
bulk  exceeding  that  of  the  Earth  nearly  1300  times.  It  is,  moreover, 
dignified  by  the  attendance  of  four  moons,  sateliitcs,  or  sccondari/  j^lanetSy 
as  they  are  called,  which  constantly  accompany  and  revolve  about  it,  as 
the  Moon  does  round  the  Earth,  and  in  the  same  direction,  forming  with 
their  principal,  ox  primary,  a  beautiful  miniature  system,  entirely  analo- 
gous to  that  greater  one  of  which  their  central  body  is  itself  a  member, 
obeying  the  same  laws,  and  exemplifying,  in  the  most  striking  and  in- 
structive manner,  the  prevalence  of  the  gravitating  power  as  the  ruling 
principle  of  their  motions:  of  these,  however,  we  shall  speak  more  at 
large  in  the  next  chapter. 

(512.)  The  disc  of  Jupiter  is  always  observed  to  be  crossed  in  one 
certain  direction  by  dark  bands  or  belts  presenting  the  appearance,  in 
Plate  III.  fig.  2.,  which  represents  this  planet  as  seen  on  the  23d  of  Sep- 
tember, 1832,  in  the  20-feet  reflector  at  Slough.  These  belts  are,  how- 
ever, by  no  means  alike  at  all  times  j  they  vary  in  breadth  and  in  situa- 
tion on  the  disc  (though  never  in  their  general  direction).  They  have 
even  been  seen  broken  up  and  distributed  over  the  whole  face  of  the 
planet ;  but  this  pbajuomonon  is  extremely  rare.  Branches  running  out 
from  them,  and  subdivisions,  as  represented  in  the  figure,  as  well  as  evi- 
dent dark  spots,  are  by  no  means  uncommon ;  and  from  these,  attentively 
watched,  it  is  concluded  that  this  planet  revolves  in  the  surprisingly  short 
period  of  9"  55  "  50'  (sid.  time),  on  an  axis  perpendicular  to  the  direction 


c: 


*%»s, 


•''•■■'.'■■v.'  ,1 

-  ■  piavmM 


& 


ill  ■-*»i«r„ 


18 


Beer  and  Madler,  Astr.  Nachr.  349. 


274 


OUTLINES   OF  ASTRONOMY, 


of  the  belts.  NoTv,  >t  is  very  remarkublc,  mid  fornix  a  most  satisfiictory 
comment  on  the  rci  luiiig  by  which  the  spin  r(ii(hil  figure  of  the  Earth 
has  been  deducod  from  its  diurnal  rotation,  that  the  outline  of  Jupiter's 
disc  is  evidently  not  circulai,  but  elliptic,  being  cnnsidunibly  flattened  in 
tUi'.  direction  of  its  axis  of  rotation.  This  appoaruuce  is  no  optical  illu- 
fcioij,  but  is  authenticated  by  inidometrical  measures,  which  assign  107  to 
100  for  the  proportion  of  the  equatorial  and  polar  diameters.  And  to 
confirm  in  the  strongest  manner,  th-^  truth  of  those  principles  on  which 
our  former  conclusions  have  been  founded,  and  fully  to  authorize  their 
extension  to  this  remote  systcfn,  it  appears,  on  calculation,  that  this  is 
really  the  degree  of  oblatencss  which  corresponds,  on  those  principles,  to 
the  dimensions  of  Jupiter,  and  to  the  time  of  his  rotation. 

(513.)  The  parallelism  of  the  bolts  to  the  equator  of  Jupiter,  *' 
occasional  variations,  and  the  appearnncos  of  spots  seen  upon  them,  ren- 
it  extremely  probable  that  they  subsist  in  the  atmosphere  of  the  plant, 
forming  tracts  of  comparatively  clear  sky,  determined  by  currents  analo- 
gous  to  our  trade-winds,  but  of  a  much  more  steady  and  decided  character, 
as  might  indeed  be  expected  from  the  immense  velocity  of  its  rotation. 
That  it  is  the  comparatively  darker  body  of  the  planet  which  appears  in 
the  belts  is  evident  from  this, — that  they  do  not  come  up  in  all  their 
strength  to  the  edge  of  the  disc,  but  fade  away  gradual  v  before  they 
reach  it.     (See  Plate  III.  Ji</.  2.)     The  apparent  diameter  of  Jupiter 
varies  from  30"  to  46". 

(514.)  A  still  more  wonderful,  and,  as  it  may  be  termed,  elaborately 
artificial  mechanism,  is  displayed  in  Saturn,  the  next  in  order  of  remote- 
ness to  Jupiter,  to  which  it  is  not  much  inferior  in  magnitude,  being  about 
79,000  miles  iu  diameter,  nearly  1000  times  exceeding  the  earth  in  bulk, 
and  subtending  an  apparent  angular  diameter  at  the  earth,  of  about  18" 
at  its  moan  distance.  This  stupendous  globe,  besides  being  attended  by 
no  less  than  seven  satellites,  or  moons,  is  surrounded  by  two  broad,  fla.t, 
extremely  thin  rings,  concentric  with  the  planet  and  with  each  other; 
both  lying  in  one  plane,  and  separated  by  a  very  narrow  interval  from 
each  other  throughout  their  whole  circumference,  as  they  are  from  the 
planet  by  a  much  wider.  The  dimensions  of  this  extraordinary  appendage 
are  as  follows ' : — 


'  These  dimensions  are  calculated  from  Prof.  Struve's  micrometric  measures,  Mem. 
Art.  Soc.  iii.  301,  with  'he  exception  of  the  thickness  of  the  ring,  which  is  concluded 
from  its  total  disappearance  in  1833,  in  a  telescope  which  would  certainly  have  shown, 
as  a  visible  object,  a  line  of  light  one-twentieth  of  a  second  in  breadth.  The  interval 
of  the  rings  here  stated  is  possibly  eomewliat  too  small. 


I 


SATURN.  275 

Mllei. 

Exterior  diameter  of  exterior  ring 40095  =  176,418 

Interior  ditto ....  35'289=  155,272 

Kxterior  diiimetor  of  interior  ring 34'475s=  151,090 

Interior  ditto a(i-6ti8=  1 17,339 

Equatorial  diuinotcr  of  the  body 17991=  79,160 

Interval  between  the  planet  and  interior  ring 4*339  =   19,090 

Interval  of  the  rings 0'408=:     1,791 

ThicitnoBS  of  the  rings  not  exceeding =        250 

Tlic  figure  (^fvj.  8,  Plato  III.)  represents  Saturn  surrounded  by  its  rings, 
and  having  its  body  striped  with  dark  belts,  sornewhat  similar,  but  broader 
and  less  strongly  marked  than  those  of  Ji'pitf.'):)  '-nd  owing,  doubtless,  to 
a  similar  cause.'    That  the  ring  is  a  suli'l  '<i):ik<:  isubstancc  is  shown  by  its 

'  '•owing  its  shadow  on  the  body  of  the  plan-  ■     u  the  side  nearest  the 
and  on  the  other  side  receiving  that  of  the  body,  as  shown  in  the 

^are.  From  the  parallelism  of  the  belts  with  the  plane  of  the  ring  it 
may  bo  conjectured  that  the  axis  cf  rotation  of  the  planet  is  perpendicular 
to  that  plane ;  and  this  conjecture  is  confirmed  by  the  occasional  appearance 
of  extensive  dusky  spots  on  its  surface,  which  when  watched,  like  the 
spots  on  Mars  or  Jupiter,  indicate  a  rotation  in  10"  29'>  17'  about  an  axis 
so  situated. 

(515.)  The  axis  of  rotation,  like  that  of  the  earth,  preserves  its  paral- 
lelism to  itself  during  the  motion  of  the  planet  in  its  orbit ;  and  the  same 
is  also  the  case  with  the  ring,  whose  plane  is  constantly  inclined  at  the 
same,  or  very  nearly  the  same,  angle  to  that  of  the  orbit,  and,  therefore, 
to  the  ecliptic,  viz^.  28°  11';  and  intersects  the  latter  plane  in  a  line, 
which  makes  at  present'  an  angle  with  the  line  of  equinoxes  of  167°  31'. 
S  >  that  the  nodcz  of  the  ring  lie  in  167°  31'  and  347°  31'  of  longitude. 
^Vhenever,  then,  the  planet  happens  to  be  situated  in  one  or  other  of  these 
longitudes,  as  at  C,  the  plane  of  the  ring  passes  through  the  sun,  which 
then  illuminates  only  the  edge  of  it.  And  if  the  earth  at  that  moment 
be  in  F,  it  will  see  the  ring  edgeways,  the  planet  being  in  opposition,  and 
therefore  most  favourably  situated  (extern  paribus)  for  observation. 
Under  these  circumstances  the  ring,  if  seen  at  all,  can  only  appear  as  a 
very  .narrow  straight  line  of  light  projecting  on  either  side  of  the  body  as 
a  prolongation  of  its  diameter.  In  fact,  it  is  quite  invisible  in  any  but 
telescopes  of  extraordinary  power."    This  remarkable  phenomenon  takes 

'  The  equatorial  bright  belt  is  generally  well  seen.  Tho  subdivision  of  the  dark  one 
by  two  narrow  bright  bands  is  seldom  eo  distinct  as  represented  in  the  plate. 

'^According  to  Bessel,  the  longitude  of  the  node  of  the  ring  increases  46""462  per 
annum.    In  1800  it  wos  166°  53'  8"-9. 

'  Its  disappearance  was  complete  when  observed  with  a  reflector  eighteen  inches  in 
aperture  and  twenty  feet  in  focal  length,  on  the  29th  of  April,  1833,  by  the  author. 


k'. ij'  .i-a 


jtMiciny 


::^i 


s^, 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


'^ 


1.0 


1.1 


11.25 


^   1^    |20 

U    1 1.6 


Photographic 

Sciences 

Corporation 


33  WIST  MAIN  STRHT 

WnSTM,N.Y.  14510 

(71*)t73-4503 


,    ■mil  !■■■ 

1^ 


276 


OUTLINES  OF  ASTRONOMY. 


Fig.  78. 


It^..l: 


place  at  intervals  of  fifteen  years  nearly  (being  a  semi-period  of  Saturn  in 
its  orbit).  One  disappearance  at  least  must  take  place  whenever  Saturn 
passes  either  code  of  its  orbit ;  but  three  roust  frequently  happen,  and 
two  are  possible.  To  show  this,  suppose  S  to  be  the  sun,  A  B  C  D  part 
of  Saturn's  orbit  situated  so  as  to  include  the  node  of  the  ring  (at  C) ; 
E  F  G  H  the  earth's  orbit:  S  C  the  line  of  the  nodej  EB,  G-D  parallel 
to  S  C  touching  the  earth's  orbit  in  E  Gr ;  and  let  the  direction  of  motion 
of  both  bodies  be  that  indicated  by  the  arrow.  Then  since  the  ring  pre- 
serves its  parallelism,  its  plane  can  nowhere  intersect  the  earth's  orbit,  and 
therefore  no  disappearance  can  take  place,  unless  the  planet  be  between  B 
and  D :  and,  on  the  other  hand,  a  disappearance  is  possible  (if  the  earth 
be  rightly  situated)  during  the  whole  time  of  the  description  of  the  are 
B  D.  Now,  since  S  B  or  S  D,  the  distance  of  Saturn  from  the  Sun,  is  to 
S  E  or  S  a,  that  of  the  Earth,  as  9-54  to  1,  the  angle  CSDorGSB« 
6°  1',  and  the  whole  angle  BSD  =  12°  2',  which  is  described  by  Saturn 
(on  an  average)  in  35946  days,  wanting  only  5-8  days  of  a  complete 
year.  The  Earth  then  describes  very  nearly  an  entire  revolution  within 
the  limits  of  time  when  a  disappearance  is  possible ;  and  since,  in  either 
half  of  its  orbit  E  F  G-  or  Gr  H  F,  it  may  equally  encounter  the  plane 
of  the  ring,  one  such  encounter  at  least  is  unavoidable  within  the  time 
specified.  , 

(516.)  Let  G  a  be  the  arc  of  the  Earth's  orbit  described  from  Gt  in 
5-8  days.  Then  if,  at  the  moment  of  Saturn's  arrival  at  6,  the  Earth  be 
at  a,  it  will  encounter  the  plane  of  the  ring  advancing  parallel  to  itself 
and  to  B  E  to  meet  it,  somewhere  in  the  quadrant  H  E,  as  at  M,  after 
which  it  will  be  behind  that  plane  (with  reference  to  the  direction  of 
Saturn's  motion)  through  all  the  arc  M  E  F  G  up  to  G,  where  it  will 


DISAPPEARANCE   OF  SATURN  S  RING. 


2YT 


R    a 


od  of  Saturn  in 
henever  Saturn 
ly  happen,  and 
I,  ABCDpart 
he  ring  (at  C) ; 
1,0  D  parallel 
lotion  of  motion 
ice  the  ring  pre- 
rth's  orbit,  and 
it  be  between  B 
»le  (if  the  earth 
ition  of  the  arc 
the  Sun,  is  to 
DorCSB  = 
ibed  by  Saturn 
of  a  complete 
ivolution  within 
since,  in  either 
inter  the  plane 
ithin  the  time 

tibed  from  G  in 

J,  the  Earth  be 

larallel  to  itsoK 

B,  as  at  M,  after 

Ithe  direction  of 

\y  where  it  will 


again  overtake  it  at  the  very  moment  of  the  planet  quitting  the  arc  B  D. 
In  this  state  of  things  tbere  will  be  two  disappearances.  If,  when  Saturn 
is  at  B,  the  Earth  be  anywhere  in  the  arc  a  H  E,  it  is  equally  evident 
that  it  will  maet  and  pass  through  the  advancing  plane  of  the  ring  some- 
where in  the  quadrant  H  E,  that  it  will  again  overtake  and  pass  through 
it  somewhere  in  the  semicircle  E  F  G,  and  again  meet  it  in  some  point 
of  the  quadrant  G  H,  so  that  three  disappearances  will  take  place.  So, 
also,  if  the  Earth  be  at  E  when  Saturn  is  at  B,  the  motion  of  the  Earth 
being  at  that  instant  directly  towards  B,  the  plane  of  the  ring  will  for  a 
short  time  leave  it  behind ;  but  the  ground  so  lost  being  rapidly  regained 
as  the  earth's  motion  becomes  oblique  to  the  line  of  junction,  it  will  soon 
overtake  and  pass  through  the  plane  in  the  early  part  of  the  quadrant 
E  F,  and  passing  on  through  G  before  Saturn  arrives  at  D,  will  meet  the 
plane  again  in  the  quadrant  G  H.  The  same  will  continue  up  to  a  certain 
poiut  5,  at  which,  if  the  Earth  be  initially  situated,  there  will  be  but  two 
disappearances  —  the  plane  of  the  ring  there  overtaking  the  Earth  for  an 
instant,  and  being  immediately  again  left  behind  by  it,  to  be  again  en- 
countered by  it  in  G  H.  Finally,  if  the  initial  place  of  the  Earth  (when 
Saturn  is  at  B)  be  in  the  arc  b  F  a,  there  will  be  but  one  passage  through 
the  plane  of  the  ring,  viz.,  in  the  semicircle  G  H  E,  the  Earth  being  in 
advance  of  that  plane  throughout  the  whole  of  b  G. 

(517.)  The  appearances  will  moreover  be  varied  according  as  the  Earth 
passes  from  the  enlightened  to  the  unenlightened  side  of  the  ring,  or  vice 
va'sd.  If  C  be  the  ascending  node  of  the  ring,  and  if  the  under  side  of 
the  paper  be  supposed  south  and  the  upper  north  of  the  ecliptic,  then, 
when  the  Earth  meets  the  plane  of  the  ring  in  the  quadrant  H  E,  it 
passes  from  the  bright  to  the  dark  side :  where  it  overtakes  it  in  the 
quadrant  E  F,  the  contrary.  Vice  versd,  when  it  overtakes  it  in  F  G, 
the  transition  is  from  the  bright  to  the  dark  side,  and  the  contrary  where 
it  meets  it  in  G  H.  On  the  other  hand,  when  the  Earth  is  overtaken  by 
the  ring-plane  in  the  interval  E  b,  the  change  is  from  the  bright  to  the 
dark  side.  When  the  dark  side  is  exposed  to  sight,  the  aspect  of  the 
planet  is  very  singular.  It  appears  as  a  bright  round  disc,  with  its  belts, 
&c.,  but  crossed  equatorially  by  a  narrow  and  perfect  black  line.  This 
can  never  of  course  happen  when  the  planet  is  more  than  6°  1'  from  the 
node  of  the  ring.  Generally,  the  northern  side  is  enlightened  and  visible 
when  the  heliocentric  longitude  of  Saturn  is  between  173°  82'  and 
34P  80',  and  the  southern  when  between  353<»  32'  and  161°  80'.  The 
greatest  opening  of  the  ring  occurs  when  the  planet  is  situated  at  90°  dis- 
I  tancc  from  the  bode  of  the  ring,  or  in  longitudes  77°  31'  and  257^  31', 


^  *"•'«'•  vv.-.) 

tnssi'sfijjl 


'I 


4 


m^ 


278 


OUTLINES  OF  ASTRONOMT. 


1"     ■  ':i- 


and  at  these  points  the  longer  diameter  of  its  apparent  ellipse  is  almost 
exactly  double  the  shorter. 

(518.)  It  will  naturally  be  asked  how  so  stupendous  an  aroh,  if  com- 
posed of  solid  and  ponderous  materials,  can  be  sustained  without  collaps- 
ing and  falling  in  upon  the  planet  ?  The  answer  to  this  is  to  be  found  in 
a  swift  rotation  of  the  ring  in  its  own  plane,  which  observation  has  de- 
tected, owing  to  some  portion  of  the  ring  being  a  little  less  bright  than 
others,  and  assigned  its  period  at  lOi*  32i°  15*,  which,  from  what  we  know 
of  its  dimensions,  and  of  the  force  of  gravity  in  the  Saturnian  system,  is 
very  nearly  the  periodic  time  of  a  satellite  revolving  at  the  same  distance 
as  the  middle  of  its  breadth.  It  is  the  centrifugal  force,  then,  arising 
from  this  rotation,  which  sustains  it;  and,  although  no  observation  nice 
enough  to  exhibit  a  difference  of  periods  between  the  outer  and  inner 
rings  have  hitherto  been  made,  it  is  more  than  probable  that  such  a  diffe- 
rence does  subsist  as  to  place  each  independently  of  the  other  in  a  similar 
state  of  equilibrium. 

(519.)  Although  the  rings  are,  as  we  have  said,  ^ery  nearly  concentric 
with  the  body  of  Saturn,  yet  micrometrical  measurements  of  extreme 
delicacy  have  demonstrated  that  the  coincident  is  not  mathematically  ex- 
act, but  that  the  centre  of  gravity  of  the  rings  oscillates  round  that  of  the 
body  describing  a  very  minute  orbit,  probably  under  laws  of  much  com- 
plexity. Trifling  as  this  remark  may  appear,  it  is  of  the  utmost  import- 
ance to  the  stability  of  the  system  of  the  rings.  Supposing  them  mathe- 
matically perfect  in  their  circular  form,  and  exactly  concentric  vrith  the 
planet,  it  is  demonstrable  that  they  would  form  a  system  in  a  state  of  un- 
stable equilibrium,  which  the  slightest  ex'  1  power  would  subvert  — 
not  by  causing  a  rupture  in  the  substance  he  rings  —  but  by  precipi- 
tating them,  unhroken,  on  the  surface  of  the  planet.  For  the  attraction 
of  such  a  ring  or  rings  on  a  point  or  sphere  excentrically  within  them,  is 
not  the  same  in  all  directions,  but  tends  to  draw  the  point  or  sphere 
towards  the  nearest  part  of  the  ring,  or  away  from  the  centre.  Hence, 
supposing  the  body  to  become,  from  any  cause,  ever  so  little  excentrio  to 
the  ring,  the  tendency  of  their  mutual  gravity  is  not  to  correct  but  to 
increase  this  excentricity,  and  to  bring  the  nearest  parts  of  them  together. 
Now,  external  powers,  capable  of  producing  such  excentricity,  exist  in  the 
attractions  of  the  satellites,  as  will  be  shown  in  Chap.  XII. ;  and  in  order 
that  the  system  may  be  stable,  and  possess  within  itself  a  power  of  resist- 
ing the  first  inroads  of  such  a  tendency,  while  yet  nascent  and  feeble,  and 
opposing  them  by  an  opposite  or  maintaining  power,  it  has  been  shoirn 
that  it  is  sufficient  to  admit  the  rings  to  be  loaded  in  sodie  part  of  their 
circumference,  either  by  some  minute  inequality  of  thickness,  or  by  some 


EQUILIBRIUM   OF  SATURN'S  RINGS. 


279 


portions  being  denser  than  others.  Such  f.  load  would  give  to  the  whole 
ring  to  which  it  was  attached  somewhat  of  the  character  of  a  heavy  and 
sluggish  satellite  maintaining  itself  in  an  orbit  with  a  certain  energy  suffi- 
cient to  overcome  minute  onuses  of  disturbance,  and  establish  an  average 
bearing  on  its  centre.  But  even  without  supposing  the  existence  of  any 
such  load, — of  which,  after  all,  we  have  no  proof, — and  granting,  in  its 
full  extent,  the  general  instability  of  the  equilibrium,  we  think  we  per- 
ceive, in  the  rapid  periodicity  of  all  the  causes  of  disturbance,  a  sufficient 
guarantee  of  its  preservation.  However  homely  be  the  illustration,  we 
can  conceive  nothing  more  apt,  in  every  way,  to  give  a  general  conception 
of  this  maintenance  of  equilibrium  under  a  constant  tendency  to  subver- 
sion, than  the  mode  in  which  a  practised  hand  will  sustain  a  long  pole  in 
a  perpendicular  position  resting  on  the  finger  by  a  continual  and  almost 
imperceptible  variation  of  the  point  of  support.  Be  that,  however,  as  it 
may,  the  observed  oscillation  of  the  centres  of  the  rings  about  that  of  the 
planet  ia  in  itself  the  evidence  of  a  perpetual  contest  between  conserva- 
tive and  destructive  powers  —  both  extremely  feeble,  but  so  antagonizing 
oue  another  as  to  prevent  the  latter  from  ever  acquiring  an  uncontrollable 
ascendancy,  and  rushing  to  a  catastrophe. 

(520.)  This  is  also  the  place  to  observe,  that  as  the  smallest  difference 
of  velocity  between  the  body  and  the  rings  must  infallibly  precipitate  the 
latter  on  the  former,  never  more  to  separate,  (for  they  would,  once  in 
contact,  have  attained  a  position  of  stable  equilibrium,  and  be  held  toge- 
ther ever  after  by  an  immense  force ;)  it  follows,  either  that  their  motions 
in  their  common  orbit  round  the  sun  must  have  been  adjusted  to.  each 
other  by  an  external  power,  with  the  minutest  precision,  or  that  the  rings 
must  have  been  formed  about  the  planet  while  subject  to  their  common 
orbitual  motion,  and  under  the  full  and  free  influence  of  all  the  acting 
forces. 

(521.)  Several  astronomers  have  suspected,  and  even  consider  them- 
selves to  have  certainly  observed,  the  rings  of  Saturn  to  be  occasionally, 
at  least,  streaked  with  more  or  less  numerous  dark  lines  parallel  to  the 
decided  black  interval  which  separates  the  two  rings,  which  latter  being 
permanent,  and  seen  equally  and  in  the  same  part  of  the  breadth  on  both 
sides  of  the  ring,  cannot  be  doubted  to  be  a  real  separation.' 

(522.)  [The  exterior  ring  of  Saturn  is  described  by  many  observers  as 
rather  less  luminous  than  the  interior,  and  the  inner  portion  of  this  latter 


•  I- 
I         .;  ■ 


'M^tlf 


'  The  passage  of  Saturn  across  any  considerable  star  would  aflford  an  admirable 
opportunity  of  testing  the  reality  of  such  fissures,  as  it  would  flash  in  succession 
through  them.  The  opportunity  of  watching  for  such  occultations  —  when  Saturn 
treverB«98  the  Milky- Way,  for  instance — should  not  be  neglected. 


280 


OUTLINES  OF  ASTRONOMY. 


than  its  outer.  On  the  night  of  Nov.  11,  1850,  however,  Mr.  G.  B. 
Bond,  of  the  Harvard  Observatory  (Cambridge,  U.  S.,)  using  the  great 
Fraunhofer  equatorial  of  that  institution,  became  aware  of  a  line  of 
demarcation  between  these  two  portions  so  definite,  and  an  extension 
inwards  of  the  dusky  border  to  such  an  extent  (one  fifth,  hy  measure' 
ment,  of  the  joint  breadth  of  the  two  old  rings,)  as  to  justify  him  in 
considering  it  as  a  newly-discovered  ring.  On  the  nights  of  the  25th 
and  29th  of  the  same  month,  and  without  knowledge  of  Mr.  Bond's 
observations,  Mr.  Dawes,  at  his  observatory  at  Wateringbury,  by  the  aid 
of  an  exquisite  achromatic  by  Merz,  of  6^  inches  aperture,  observed  the 
very  same  fact,  and  even  more  distinctly,  so  as  to  be  sure  of  a  decidedly 
darker  interval  between  the  old  and  new  rings,  and  even  to  subdivide  the 
latter  into  two  of  unequal  degrees  of  obscurity,  separated  by  a  line  more 
obscure  than  either.] 

(523.)  Of  Uranus  we  see  nothing  but  a  small  round  uniformly  illumi- 
nated disc,  without  rings,  belts,  or  discernible  spots.  Its  apparent  dia- 
meter is  about  4",  from  which  it  never  varies  much,  owing  to  the  small- 
ness  of  our  orbit  in  comparison  of  its  own.  Its  real  diameter  is  about 
35,000  miles,  and  its  bulk  82  times  that  of  the  earth.  It  is  attended  by 
satellites — ^four  at  least,  probably  five  or  six — whose  orbits  (as  will  be  seen 
in  the  next  chapter)  offer  remarkable  peculiarities. 

(524.)  The  discovery  of  Neptune  is  so  recent,  and  its  situation  in  the 
ecliptic  at  present  so  little  favourable  for  seeing  it  with  perfect  distinctness, 
that  nothing  very  positive  can  be  stated  as  to  its  physical  appearance.  To 
two  observers  it  has  afforded  strong  suspicion  of  being  surrounded  with  a 
ring  very  highly  inclined.  And  from  the  observations  of  Mr.  Lassell, 
M.  Otto  Struve,  and  Mr.  Bond,  it  appears  to  be  attended  certainly  by  one, 
and  very  probably  by  two  satellites — though  the  existence  of  the  second 
can  hardly  yet  be  considered  as  quite  demonstrated. 

(525.)  If  the  immense  distance  of  Neptune  precludes  all  hope  of 
coming  at  much  knowledge  of  its  physical  state,  the  minuteness  of  the 
ultra-zodiacal  planets  is  no  less  a  bar  into  any  inquiry  into  theirs.  One 
of  them,  Pallas,  has  been  said  to  have  somewhat  of  a  nebulous  or  hazy 
appearance,  indicative  of  an  extensive  and  vaporous  atmosphere,  little 
repressed  and  condensed  by  the  inadequate  gravity  of  so  small  a  mass. 
It  is  probable,  however,  that  the  appearance  in  question  has  originated 
in  some  imperfection  in  the  telescope  employed  or  other  temporary  causes 
of  illusion.  In  Vesta  and  Pallas  only  have  sensible  discs  been  hitherto 
observed,  and  those  only  with  very  high  magnifying  powers.  Vesta  was 
once  seen  by  Schroeter  with  the  naked  eye.  No  doubt  the  most  remark- 
able of  their  peculiarities  must  lie  in  this  condition  of  their  state.    A 


if 


GENERAL  VIEW  OF  THE   SOLAR   SYSTEM. 


281 


r,  Mr.  G.  B. 

ing  tbo  great 

of  a  lino  of 

aD   extension 

I,  hy  measure- 

ustify  hitn  in 

s  of  tbo  25th 

f  Mr.  Bond's 

iry,  by  the  aid 

B,  observed  the 

of  a  decidedly 

0  subdivide  the 
by  a  line  more 

liforraly  illumi- 

1  apparent  dia* 
^  to  the  small- 
imeter  is  about 
t  is  attended  by 
(as  will  be  seen 

situation  in  the 
ect  distinctness, 
ppearance.  To 
rrounded  with  a 
of  Mr.  Lassell, 
ertainly  by  one, 
of  the  second 

es  all  hope  of 
luteness  of  the 
o  theirs.     One 
mlous  or  hazy 
nosphere,  little 
email  a  mass, 
has  originated 
imporary  causes 
been  hitherto 
irs.     Vesta  was 
most  remark- 
iheir  state.    A 


man  placed  on  one  of  them  would  spring  with  ease  60  feet  high,  and 
sustain  no  greater  shock  in  his  descent  than  he  does  on  the  earth  from 
leaping  a  yard.  On  such  planets  giants  might  exist ;  and  those  enormous 
animals,  which  on  earth  require  the  buoyant  power  of  water  to  counteract 
their  weight,  might  there  be  denizens  of  thd  land.  But  of  such  specula- 
tions there  is  no  end. 

(52G.)  We  shall  close  this  chapter  with  an  illustration  calculated  to 
convey  to  the  minds  of  our  readers  a  general  impression  of  the  relative 
magnitudes  and  distances  of  the  parts  of  our  system.  Choose  any  well 
levelled  field  or  bowling-green.  On  it  placo  a  globe,  two  feet  in  diameter; 
this  will  represent  the  Sun ;  Mercury  will  bo  represented  by  a  grain  of 
mustard  seed,  on  the  circumference  of  a  circle  164  feet  in  diameter  for  its 
orbit;  Venus  a  pea,  on  a  circle  284  feet  in  diameter;  the  Earth  also  a 
pea,  on  a  circle  of  430  feet;  Mars  a  rather  largo  pin's  head,  on  a  circle 
of  654  feet;  Juno,  Geres,  Vesta,  and  Pallas,  grains  of  sand,  in  orbits  of 
from  1000  to  1200  feet;  Jupiter  a  moderate-sized  orange,  in  a  circle  nearly 
half  a  mile  across,  Saturn  a  small  orange,  on  a  circle  of  four-fifths  of  a 
mile ;  Uranus  a  full-sized  cherry,  or  small  plum,  upon  the  circumference 
of  a  circle  more  than  a  mile  and  a  half,  and  Neptune  a  good-sized  plum 
on  a  circle  about  two  miles  and  a  half  in  diameter.  As  to  getting  correct 
notions  on  this  subject  by  drawing  circles  on  paper,  or,  still  worse,  from 
those  very  childish  toys  called  orreries,  it  is  out  of  the  question.  To  imi- 
tate the  motions  of  the  planets,  in  the  above-mentioned  orbits,  Mercury 
must  describe  its  own  diameter  in  41  seconds;  Venus  in  4"  14»;  the 
Earth,  in  7  minutes;  Mars,  in  4-  48»;  Jupiter,  2"'  66";  Saturn,  in  3"' 
13";  Uranus,  in  2"  16";  and  Neptune  in  3"  30".  >.  .. - 


-\i\ 


.  •■'.'-'1     .vt\ 


'}     ■■'i.      ;>>. 


'>«a:^ 


'Mnwlj;' 


m 


282 


OUTLINES   OF  ASTRONOMT. 


CHAPTER  X. 
OP    THE    SATELLITES. 

OF  THE  MOON,  AS  A  SATELLITE  OF  THE  EARTH. — GENERAL  PROXIMITT 
OF  SATELLITES  TO  THEIR  PRIMARIES,  AND  CONSEQUENT  SUBORDINA- 
TION OF  THEIR  MOTIONS.  —  MASSES  OF  THE  PRIMARIES  CONCLUDED 
FROM  THE  PERIODS  OF  THEIR  SATELLITES.  —  MAINTENANCE  OF  KEP- 
LER's  laws  in  THE  SECONDARY  SYSTEMS. — OP  JUPITER's  SATEL- 
LITES. —  THEIR  ECLIPSES,  ETC.  —  VELOCITY  OF  LIGHT  DISCOVERED 
BY  THEIR  MEANS.  —  SATELLITES  OF  SATURN — OF  URANUS  —  OP 
NEPTUNE. 

(527.)  In  the  annual  circuit  of  the  earth  about  tLo  sun,  it  is  constantly 
attended  by  its  satellite,  the  moon,  which  revolves  round  it,  or  rather 
both  round  their  common  centre  of  gravity;  while  this  centre,  strictly 
speaking,  and  not  either  of  the  two  bodies  thus  connected,  moves  in  an 
elliptic  orbit,  undisturbed  by  their  mutual  action,  just  as  the  centre  of 
gravity  of  a  large  and  small  stone  tied  together  and  flung  into  the  air 
describes  a  parabola  as  if  it  were  a  real  material  substance  under  the 
earth's  attraction,  while  the  stones  circulate  round  it  or  round  each  other, 
as  we  choose  to  conceive  the  matter. 

(528.)  If  we  trace,  therefore,  the  real  curve  actually  described  by 
either  the  moon's  or  the  earth's  centres,  in  virtue  of  this  compound  mo- 
tion, it  will  appear  to  be,  not  an  exact  ellipse,  but  an  undulated  curve, 
like  that  represented  in  the  figure  to  article  324,  only  that  the  number 
of  undulations  in  a  whole  revolution  is  but  13,  and  their  actual  deviation 
from  the  general  ellipse,  which  serves  them  as  a  central  line,  is  compara- 
tively very  much  smaller — so  much  so,  indeed,  that  every  part  of  the 
curve  described  by  either  the  earth  or  moon  is  concave  towards  the  sun. 
The  excursions  of  the  earth  on  either  side  of  the  ellipse,  indeed,  are  so 
very  small  as  to  be  hardly  appreciable.  In  fact,  the  centre  of  gravity  of 
the  earth  and  moon  lies  always  within  the  surface  of  the  earth,  so  that 
the  monthly  orbit  described  by  the  earth's  centre  about  the  common 
centre  of  gravity  is  comprehended  within  a  space  less  than  the  size  of  the 
earth  itself.    The  effect  ts,  nevertheless,  sensible,  in  producing  an  appa* 


OF  THE  MOON  AS  A  SATELLITE. 


288 


rent  monthly  displacement  of  the  ran  in  longitude,  of  a  parallactic  kind, 
which  is  called  the  menstrual  equation ;  whoso  greatest  amount  is,  how- 
ever, less  than  the  sun's  horizontal  parallax,  or  than  8'6".  | 

(529.)  The  moon,  as  we  have  seen,  is  ahout  GO  radii  of  the  earth  dis- 
tant from  the  centre  of  the  latter.  Its  proximity,  therefore,  to  its  ceiitro 
of  attraction,  thus  estimated,  is  much  greater  than  that  of  the  planets  to 
the  sun ;  of  which  Mercury,  the  nearest,  is  84,  and  Uranus  202G  solar 
radii  from  its  centre.  It  is  owing  to  this  proximity  that  the  moon 
remains  attached  to  the  earth  as  a  satellite.  Were  it  much  further,  the 
feebleness  of  its  gravity  towards  the  earth  would  be  inadequate  to  produce 
that  alternate  acceleration  and  retardation  in  its  motion  about  the  sun, 
which  divests  it  of  the  character  of  an  independent  planet,  and  keeps  its 
movements  subordinate  to  those  of  the  earth.  The  one  would  outrun,  or 
be  left  behind  the  other,  in  their  revolutions  round  the  sun  (by  reason  of 
Kepler's  third  law,)  according  to  the  relative  dimensions  of  their  helio- 
centric orbits,  after  which  the  whole  influence  of  the  earth  would  be 
confined  to  producing  some  considerable  periodical  disturbance  in  the 
moon's  motion,  as  it  passed  or  was  passed  by  it  in  each  synodioal  revolu- 
tion. 

(580.)  At  the  distance  at  which  the  moon  really  is  from  us,  its  gravity 
towards  the  earth  is  actually  less  than  towards  the  sun.  That  this  is  the 
case,  appears  sufficiently  from  what  we  have  already  stated,  that  the 
moon's  real  path,  even  when  between  the  earth  and  sun,  is  concave 
towards  the  latter.  But  it  will  appear  still  more  clearly  if,  from  the 
known  periodic  times '  in  which  the  earth  completes  its  annual  and  the 
moon  its  monthly  orbit,  and  from  the  dimensions  of  those  orbits,  wo 
calculate  the  amount  of  deflection,  in  either,  from  their  t"iu<ents,  in  equal 
very  minute  portions  of  time,  as  one  second.  These  are  t<bo  versed  sines 
of  the  arcs  described  in  that  time  in  the  two  orbits,  and  these  are  the 
measures  of  the  acting  forces  which  produce  those  deflections.  If  wo 
execute  the  numerical  calculation  in  the  case  before  us,  we  shall  find 
2.233 :  1  for  the  proportion  in  which  the  intensity  of  the  force  which 
retains  the  earth  in  its  orbit  round  the  sun  actually  exceeds  that  by  which 
the  moon  is  retained  in  its  orbit  about  the  earth. 

'  R  and  r  radii  of  two  orbits  (supposed  circular,)  P  and  p  the  periodic  times ;  then 
the  arcs  in  question  (A  and  a)  are  to  each  other  as  ■=;■  to  — ;  and  since  the  versed  sines 
are  as  the  squares  of  the  arcs  directly  and  the  radii  inversely,  these  are  to  each  other 
as  —  to  —  :  and  in  this  ratio  are  the  forces  acting  on  the  revolving  bodies  in  either 
case. 


284 


OUTLINES  OF  ASTRONOMY. 


(581.)  Now  the  sun  is  800  times  more  remote  from  the  earth  than  the 
moon  is.  And,  ns  gravity  increases  as  the  squares  of  the  distances  de- 
crease, it  must  follow  that  at  tquul  distances,  the  intensity  of  solar  would 
exceed  that  of  terrestrial  gravity  in  the  ahovo  proportion,  augmented  iu 
the  further  ratio  of  the  square  of  400  to  1 ;  that  is,  in  the  proportion  of 
855000  to  1 ;  and  therefore,  if  wo  grant  that  the  intensity  of  the  gravi- 
tating energy  is  commensurate  with  the  muss  or  inertia  of  the  attracting 
hody,  we  are  compelled  to  admit  the  mass  of  the  earth  to  be  no  more 

than  ^33*000  ^^  *^'''  °^  ^^^  *""• 

(532.)  The  argument  is,  in  fact,  nothing  more  than  a  recapitulation  of 
what  has  been  adduced  in  Chap.  VIII.  (art.  448.)  But  it  is  here  re- 
introduced, in  order  to  show  how  the  mass  of  a  planet  which  is  attended 
by  one  or  more  satellites  can  bo  as  it  were  weighed  against  the  sun,  pro- 
vided we  have  learned  from  observation  the  dimensions  of  the  orbits 
described  by  the  planet  about  the  sun,  and  by  the  satellites  about  the 
planet,  and  also  the  periods  in  which  these  orbits  are  respectively 
described.  It  is  by  this  method  that  the  masses  of  Jupiter,  Saturn, 
Uranus,  and  Neptune  have  been  ascertained.  (See  Synoptic  Table.) 

(583.)  Jupiter,  as  already  stated,  is  attended  by  four  satellites,  Saturn 
by  seven ;  Uranus,  certainly  by  four,  and  perhaps  by  six ;  and  Neptune 
by  two  or  more.  These,  with  their  respective  primaries  (as  the  central 
planets  are  called,)  form  in  each  case  miniature  systems  entirely  analogous, 
in  tho  general  laws  by  whicn  their  motions  are  governed,  to  the  great 
system  in  which  the  sun  acts  the  part  of  the  primary,  and  the  planets  of 
its  satellites.  In  each  of  these  systems  tho  laws  of  Kepler  are  obeyed, 
in  the  sense,  that  is  to  say,  in  which  they  are  obeyed  in  the  planetary 
system  —  approximately,  and  without  prejudice  to  the  effects  of  mutual 
perturbation,  of  extraneous  interference,  if  any,  and  of  that  small  but 
not  imperceptible  correction  which  arises  from  the  elliptic  form  of  the 
central  body.  Their  orbits  are  circles  or  ellipses  of  very  moderate  excen- 
tricity,  the  primary  occupying  one  focus.  About  this  they  describe  areas 
very  nearly  proportional  to  the  times ;  and  the  squares  of  the  periodical 
times  of  all  the  satellites  belonging  to  each  planet  are  in  proportion  to 
each  other  as  the  cubes  of  their  distances.  The  tables  at  the  end  of  the 
volume  exhibit  a  synoptic  view  of  the  distances  and  periods  in  these 
several  systems,  so  far  as  they  are  at  present  known ;  and  to  all  of  them 
it  will  be  observed  that  the  same  remark  respecting  their  proximity  to 
their  primaries  holds  good,  as  in  the  case  of  the  moon,  with  a  simibr 
reason  for  such  close  connection. 

(534.)  Of  these  systems,  however,  the  only  one  which  has  been  studied 


SATELLITES   OF  JUPITER. 


285 


>th  than  the 
istanccs  de- 
solar  would 
igmcnted  in 
iroportion  of 
of  the  gravi- 
ho  attracting 
)  be  DO  more 

ipitulation  of 
it  is  here  re- 
ch  is  attended 
the  Bun,  pro- 
of  the  orbits 
ites  about  the 
0   respectively 
ipiter,  Saturn, 
c  Table.) 
telUtes,  Saturn 
and  Neptune 
as  the  central 
rely  analogous, 
1,  to  the  great 
the  planets  of 
er  are  obeyed, 
the  planetary 
eots  of  mutual 
that  small  but 
ic  form  of  the 
loderate  excen- 
describe  areas 
the  periodical 
I  proportion  to 
the  end  of  the 
sriods  in  these 
to  all  of  them 
lir  proximity  to 
mt\x  a  similar 

las  been  studied 


with  attention  to  all  its  details,  is  that  of  Jupiter ;  partly  on  account  of 
the  conflpicuous  brilliancy  of  its  four  attendants,  which  are  largo  enough 
to  offer  visible  and  measurable  discs  in  telescopes  of  great  power;  but 
more  fur  the  sake  of  their  eclipses,  which,  as  they  happen  very  frcqucntlyi 
and  are  easily  observed,  afford  signals  of  considerable  use  for  the  dcteriui- 
nation  of  terrestrial  longitudes  (art.  266).     This  method,  indeed,  until 
thrown  into  the  back  ground  by  the  greater  facility  and  exactness  now 
attainable  by  lunar  observations  (art.  267)  was  the  best,  or  rather  the 
only  one,  which  could  be  relied  on  for  great  distances  and  long  intenrals. 
(535.)  The  satellites  of  Jupiter  revolve  from  west  to  east  (following  the 
analogy  of  the  planets  and  moon,)  in  planes  very  nearly,  althorgh  not  ex- 
actly,  coincident  with  that  of  the  equator  of  the  planet,  or  parallel  to  its 
belts.     This  latter  plane  is  inclined  3°  5'  30"  to  the  orbit  of  the  planet, 
and  is  therefore  but  little  different  from  the  plane  of  the  ecliptic.    Accord- 
ingly, wo  see  their  orbits  projected  very  nearly  into  straight  lines,  in  which 
they  appear  to  oscillate  to  and  fro,  sometimes  passing  before  Jupiter,  and 
costing  shadows  on  his  disc,  (which  are  very  visible  in  good  telescopes, 
like  small  round  ink  spots,  the  circular  form  of  which  is  very  evident,) 
and  sometimes  disappearing  behind  the  body,  or  being  eclipsed  in  its 
shadow  at  a  distance  from  it.    It  is  by  these  eclipses  that  we  are  furnished 
with  accurate  data  for  the  construction  of  tables  of  the  satellites'  motions, 
as  well  as  with  signals  for  determining  differences  of  longitude. 

(580.)  The  eclipses  of  the  satellites,  in  their  general  conception,  are 
perfectly  analogous  to  those  of  the  moon,  but  in  their  detail  they  differ  in 
several  particulars.  Owing  to  the  much  greater  distance  of  Jupiter  from 
the  sun,  and  its  greater  magnitude,  the  cone  of  its  shadow  or  umbra 
(art.  420)  is  greatly  more  elongated,  and  of  far  greater  dimension,  than 
that  of  the  earth.  The  satellites  are,  moreover,  much  less  in  proportion 
to  their  primary,  their  orbits  less  inclined  to  its  ecliptic,  and  (compara- 
tively to  the  diameter  of  the  planet)  of  smaller  dimensions,  than  is  the 
case  with  the  moon.  Owing  to  these  causes,  the  three  interior  satellites 
of  Jupiter  pass  through  the  shadow,  and  are  totally  eclipsed,  every  revo- 
lution ;  and  the  fourth,  though,  from  tho  greater  inclination  of  its  orbit,  it 
sometimes  escapes  eclipse,  and  mat/  occasionally  graze  as  it  were  the  border 
of  the  shadow,  and  suffer  partial  eclipse,  yet  does  so  comparatively  seldom, 
and,  ordinarily  speaking,  its  eclipses  happen,  like  those  of  the  rest,  each 
1  revolution. 

(537.)  These  eclipses,  moreover,  are  not  seen,  as  is  the  case  with  those 
I  of  the  moon,  from  the  centre  of  their  motion,  but  from  a  remote  station, 
land  one  whose  situation  with  respect  to  the  line  of  shadow  is  variable. 


ni»wtaiinW|ii 


286 


OUTLINES  OF  ASTRONOMY. 


This,  of  oourae,  makes  no  diffuronco  in  the  lime$  of  the  eolipscs,  but  • 
very  great  one  in  their  vJHibility,  and  in  their  apparent  situations  with 
respect  to  the  planet  at  the  moments  of  their  entering  and  quitting  the 
shadow. 

(588.)  Suppose  S  to  be  the  sun,  E  the  earth  in  its  orbit  E  F  G  K,  J 
Jupiter,  und  a  h  the  orbit  of  one  of  its  satellites.  '  "  e  cone  of  the  shadow, 
then,  will  have  its  vertex  at  X,  a  point  fur  beyonc.  'lo  orbits  of  all  the 
satellites ;  and  the  penumbra,  owing  to  the  great  distance  of  the  sun,  and 
the  consequent  smallness  of  the  angle  (about  6'  only)  its  disc  subtends  at 
Jupiter,  will  hardly  extend,  within  the  limits  of  the  satellites'  orbits,  to 
any  perceptible  distance  beyond  the  shadow,  —  for  which  reason  it  is  not 
represented  in  the  figure.  A  satellite  revolving  from  west  to  east  (in  the 
direction  of  the  arrows)  will  be  eclipsed  when  it  enters  the  shadov^  at  a, 
but  not  suddenly,  because,  like  the  moon,  it  has  a  considerable  diameter 
seen  from  the  planet;  so  that  the  time  elapsing  from  the  first  perceptible 
loss  of  light  to  its  total  extinction  will  be  that  which  it  occupies  in  de- 
scribing about  Jupiter  an  angle  equal  to  its  apparent  diameter  as  seen  from 
the  centre  of  the  planet,  or  rather  somewhat  more,  by  reason  of  the 

Fig.  74. 


penumbra;  and  the  same  remark  applies  to  its  emergence  at  h.  Nov, 
owing  to  the  difference  of  telescopes  and  of  eyes,  it  is  not  possible  to  assign 
the  precise  moment  of  incipient  obscuration,  or  of  total  extinction  at  a,  nor 
that  of  the  first  glimpse  of  light  falling  on  the  satellite  at  ft,  or  the  complete 
recovery  of  its  light.  The  observation  of  an  eclipse,  then,  in  which  only 
the  immersion,  or  only  the  emersion,  is  seen,  is  incomplete,  and  inadequate 
to  afford  any  precise  information,  theoretical  or  practical.  But,  if  both 
the  immersion  and  emersion  can  be  observed  with  the  same  telescope,  and 
hy  the  same  person,  the  interval  of  the  times  will  give  the  duration,  and 
their  mean  the  exact  middle  of  the  eclipse,  when  the  satellite  is  in  the 
line  S  J  X,  i.  e.  the  true  moment  of  its  opposition  to  the  sun.  Such  ob- 
servations, and  such  only,  are  of  use  for  determining  the  periods  and  other 


ECLIPSES  OF  JUPITER'S  SATELLITES. 


287 


ipsct,  but  » 
uations  with 
quitting  the 

E  F  0  K,  J 

f  tho  shadow, 
)its  of  all  the 

tho  Bun,  and 
10  subtends  at 
ites'  orbits,  to 
aaon  it  is  not 
to  east  (in  the 
a  shadov?  at  o, 
rable  diameter 
irst  perceptible 
occupies  in  de- 
ter as  seen  from 

reason  of  the 


particulars  of  the  motions  of  tho  satollitcs,  and  for  affording  data  of  any 
material  uso  for  tho  calculation  of  terrestrial  longitudes.  Tho  intervals 
of  the  eclipses,  it  will  bo  obaorvod,  give  tho  nyuodlc  periods  of  the  satel- 
lites'  revolutions ;  from  which  their  sidoroal  periods  must  be  concluded  by 
the  method  in  art.  418. 

(589.)  It  is  evident,  from  a  mere  inspection  of  our  figure,  that  the 
eclipses  take  placo  to  tho  west  of  the  planet,  when  the  earth  is  situated 
to  the  west  of  tho  Hue  8  J,  i,  e.  beforo  tho  opposition  of  Jupiter ;  and  to 
the  east,  when  in  the  other  half  of  its  orbit,  or  after  tho  opposition. 
When  the  earth  approaches  the  opposition,  the  visual  lino  becomes  more 
and  more  nearly  coincident  with  the  direction  of  the  shadow,  and  the  ap- 
parent place  where  the  eclipses  happen  will  bo  continually  nearer  and 
nearer  to  the  body  of  tho  planet.  When  tho  earth  comes  to  F,  a  point 
determined  by  drawing  2»  F  to  touch  tho  body  of  the  planet,  the  emersions 
will  cease  to  be  visible,  and  will  thenceforth,  up  to  the  time  of  the  oppo- 
sition, happen  behind  the  disc  of  the  planet.  Similarly,  fvom  the  oppo- 
sition till  the  time  when  tho  earth  arrives  at  I,  a  point  determined  by 
drawing  a  I  tangent  to  the  eastern  limb  of  Jupiter,  the  immersions  will 
be  concealed  from  our  view.  When  the  earth  arrives  at  O  (or  H)  the 
imincrsion  (or  emersion)  will  happen  at  the  very  edge  of  the  visible  disc, 
and  when  between  G  and  H  (a  very  small  space),  the  satellites  will  pau 
medipsed  behind  the  limb  of  the  planet. 

(540.)  Both  the  satellites  and  their  shadows  are  frequently  observed  to 
transit  or  pass  across  tho  disc  of  the  planet.  When  a  satellite  comes  to 
m,  its  shadow  will  be  thrown  on  Jupiter,  and  will  appear  to  move  across 
it  as  a  black  spot  till  the  satellite  comes  to  n.  But  the  satellite  itself  will 
not  appear  to  enter  on  the  disc  till  it  comes  up  to  the  line  drawn  from  E 
to  the  eastern  edge  of  the  disc,  and  will  not  leave  it  till  it  attains  a  similar 
line  drawn  to  the  western  edge.  It  appears  then  that  the  shadow  will 
precede  tho  satellite  in  its  progress  over  the  disc  before  the  opposition  of 
Jupiter,  and  vice  versd.  In  these  transits  of  the  satellites,  which,  with 
very  powerful  telescopes,  may  be  observed  with  great  precision,  it  fre- 
quently happens  that  the  satellite  itself  is  discernible  on  the  disc  as  a 
bright  spot  if  projected  on  a  dark  belt ;  but  occasionally  also  as  a  dark 
spot  of  smaller  dimensions  than  the  shadow.  This  curious  fact  (observed 
by  Schroeter  and  Harding)  has  led  to  a  conclusion  that « certain  of  the 
satellites  have  occasionally  on  their  own  bodies,  or  in  their  atmospheres, 
obscure  spots  of  great  extent.  We  say  of  great  extent ;  for  the  satellites 
of  Jupiter,  small  as  they  appear  to  us,  arc  really  bodies  of  considerable 
uie,  as  the  following  comparative  table  will  show : ' — 

'  Struve,  Mem.  Art.  Soc.  ill  301. 


:^ 


288 


OUTLINES  OP  ASTRONOMY. 


■•■ 

Mean  apparent 
diameter  as  seen; 
from  the  Karth. 

Mean  apparent 

diameter  u»  oeen 

from  Jupiter. 

Diameter  in  miles. 

Mass.* 

Jupiter 

38"-327 
1-017 
0  Jll 
1-488 
1-273 

33'     11" 

17  35 

18  0 
8      46 

87000 
2508 
2068 
3377 
2890 

1-0000000 
0-0000173 
0-0000232 
0-0000885 
0-0000427 

Ist  Kntcllitc  

2d            

3d            

4th 

f 


From  which  it  follows,  that  the  first  satellite  appears  to  a  spectator  on 
Jupiter,  as  large  as  our  moon  to  us ;  the  second  and  third  nearly  equal  to 
each  other,  and  of  somewhat  more  than  half  the  apparent  diameter  of  the 
first,  and  the  fourth  about  one  quarter  of  that  diameter.  So  seen,  they 
will  frequently,  of  course,  eclipse  one  another,  and  cause  eclipses  of  the 
sun  (the  latter  visible,  however,  only  over  a  very  small  portion  of  the 
planet),  and  their  motions  and  aspects  with  respect  to  each  other  must 
offer  a  perpetual  variety  and  singular  and  pleasing  interest  to  the  inhabi- 
tants of  their  primary. 

(541.)  Besides  the  eclipses  and  the  transits  of  the  satellites  across  the 
disc,  they  may  also  disappear  to  us  when  not  eclipsed,  by  passing  heJiind 
the  body  of  the  planet.  Thus,  when  the  earth  is  at  E,  the  immersion  of 
the  satellite  will  be  seen  at  a,  and  its  emersion  at  &,  both  to  the  west  of 
the  planet,  after  which  the  satellite,  still  continuing  its  course  in  the  di- 
rcctiou  ab,  will  pass  behind  the  body,  and  again  emerge  on  the  opposite 
side,  after  an  interval  of  occultation  greater  or  less  according  to  the  dis- 
tance of  the  satellite.  This  interval  (on  account  of  the  great  distance  of 
the  earth  compared  with  the  radii  of  the  orbits  of  the  satellites)  varies  bat 
little  in  the  case  of  each  satellite,  being  nearly  equal  to  the  time  which 
the  satellite  requires  to  describe  an  arc  of  its  orbit,  equal  to  the  angular 
diameter  of  Jupiter  as  seen  from  its  centre,  which  time,  for  the  several 
satellites,  is  as  follows :  viz.,  for  the  first,  2"  20" ;  for  the  second,  2"  56» ;  for 
the  third,  S**  43'" ;  and  for  the  fourth,  4**  56"> ;  the  corresponding  diameters 
of  the  planet  as  seen  from  these  respective  satellites  being,  19°  49' ;  12° 
25';  7°  47';  and  4°  25'.'  Before  the  opposition  of  Jupiter,  these  occul- 
tations  of  the  satellites  happen  after  the  eclipses :  after  the  opposition 
(when,  for  instance,  the  earth  is  in  the  situation  K),  the  occultations  take 
place  before  the  eclipses.  It  is  to  be  observed  that  owing  to  the  proximity 
of  the  orbits  of  the  first  and  second  satellites  to  the  planet,  both  the  im< 
mersion  and  emersion  of  either  of  them  can  never  be  observed  in  any 


'  Laplace,  Mec.  Cel.  liv.  viii.  $  27. 

*  These  data  are  taken  approximately  from  Mr.  Woodhouse's  paper  in  the  supplement 
to  the  Nautical  Almancck  for  1835. 


ECLIPSES   OP  JUPITER'S   SATELLITES. 


289 


:  in  the  eupplement 


single  eclipse,  the  immersion  being  concealed  by  the  body,  if  the  planet 
be  past  its  opposition,  the  emersion  if  not  yet  arrived  at  it.  So  also  of 
the  occultation.  The  commencement  of  the  occultation,  or  the  passage 
of  the  satellite  behind  the  disc,  takes  place  while  obscured  by  the  shadow, 
before  opposition,  and  its  re-emergence  after.  All  these  particulars  will 
be  easily  apparent  on  mere  inspection  of  the  figure  (art.  536).  It  is  only 
during  the  short  time  that  the  earth  is  in  the  arc  G  H  (i.  e.  between  the 
sun  and  Jupiter,  that  the  cone  of  the  shadow  converging  (while  that  of 
the  visual  rays  diverges)  behind  the  planet,  permits  their  occultations  to 
be  completely  observed  both  at  ingress  and  egress,  unobscured,  the  eclipses 
being  then  invisible. 

(542.)  An  extremely  singular  relation  subsists  between  the  mean 
angular  velocities  or  mean  motions  (as  they  are  termed)  of  the  three  first 
satellites  of  Jupiter.  If  the  mean  angular  velocity  of  the  first  satellite 
be  added  to  twice  that  of  the  third,  the  sum  will  equal  three  times  that 
of  the  second.  From  this  relation  it  follows,  that  if  from  the  mean  lon- 
gitude of  the  first  added  to  twice  that  of  the  third,  be  subducted  three 
times  that  of  the  second,  the  remainder  will  always  be  the  same,  or  con- 
stant, and  observation  informs  us.  that  this  constant  is  180°,  or  two  right 
angles;  so  that,  the  situations  of  any  two  of  them  being  given,  that 
of  the  third  may  be  found.  It  has  been  attempted  to  account  for  this 
remarkable  fact,  on  the  theory  of  gravity  by  their  mutual  action ;  and 
Laplace  has  demonstrated,  that  if  this  relation  were  at  any  one  epoch  ap- 
proximately true,  the  mutual  attractions  of  the  satellites  would,  in  process 
of  time,  render  it  exactly  so.  One  curious  consequence  is,  that  these 
three  satellites  cannot  be  all  eclipsed  at  once ;  for,  in  consequence  of  the 
last-mentioned  relation,  when  the  second  and  third  lie  in  the  same  direc- 
tion from  the  centre,  the  first  must  lie  on  the  opposite ;  and  therefore, 
when  at  such  a  conjuncture  the  first  is  eclipsed,  the  other  two  must  lie 
between  the  sun  and  planet,  throwing  its  shadow  on  the  disc,  and  vice 
versd.  ■'^v 

(543.)  Although,  however,  for  the  above  mentioned  reason,  the  satel- 
I  lites  cannot  be  all  eclipsed  at  once/  yet  it  may  happen,  and  occasionally 
docs  so,  that  all  are  either  eclipsed,  occulted,  or  projected  on  the  body,  in 
which  case  they  are,  gener&Uy  speaking,  equally  invisible,  since  it  requires 
an  excellent  telescope  to  discern  a  satellite  on  the  body,  except  in  peculiar 
circumstances.  Instances  of  the  actual  observations  of  Jupiter  thus 
denuded  of  its  usual  attendance  and  offering  the  appearance  of  a  solitary 
disc,  though  rare,  have  been  more  than  once  recorded.  The  first  occasion 
[in  which  this  was  noticed  was  by  Molyneux,  on  November  2d,  (old  style) 
19 


cs 

";»» 


mm 


»ii.Mirffi 


V4»^ 


gpnmmm 


290 


OUTLINES   OF  ASTRONOMY. 


1681.'  A  similar  observation  is  recorded  by  Sir  W.  Herechel  as  made 
by  him  on  May  22d,  1802.  The  phsoiiomenon  has  also  been  observed 
by  Mr.  Wallis,  on  April  15th,  1826;  (in  which  case  the  deprivation  con- 
tinned  two  whole  hours ;)  and  lastly  by  Mr.  H.  Griesbach,  on  September 
27th,  1843. 

(544.)  The  discovery  of  Jupiter's  satellites,  one  of  the  first  fruits  of 
the  invention  of  the  telescope,  and  of  Galileo's  early  and  happy  idea  of 
directing  its  new-found  powers  to  the  examination  of  the  heavens,  forms 
one  of  the  most  memorable  epochs  in  the  history  of  astronomy.  The 
first  astronomical  solution  of  the  great  problem  of  "the  longitude" — prac- 
tically the  most  important  for  the  interests  of  mankind  which  has  ever 
been  brought  under  the  dominion  of  strict  scientific  principles,  dates 
immediately  from  their  discovery.  The  final  and  conclusive  establish- 
ment of  the  Copemican  system  of  astronomy  may  also  be  considei'ed  as 
referable  to .  the  discovery  and  study  of  this  exquisite  miniature  system, 
in  which  the  laws  of  the  planetary  motions,  as  ascertained  by  Kepler, 
and  especially  that  which  connects  their  periods  and  distances,  were 
speedily  traced,  and  found  to  be  satisfactorily  maintained.  And  (as  if  to 
accumulate  historical  interest  on  this  point)  it  is  to  the  observation  of 
their  eclipses  that  we  owe  the  grand  discovery  of  the  aberration  of  light, 
and  the  consequent  determination  of  the  enormous  velocity  of  that  won- 
derful element.    This  we  must  explain  no^  at  large. 

(545.)  The  earth's  orbit  being  concentric  with  that  of  Jupiter  and 
interior   to  it  (see  /Ig.  art.  586),  their  mutual  distance  is  continually 
varying,  the  variation  extending  from  the  mm  to  the  difference  of  the 
radii  of  the  two  orbits ;  and  the  difference  of  the  greater  and  least  dis- 
tances being  equal  to  a  diameter  of  the  earth's  orbit.     Now,  it  \ras 
observed  by  Roemer,  (a  Danish  astronomer,  in  1675,)  on  comparing  to- 
gether observations  of  eclipses  of  the  satellites  during  many  successive 
years,  that  the  eclipses  at  and  about  the  opposition  of  Jupiter  (or  ita 
nearest  point  to  the  earth)  took  place  too  soon — sooner,  that  is,  than,  bj  j 
calculation  from  an  average,  he  expected  them ;  whereas  those  which  hap- 
pened when  the  earth  was  in  the  part  of  its  orbit  most  remote  from 
Jupiter  were  always  too  late.     Connecting  the  observed  error  in  their 
computed  times  with  the  variation  of  distance,  he  concluded,  that,  ^o  \ 
make  the  calculation  on  an  average  period  correspond  with  fact,  an  allow- 
ance in  respect  of  time  behoved  to  be  made  proportional  to  the  excess  or  I 
defect  of  Jupiter's  distance  from  the  earth  above  or  below  its  average 
amount,  and  such  that  a  difference  of  distance  of  one  diameter  of  the| 
earth's  orbit  should  correspond  to  16"  26*-6  of  time  allowed.    Specu- 

'  Molyneux,  Optics,  p.  271. 


SATBLLITES  OF  SATURN. 


291 


lating  on  the  prob  .;>  physical  cause,  he  was  naturally  led  to  think  of  a 
gradual  instead  oi  an  instantaneous  propagation  of  light.  This  explained 
every  particular  of  the  observed  phenomenon,  but  the  velocity  required 
(192000  miles  per  second)  was  so  great  as  to  startle  many,  and,  at  all 
events,  to  require  confirmation.  This  has  been  afforded  since,  and  of  the 
most  unequivocal  kind,  by  Bradley's  discovery  of  the  aberration  of  light 
(art.  329.)  The  velocity  of  light  deduced  from  this  last  phsenomenon 
differs  by  less  than  one^ightieth  of  its  amount  from  that  calculated  from 
the  eclipses,  and  even  this  difference  will  no  doubt  be  destroyed  by  nicer 
and  more  rigorously  reduced  observations. 

(546.)  The  orbits  of  Jupiter's  satellites  are  but  little  excentriC)  those 
of  the  two  interior,  indeed,  have  no  perceptible  excentricity.  Their 
mutual  action  produces  in  them  perturbations  analogous  to  those  of  the 
planets  about  the  sun,  and  which  have  been  diligently  investigated  by 
Laplace  and  others.  By  assiduous  observation  it  has  been  ascertained 
that  they  are  subject  to  marked  fluctuations  in  respect  of  brightness,  and 
tl  t  these  fluctuations  happen  periodically,  according  to  their  position 
with  respect  to  the  sun.  From  this  it  has  been  concluded,  apparently 
with  reason,  that  they  turn  on  their  axes,  like  our  moon,  in  periods  equal 
to  their  respective  sidereal  revolutions  about  their  primary. 

(547.)  The  satellites  of  Saturn  have  been  much  less  studied  than  those 
of  Jupiter,  being  far  more  difficult  to  observe.  The  most  distant  has  its 
orbit  materially  inclined  (no  less  than  12°  14')'  to  the  plane  of  the  ring, 
with  which  the  orbits  of  all  the  rest  nearly  coincide.  Nor  is  this  the  pnly 
circumstance  which  separates  it  by  a  marked  difference  of  character  from 
the  system  of  the  six  interior  ones,  and  renders  it  in  some  sort  an  anoma- 
lous member  of  the  Satumian  system.  Its  distance  from  the  planet's  centre 
exceeds  in  the  proportion  of  nearly  three  to  one  that  of  the  most  distant 
of  all  the  rest,  being  no  less  than  64  times  the  radius  of  the  globe  of 
Saturn,  a  distance  from  the  primary  to  which  our  own  moon  (at  60  radii) 
offers  the  only  porallel.  Its  variation  of  light  also  in  different  parts  of  its 
orbit  is  very  much  greater  than  the  case  of  any  other  secondary  planet. 
Dominic  Cassini  indeed  (its  first  discoverer,  A.  D.  1671)  found  it  to  disap- 
pear for  nearly  half  its  revolution,  when  to  the  east  of  Saturn,  and  though 
the  more  powerful  telescopes  now  in  use  enable  us  to  follow  it  round  the 
whole  of  its  circuit,  its  diminution  of  light  is  so  great  in  the  eastern  half 
of  its  orbit  as  to  render  it  somewhat  difficult  to  perceive.  From  this  cir- 
cumstance (viz.  from  the  defalcation  of  light  occurring  constantly  on  the 
same  side  of  Saturn  as  seen  from  the  earth,  the  visual  ray  from  which  is 
never  very  oblique  to  the  direction  in  which  the  sun's  light  falls  on  it)  it 

'  Lalande,  Astron.  Art.  3075.  _-- 1;-     ,   -    -^ 


frr% 


*^-^"]? 


% 


•■■»»>».>' 


t 


\s^ 


292 


OUTLINES   OP  ASTRONOMY. 


is  presumed  with  much  certainty  that  this  satellite  revolves  on  its  axis  in 
the  exact  time  of  rotation  about  the  primary ;  as  wo  know  to  be  the  case 
with  the  moon,  and  as  there  is  considerable  ground  for  believing  to  be  so 
with  all  secondaries. 

(548.)  The  next  satellite  in  order  proceeding  inwards  (the  first  in  order 
of  discovery ')  is  by  far  the  largest  and  most  conspicuous  of  all,  and  is 
probably  not  much  inferior  to  Mars  in  size.  It  is  the  only  one  of  the 
number  whose  theory  and  perturbations  have  been  at  all  inquired  into  ^ 
farther  than  to  verify  Kepler's  law  of  the  periodic  times,  which  holds 
good,  mutatis  mutandis^  and  under  the  requisite  reservations,  in  this,  as 
in  the  system  of  Jupiter.  The  three  next  satellites  still  proceeding 
inwards '  are  very  minute,  and  require  pretty  powerful  telescopes  to  see 
them ;  while  the  two  interior  satellites  which  j  ust  skirt  the  edge  of  the 
ring  *  can  only  be  seen  with  telescopes  of  extraordinary  power  and  per- 
fection, and  under  the  most  favourable  atmospheric  circumstances.  At 
the  epoch  of  their  discovery  they  were  seen  to  thread,  like  beads,  the 
almost  infinitely  thin  fibre  of  light  to  which  the  ring  then  seen  edge- 
ways, was  reduced,  and  for  a  short  time  to  advance  off  it  at  either  end, 
speedily  to  return,  and  hastening  to  their  habitual  concealment  behind 

the  body.* 

(549.)  Owing  to  the  obliquity  of  the  ring  and  of  the  orbits  of  the 

satellites  to  Saturn's  ecliptic,  there  are  no  eclipses,  occultations,  or 

*  By  Huyghens,  March  25,  1655.  ,.  .  ,'  ,■<,.:,,  ,r ',     < 
»  By  Bessel,  .4«(r.  iVacAr.  Nos.  193,  214.  ,      - 

*  Discovered  by  Dominic  Cassini  in  1672  and  1684. 

*  Discovered  by  Sir  William  Herschel  in  1789. 

■  Considerable  confusion  prevails  in  the  nomenclature  of  the  Saturnian  system, 
owing  to  the  order  of  discovery  not  coinciding  with  that  of  distances.  Astronomers 
have  not  yet  agreed  whether  to  call  the  two  interior  satellites  the  6th  and  7th  (reckon- 
ing inward)  and  the  older  ones  the  Ist,  2d,  3d,  4th,  and  5th,  reckoning  outward ;  or  to 
commence  with  the  innennost  and  reckon  outwards  from  1  to  7.  This  confusion  has 
been  attempted  to  be  obviated  by  a  mythological  nomenclature,  in  consonance  with 
that  at  length  completely  established  for  the  primary  planets.  Taking  the  names  ot 
the  Titanian  divinities,  the  following  pentameters  afford  an  easy  artificial  memory, 
commencing  with  the  most  distant. 

lapetus,  Titan ;  Rhea,  Dione,  Tethys ;  (pron.  TSthys) 

Enceladus,  Mimas 

It  is  worth  remarking  that  Simon  Marius,  who  disputed  the  priority  of  the  discovery 
of  Jupiter's  satellites  with  Galileo,  proposed  for  them  mythological  names,  viz  : — lo, 
Europa,  Ganymede,  and  Callisto.  The  revival  of  these  names  would  savour  of  a  prefe- 
rence of  Marius's  claim,  which,  even  if  an  absolute  priority  were  conceded  (which  it  is 
not),  would  still  leave  Galileo's  general  claim  to  the  use  of  the  telescope  as  a  means  of 
astronomical  discovery  intact.  But  in  the  case  of  Jupiter's  satellites  there  exists  no 
confusion  to  rectify.  They  are  constantly  referred  to  by  their  numerical  designations 
in  every  almanack. 


SATELLITES  OF   URANUS. 


298 


m  its  axis  in 
0  be  the  case 
iving  to  be  so 

5  first  in  order 
of  all,  and  is 
ily  one  of  the 
aquired  into* 
,  Mrhich  holda 
ns,  in  this,  as 
ill  proceeding 
jscopes  to  see 
e  edge  of  the 
5wer  and  per- 
rnstances.     At 
ike  beads,  the 
en  seen  cdge- 
at  either  end, 
alment  behind 

orbits  of  the 
ccultations,  or 


aturnian  syBtem, 
la.    Astronomers 

and  7  th  (reckon- 
outward;  or  to 

lis  confusion  has 

consonance  with 
ig  the  names  ot 

tiiicial  memory, 

I)  • 

(r  of  the  discovery 
lames,  viz:— lo, 
savour  of  a  prefe- 
ledcd  (which  it  is 
pe  as  a  means  of 
there  exists  no 
rical  designations 


transits  of  these  bodies  or  their  shadows  across  the  disc  of  their  primary 
(the  interior  ones  excepted),  until  near  the  time  when  the  ring  is  seen 
edgewise,  and  when  they  do  take  place,  their  observation  is  attended  with 
too  much  difficulty  to  be  of  any  practical  use,  like  the  eclipses  of  Jupiter's 
satellites,  for  the  determination  of  longitudes,  for  which  reason  they 
have  been  hitherto  little  attended  to  by  astronomers. 

(550.)  A  remarkable  relation  subsists  between  the  periodic  times  of  the 
two  interior  satellites  of  Saturn,  and  thoso  of  the  two  next  in  order  of 
distance;  viz.  that  the  period  of  the  third  (Tethys)  is  double  that  of  the 
first  (Mimas),  and  that  of  the  fourth  (Dione)  double  that  of  the  second 
(Enceladus).  The  coincidence  is  exact  in  either  case  to  about  one-SOOth 
part  of  the  larger  period. 

(551.)  The  satellites  of  Uranus  require  very  powerful  and  perfect  tele- 
scopes for  their  observation.  Two  are,  however,  much  more  conspicuous 
than  the  rest,  and  their  periods  and  distances  from  the  planet  have  been 
ascertained  with  tolerable  certainty.  They  are  the  second  and  fourth  of 
those  set  down  in  the  synoptic  table.  Of  the  remaining  four,  whose  ex- 
istence, though  announced  with  considerable  confidence  by  their  original 
discoverer,  could  hardly  be  regarded  as  fully  demonstrated,  two  only  have 
been  hitherto  reobserved ;  viz.  the  first  of  our  table,  interior  to  the  two 
larger  ones,  by  the  independent  observations  of  Mr.  Lassell,'  and  M. 
Otto  Struve,*  and  the  fourth,  intermediate  between  the  larger  ones,  by 
the  former  of  these  astronomers.  The  remaining  two,  if  future  observa- 
tion should  satisfactorily  establish  their  real  existence,  will  probably  be 
found  to  revolve  in  orbits  exterior  to  all  these. 

(552.)  The  orbits  of  these  satellites  offer  remarkable,  and,  indeed, 
quite  unexpected  and  unexampled  peculiarities.  Contrary  to  the  un- 
broken analogy  of  the  whole  planetary  system  —  whether  of  primaries  or 
secondaries  —  the  planes  of  their  orbits  are  nearly  perpendicular  to  the 
ecliptic,  being  inclined  no  leso  than  78°  58'  to  that  .plane,  and  in  these 
orbits  their  motions  are  retrograde ;  that  is  to  say,  their  positions,  when 
projected  on  the  ecliptic,  instead  of  advancing /rom  west  to  east  round  the 
centre  of  their  primary,  as  is  the  case  with  every  other  planet  and  satel- 
lite, move  in  the  opposite  direction.  Their  orbits  are  nearly  or  quite 
circular,  and  they  do  not  appear  to  have  any  sensible,  or,  at  least,  any 
rapid  motion  of  nodes,  or  to  have  undergone  any  material  change  of  incli- 
nation, in  the  course,  at  least,  of  half  a  revolution  of  their  primary  round 
the  sun.  When  the  earth  is  in  the  plane  of  their  orbits,  or  nearly  so, 
their  apparent  paths  are  straight  lines  or  very  elongated  ellipses,  in  which 

'  September  14th  to  November  9th,  1847. 

*  October  8th  to  December  10th,  1847.  '' 


mm 


Ills  ^■-.■vvi 


^•"••■r 


I 


I 


294 


OUTLINES  OF  ilSTRONOMT. 


n 


case  they  become  invisible,  their  feeble  light  being  effaced  by  the  superior 
light  of  the  planet,  long  before  they  come  up  to  its  disc,  so  that  the  ob- 
servation of  any  eclipses  or  occultations  they  may  undergo  is  quite  out 
of  the  question,  with  our  present  telescopes. 

(558.)  If  the  observation  of  the  satellites  of  Uranus  be  difficult,  those 
of  Neptune,  owing  to  the  immense  distance  of  that  planet,  may  be  readily 
imagined  to  offer  still  greater  difficulties.  Of  the  existence  of  one,  dis- 
covered by  Mr.  Lassell,'  there  can  remain  no  doubt,  it  having  also  been 
observed  by  other  astronomers,  both  in  Europe  and  America.  Acced- 
ing to  M.  Otto  Struve'  its  orbit  is  inclined  to  the  ecliptic  at  the  considera- 
ble angle  of  85° ;  but  whether,  as  in  tho  case  of  the  satellites  of  Uranus, 
the  direction  of  its  motion  be  retrograde,  it  is  not  possible  to  say,  until  it 
shall  have  been  longer  observed. 

»  On  July  8th,  1847. 

*  Astron.  Nachr.  No.  629,  from  his  own  observations,  September  llth  to  Decem- 
ber 20tb,  1847. 


ill  '^ 


•;  .-Kiit 


.-» 


I.      >';}       .fV;,:-!      -f 


.1  -^ 


'■\ 


p 


;!*        ■    ■.     J*.' 


I    11<    i;Oii  ,>i! !,vv^v 


'  .;•>  .J-  rtvl    ^Ji  •5i* 


'  '   .    •■    r  /,- 


.y:t">S<     OP  COMETS. 


295 


II    I  ;'■■•>■!? 


)\<'J>> 


.V'>r 


n  11th  to  Decern- 


CHAPTER  XL 
OF    COMETS. 


I 


GREAT  NUMBER  OF  RECORDED  COMETS.  —  THE  NUMBER  OF  THOSE 
UNRECORDED  PROBABLY  MUCH  GREATER. — GENERAL  DESCRIPTION 
OP  A  COMET.  —  COMETS  WITHOUT  TAILS,  OR  WITH  MORE  THAN 
ONE.  —  THEIR  EXTREME  TENUITY.  —  THEIR  PROBABLE   STRUCTURE. 

—  MOTIONS  CONFORMABLE  TO  THE  LAW  OP  GRAVITY. — ACTUAL 
DIMENSIONS  OF  COMETS.  —  PERIODICAL  RETURN  OP  SEVERAL.  — 
HALLEY'S  comet. — OTHER  ANCIENT   COMETS  PROBABLY   PERIODIC. 

—  ENCKE's  comet. — BIELA's.  —  PAYE's.  —  LEXELL'S.  —  DE  vico's. 
— BRORSEN'S. — PETERS*  S. — GREAT  COMET  OF  1843. — ITS  PROBABLE 
IDENTITY  WITH  SEVERAL  OLDER  COMETS.  —  GREAT  INTFJIEST  AT 
PRESENT  ATTACHED  TO  COMETARY  ASTRONOMY,  AND  ITS  REASONS. 

—  REMARKS  ON  COMETARY  ORBITS  IN  GENERAL. 

(554.)  The  extraordinary  aspect  of  comets,  their  rapid  and  seemingly 
irregular  motions,  the  unexpected  manner  in  which  they  often  burst  upon 
us,  and  the  imposing  magnitudes  which  they  occasionally  assume,  have  in 
all  ages  rendered  them  objects  of  astonishment,  not  unmixed  with  super- 
stitious dread  to  the  uninstructed,  and  an  enigma  to  those  most  conversant 
with  the  wonders  of  creation  and  the  operations  of  natural  causes.  Even 
now,  that  we  have  ceased  to  regard  their  movements  as  irregular,  or  as 
governed  by  other  laws  than  those  which  retain  the  planets  in  their  orbits, 
their  intimate  nature,  and  the  offices  they  perform  in  the  economy  of  our 
system,  are  as  much  unknown  as  ever.  No  distinct  and  satisfactory 
account  has  yet  been  rendered  of  those  immensely  voluminous  append- 
ages which  they  bear  about  with  them,  and  which  are  known  by  the  name 
of  their  tails,  (though  improperly,  since  they  often  precede  them  in  their 
motions,)  any  more  than  of  several  other  singularities  which  they 
present. 

(555.)  The  number  of  comets  which  have  been  astronomically  observed, 
or  of  which  notices  have  been  recorded  in  history,  is  very  great,  amount- 


c;:: 


fin 


V'Jf 


r^ 


296 


OUTLINES  OF  ASTRONOMT. 


ing  to  several  hundreds ; '  and  \vhen  we  consider  that  in  the  earlier  ages 
of  astronomy,  and  indeed  in  more  recent  times,  before  the  invention  of 
the  telescope,  only  large  and  conspicuous  ones  were  noticed ;  and  that, 
since  duo  attention  has  been  paid  to  the  subject,  scarcely  a  year  has  passed 
without  the  observation  of  one  or  two  of  these  bodies,  and  that  sometimes 
two  and  even  three  have  appeared  at  once ;  it  will  be  easily  supposed  that 
their  actual  number  must  be  at  least  many  thousands.  Multitudes, 
indeed;  must  escape  all  observation,  by  reason  of  their  paths  traversing 
only  that  part  of  the  heavens  which  is  above  the  horizon  in  the  daytime. 
Comets  so  circumstanced  can  only  become  visible  by  the  rare  coincidence 
of  a  total  eclipse  of  the  sun,  —  a  coincidence  which  happened,  as  related 
by  Seneca,  sixty-two  years  before  Christ,  when  a  large  comet  was  actually 
observed  very  near  the  sun.  Several,  however,  stand  on  record  as  having 
been  bright  enough  to  be  seen  with  the  naked  eye  in  the  daytime,  even 
at  noon  and  in  bright  sunshine.  Such  were  the  comets  of  1402,  1582, 
and  1843,  and  that  of  43  b.  c.  which  appeared  during  the  games  cele- 
brated by  Augustus  in  honour  of  Venus  shortly  after  the  death  of  Caesar, 
and  which  the  flattery  of  poets  declared  to  be  the  soul  of  that  hero  taking 
its  place  among  the  divinities. 

(556.)  That  feelings  of  awe  and  astonishment  should  be  excited  by  the 
sudden  and  unexpected  appearance  of  a  great  comet,  is  no  way  surprising; 
being,  in  fact,  according  to  the  accounts  we  have  of  such  events,  one  of 
the  most  imposing  of  all  natural  phenomena.  Comets  consist  for  the  most 
part  of  a  large  and  more  or  less  splendid,  but  ill-defined  nebulous  mass 
of  light,  called  the  head,  which  is  usually  much  brighter  towards  its 
centre,  and  offers  the  appearance  of  a  vivid  nucleus,  like  a  star  or  planet 
From  the  head,  and  in  a  direction  opposite  to  that  in  which  the  sun  ts 
situated  from  the  comet,  appear  to  diverge  two  streams  of  light,  which 
grow  broader  and  more  diffused  at  a  distance  from  the  head,  and  which 
most  commonly  close  in  and  unite  at  a  little  distance  behind  it,  but  some- 
times continue  distinct  for  a  great  part  of  their  course ;  producing  an  effect 
like  that  of  the  trains  left  by  some  bright  meteors,  or  like  the  diverging 
fire  of  a  sky-rocket  (only  without  sparks  or  perceptible  motion.)    This  is 


'  See  catalogues  in  the  Almagest  of  Riccioli ;  Pingre's  Cometographie ;  Delatnbre's 
Astron.  vol.  iii. ;  Astronomische  Abhandlungen,  No.  1,  (which  contains  the  elements 
of  all  the  orbits  of  comets  which  have  been  computed  to  the  time  of  its  publication. 
1823 ;)  also  a  catalogue,  by  the  Rev.  T.  J.  Hussey.  Lond.  &  Ed.  Phil.  Mag.  vol.  ii. 
No.  9,  e(  »eq.  In  a  list  cited  by  Lalande  from  the  1st  vol.  of  the  Tables  de  Berlin, 
700  comets  are  enumeraled.  See  alno  notices  of  the  Astronomical  Society  and  Astron. 
Nachr.  passin).  A  great  many  of  the  more  ancient  comets  are  recorded  in  the  Chiffese 
Annals,  and  in  some  cases  with  sufficient  precision  to  allow  of  the  calculation  of 
rudely  approjftimate  orbits  from  their  motions  so  described. 


EXTREME  TENUITY  OF  COMETS. 


297 


e  earlier  ages 
)  invention  of 
ed;  and  that, 
ear  has  passed 
hat  sometimes 

supposed  that 
Multitudes, 
itbs  traversing 
n  the  daytime, 
ire  coincidence 
incd,  as  related 
et  was  actually 
jcord  as  having 

daytime,  even 
rf  1402,  1532, 
he  games  cclc- 
leath  of  Caesar, 
hat  hero  taking 

3  excited  by  the 
way  surprising; 
events,  one  of 
sist  for  the  most 
nebulous  mass 
iter  towards  its 
a  star  or  planet. 
huh  the  sun  u 
of  ligbt,  which 
lead,  and  which 
nd  it,  but  some- 
iducing  an  effect 
ce  the  diverging 
otion.)    This  is 

phie ;  Delambre's 
tains  the  elements 
of  its  publication. 
Phil.  Mag.  vol.  ii. 
Tables  de  Berlin, 
ociety  and  Astron. 
•ded  in  the  Chiffese 
the  calculation  of 


the  tnil.  This  magnificent  appendage  attains  occasionally  an  immense 
appn'^nt  length.  Aristotle  relates  of  the  tail  of  the  comet  of  371  b.  o., 
that  II  occupied  a  third  of  the  hemisphere,  or  60°;  that  of  A.  D.  1618  is 
stated  to  have  been  attended  by  a  train  no  less  than  104°  in  length.  The 
comet  of  1680,  the  most  celebrated  of  modern  times,  and  on  many  ac- 
counts  the  most  remarkable  of  all,  with  a  head  not  exceeding  in  bright- 
ness a  star  of  the  second  magnitude,  covered  with  its  tail  an  extent  of 
more  than  70°  of  the  heavens,  or,  as  some  accounts  state,  90°;  that  of 
the  comet  of  1769  extended  97°,  and  that  of  the  last  f/reat  comet  (1843) 
was  estimated  at  about  65°  when  longest.  The  figure  (fg.  2,  Plate  II.) 
is  a  representation  of  the  comet  of  1819  —  by  no  means  one  of  the  most 
considerable,  but  which  was,  however,  very  conspicuous  to  the  naked  eye. 

(557.)  The  tail  is,  however,  by  no  means  an  invariable  appendage  of 
comets.  Many  of  the  brightest  have  been  observed  to  have  short  and 
feeble  tails,  and  a  few  great  comets  have  been  entirely  without  them. 
Those  of  1585  and  1763  offered  no  vestige  of  a  tail ;  and  Gassini  describes 
the  comets  of  1665  and  1682  as  being  as  round'  and  as  well  defined  as 
Jupiter.  On  the  other  hand,  instances  are  not  wanting  of  comets  fur- 
nished with  many  tails  or  streams  of  diverging  light.  That  of  1744  had 
DO  less  than  six,  spread  out  like  an  immense  fan,  extending  to  a  distance 
of  nearly  30°  in  length.  The  sm^ll  comet  of  1823  had  two,  making  an 
angle  of  about  160°,  the  brighter  turned  as  usual  from  the  sun,  the  fainter 
towards  it,  or  nearly  so.  The  tails  of  comets,  too,  are  often  somewhat 
curved,  bending,  in  general,  towards  the  region  which  the  comet  has  left, 
as  if  moving  somewhat  more  slowly,  or  as  if  resisted  in  their  course. 

(658.)  The  smaller  comets,  such  as  are  visible  only  in  telescopes,  or 
with  difficulty  by  the  naked  eye,  and  which  are  by  far  the  most  numerous, 
offer  very  frequently  no  appearance  of  a  tail,  and  appear  only  as  round 
or  somewhat  oval  vaporous  masses,  more  dense  towards  the  centre,  where, 
however,  they  appear  to  have  no  distinct  nucleus,  or  anything  which  seems 
entitled  to  be  considered  as  a  solid  body.  Stars  of  the  smallest  magni- 
tudes remain  distinctly  visible,  though  covered  by  what  appears  to.  be  the 
densest  portion  of  their  substance;  although  the  same  stars  would  be 
completely  obliterated  by  a  moderate  fog,  extending  only  a  few  yards  from 
the  surface  of  the  earth.   And  since  it  is  an  observed  fact,  that  even  those 

'  This  description  however  applies  to  the  "  disc"  of  the  head  of  these  comets  as  seen 
in  a  telescope.  Cassini's  expressions  are,  "aussi  rond,  aussi  net,  et  aussi  clair  que 
Jupiter,"  (where  it  is  (o  be  observed  that  the  latter  epithet  must  by  no  means  be  trans- 
lated bright).  To  understand  this  passage  fully,  the  reader  must  refer  to  the  descrip- 
tion given  further  on,  of  the  "disc"  of  Halley's  comet,  after  its  perihelion  passage 
in  1835-6. 


•w.  ••>*■. -All 


298 


OUTLINES  OF  ASTRONOMT. 


I     I M 


m 


larger  comets  which  have  presented  the  appearance  of  a  nucleus  have  yet 
exhibited  no  phases,  though  we  cannot  doubt  that  they  shine  by  the  re- 
flected solar  light,  it  follows  that  even  these  can  only  be  regarded  as  great 
masses  of  thin  vapour,  susceptible  of  being  penetrated  through  their 
whole  substance  by  the  sunbeams,  and  reflecting  them  alike  from  their 
interior  parts  and  from  their  surfaces.  Nor  will  any  one  regard  this  ex- 
planation as  forced,  or  feel  disposed  to  resort  to  a  phosphorescent  quality 
in  the  comet  itself,  to  account  for  the  phenomena  in  question,  when  we 
consider,  (what  will  hereafter  be  shown)  the  enormous  magnitude  of  the 
space  thus  illuminated,  and  the  extremely  small  mass  which  there  is 
ground  to  attribute  to  these  bodies.  It  will  then  be  evident  that  the  most 
unsubstantial  clouds  which  float  in  the  highest  regions  of  our  atmosphere, 
and  seem  at  sunset  to  be  drenched  in  light,  and  to  glow  throughout  their 
whole  depth  as  if  in  actual  ignition,  without  any  shadow  or  dark  side, 
must  be  looked  upon  as  dense  and  massive  bodies  compared  with  the  filmy 
and  all  but  spiritual  texture  of  a  comet.  Accordingly,  whenever  powerful 
telescopes  have  been  turned  on  these  bodies,  they  have  not  failed  to  dispel 
the  illusion  which  attributes  solidity  to  that  more  condensed  part  of  the 
head,  which  appears  to  the  naked  eye  as  a  nucleus ;  though  it  is  true  that 
in  some,  a  very  minute  stellar  point  has  been  seen,  indicating  the  existence 
of  a  solid  body. 

(559.)  It  is  in  all  probability  to  the  feeble  coercion  of  the  elastic  power 
of  their  gaseous  parts,  by  the  gravitation  of  so  small  a  central  mass,  that 
we  must  attribute  this  extraordinary  development  of  the  atmospheres  of 
comets.  If  the  earth,  retaining  its  present  size,  were  reduced,  by  any  in- 
ternal change  (as  by  hollowing  out  its  central  parts)  to  one  thousandth  part 
of  its  actual  mass,  its  coercive  power  over  the  atmosphere  would  be  dimi- 
nished in  the  same  proportion,  and  in  consequence  the  latter  would  expand 
to  a  thousand  times  its  actual  bulk ;  and  indeed  much  more,  owing  to  the 
still  farther  diminution  of  gravity,  by  the  recess  of  the  upper  parts  from 
the  centre.'  An  atmosphere,  however,  free  to  expand  equally  in  all  di- 
rections, would  envelope  the  nucleus  spherically,  so  that  it  becomes  neces- 
sary to  admit  the  action  of  other  causes  t»  account  for  its  enormous  exten- 
sion in  the  direction  of  the  tail,  —  a  subject  to  which  we  shall  presently 
take  occasion  to  recur. 

(560.)  That  the  luminous  part  of  a  comet  is  something  in  the  nature  of 


I  . 


'  Newton  has  calculated  (Princ.  III.  p.  512,)  that  a  globe  of  air  of  ordinary  density 
at  the  earth's  surface,  of  one  inch  in  diameter,  if  reduced  to  the  density  due  to  the 
altitude  above  the  surface  of  one  radius  of  the  earth,  would  occupy  a  sphere  exceeding 
in  radius  the  orbit  of  Saturn.  The  tail  of  a  great  comet  then,  for  aught  we  can  tell, 
may  consist  of  only  a  very  few  pounds  or  even  ounces  of  matter. 


tiii     *i' 


MOTIONS  OF  COMETS. 


299 


in  the  nature  of 


a  smoke,  fog,  or  cloud,  suspended  in  a  transparent  atmosphere,  is  evident 
from  a  fact  which  has  been  often  noticed,  viz. — that  the  portion  of  the  tail 
where  it  comes  up,  and  surrounds  the  head,  is  yet  separate  from  it  by  an 
interval  less  luminous,  as  if  sustained  and  kept  off  from  contact  by  a 
transparent  stratum,  as  we  often  see  one  layer  of  clouds  over  another  with 
a  considerable  clear  space  between.  These  and  most  of  the  other  facts  ob- 
served  in  the  history  of  comets,  appear  to  indicate  that  the  structure  of  a 
comet,  as  seen  in  section  in  the  direction  of  its  length,  must  be  that  of  a 
hollow  envelope,  of  a  parabolic  form,  enclosing  near  its  vertex  the  nucleus 
and  head,  something  as  represented  in  the  annexed  figure.  This  would 
account  for  the  apparent  division  of  the  tail  into  two  principal  lateral 

•     i,      .  ■<    -    ■    -  Fig.  75.  . 


••••■•■•••i« ••••••••• 


branches,  the  envelope  being  oblique  to  the  line  of  sight  at  its  borders, 
and  therefore  a  greater  depth  of  illuminated  matter  being  there  exposed 
to  the  eye.  In  all  probability,  however,  they  admit  great  varieties  of 
structure,  and  among  them  may  very  possibly  be  bodies  of  widely  diffe- 
rent physical  constitution,  and  there  is  no  doubt  that  one  and  the  snme 
comet  at  different  epochs  undergoes  great  changes,  both  in  the  disposition 
of  its  materials  and  in  their  physical  state. 

(561.)  We  come  now  to  speak  of  the  motions  of  comets.  These  are 
apparently  most  irregular  and  capricious.  Sometimes  they  remain  in 
sight  only  for  a  few  days,  at  others  for  many  months ;  some  move  with 
extreme  slowness,  others  with  extraordinary  velocity;  while  not  unfre- 
quently,  the  two  extremes  of  apparent  speed  are  exhibited  by  the  same 
comet  in  different  parts  of  its  course.  The  comet  of  1472  described  an 
arc  of  the  heavens  of  40**  of  a  great  circle'  in  a  single  day.  Some 
pursue  a  direct,  some  a  retrograde,  and  others  a  tortuous  and  very  irregu- 
lar course ;  nor  do  they  confine  themselves,  like  the  planets,  within  any 
certain  region  of  the  heavens,  but  traverse  indifferently  every  part.  Their 
variations  in  apparent  size,  during  the  time  they  continue  visible,  are  no 
less  remarkable  than  those  of  their  velocity ;  sometimes  they  make  their 
first  appearance  as  faint  and  slow  moving  objects,  with  little  or  no  tail ; 

'  1?0°  in  extent  in  the  former  editions.  But  this  was  the  arc  described  in  longitude. 
and  the  comet  at  the  time  referred  to  had  great  north  latitude. 


it^ 


•«*!*■•• 


I 


OUTLINES  OF  ASTRONOMY. 


but  by  degrees  accelerate,  enlarge,  and  throw  out  from  them  this  appeu* 
dago,  which  increases  in  length  and  brightnoHs  till  (as  always  happens  in 
such  cases)  they  approach  the  sun,  and  arc  lost  in  his  >^ani6.  After  a 
time  they  again  emerge,  on  the  other  side,  receding  from  the  sun  with  a 
velocity  at  first  rapid,  but  gradually  decaying.  It  is  for  the  most  part 
after  thus  passing  the  eun,  that  they  shine  forth  in  all  their  splendour, 
and  that  their  tails  acquire  their  greatest  length  and  developoment ;  thus 
indicating  plainly  the  action  of  the  sun's  rays  as  the  exciting  cause  of  that 
extraordinary  emanation.  As  they  continue  to  recede  from  the  sun,  their 
motion  diminishes  and  the  tail  dies  away,  or  is  absorbed  into  the  leu 
which  itself  grows  continually  feebler,  and  is  at  length  altogether  1  , . 
sight  of,  in  by  far  the  greater  number  of  cases  never  to  be  F«^cn  ii'oro. 

(562.)  Without  the  clue  furnished  by  the  theory  of  grnvlUitioii,  tbo 
enigma  of  these  seemingly  irregular  and  capricious  movements  might 
have  remained  for  ever  unresolved.  But  Newton,  having  demonstrated 
the  possibility  of  any  conio  section  whatever  being  described  about  the 
BUD,  by  a  body  rpvolving  under  the  dominion  of  that  law,  immediately 
perceived  the  applicability  of  the  general  proposition  to  the  cado  of  come* 
tary  orbits;  and  the  great  comet  of  1G80,  one  of  the  most  remarkable  on 
record,  both  for  the  immense  length  of  its  tail  and  for  the  excessive  close- 
ness of  its  approach  to  tbo  sun  (within  one-sixth  of  the  diameter  of  that 
luminary),  afforded  him  an  excellent  opportunity  for  the  trial  of  his 
theory.  The  succchs  of  the  attempt  wn^  complete.  He  ascertained  that 
this  comet  described  about  the  sun  as  its  focus  an  elliptic  orbit  of  so  great 
an  excentricity  as  to  bo  undistinguishable  from  a  parabola,  (which  is  the 
extreme,  or  limiting  form  of  the  ellipse  when  the  axis  becomes  infinite,) 
and  that  in  this  orbit  the  areas  described  about  the  sun  were,  as  in  the 
planetary  ellipses,  proportional  to  the  times.  The  representation  of  the 
apparent  motions  of  this  comet  by  such  an  orbit,  throughout  its  whole 
observed  course,  was  found  to  be  as  satisfactory  ns  those  of  the  motions 
of  the  planets  in  their  nearly  circular  paths.  Kivra  ihat  time  it  became 
a  received  truth,  that  the  motions  of  coroLi.s  n^-c  u  <.y.lated  b)  tuo  same 
general  laws  as  those  of  the  planets — the  diliercnce  of  the  cases  consisting 
only  in  the  extravagant  elongation  of  their  ellipses,  and  in  the  absence 
of  any  limit  to  the  inclinations  of  their  planes  to  that  of  the  ecliptic — or 
any  general  coincidence  in  the  direction  of  their  motions  from  west  to 
•j^iat,  r»*Iier  thun  from  east  to  west,  like  what  is  observed  among  the 
piaMi.-;. 

(•/63.)  It  is  a  problem  of  pure  geometry,  from  the  general  laws  of 
elliptic  or  parabolic  motion,  to  find  the  situation  and  dimensions  of  the 
ellipse  or  parabola  which  shall  represent  the  motion  of  any  given  comet. 


MOTIONS  OP   COMETS. 


801 


I  ibis  appen- 
ra  kappoDs  in 
D6.     After  a 
lO  sun  with  a 
bo  most  part 
Qir  splendour, 
pomont;  thus 
;  cause  of  that 
the  sun,  their 
ito  the  be  ii. 
Itogcthcr  1m 
.)en  \\'nt\ 
ravil  livJii,  the 
cnients  might 
demonstrated 
bed  about  the 
IT,  immediately 
5  caac  of  come- 
rcmarkable  on 
izcessive  close- 
jameter  of  that 
trial  of  his 
scertaincd  that 
)it  of  so  great 
[which  is  the 
omes  infinite,) 
rere,  as  in  the 
intation  of  the 
lout  its  whole 
if  the  motions 
me  it  became 
bj  biio  same 
ases  consisting 
the  absence 
e  ecliptic — or 
from  west  to 
ed  among  the 

neral  laws  of 
ensions  of  the 
given  comet. 


In  general,  throe  oompleto  ubsrrvations  uf  il«  right  usoension  and  dcclina* 
tion,  with  the  times  at  which  tliuy  were  ni««ie,  suffice  for  the  solutiun  of 
this  problem,  (which  is,  ho\  ''vcr,  by  i. ,  .iwmB  un  easy  one,)  und  fur  tho 
determination  of  the  elements  of  tho  orbit.  Thc^'  coaaiiit,  mutatis  ni**^ 
tandix,  of  the  same  data  as  are  required  for  tho  cnmputatich  of  the  mu- 
tion  of  a  planet;  (that  is  to  say,  tho  longitude  of  tliu  periliolion,  tlmt  of 
the  ascending  node,  the  inclination  to  the  ecliptic,  tho  semiaxiH,  (<f«ccn- 
triii^y,  and  time  of  perihelion  passage,  as  also  whether  the  notion  is 
lirr'  t  or  retrograde;)  and,  onoe  determined,  it  becomes  very  (tuty  to  com- 
l).,u  ihem  with  the  whole  observed  course  of  the  comet,  hy  a  process 
cxacily  similar  to  that  of  art.  502,  and  thus  at  once  to  ascertain  their 
correctness,  and  to  put  to  the  severest  trial  tho  truth  of  those  general 
laws  on  which  all  such  calculations  are  founded. 

(564.)  For  the  most  part,  it  is  found  that  the  motions  of  com  on  may 
bo  sufficiently  well  represented  by  parabolic  orbits,  —  that  is  to  say, 
ellipses  whose  axes  are  of  infinite  length,  or,  at  least,  so  vor  ^  long  that 
no  appreciable  error  in  tho  calculation  of  their  motions,  during  all  the 
tiino  they  continue  visible,  would  be  incurred  by  supposing  thor  i  actually 
inhuite.  Tho  parabola  is  that  conic  section  which  is  the  limit  between 
the  ellipse  on  the  one  hand,  which  returns  into  itself,  and  tho  hyperbola 
on  tho  other,  which  runs  out  to  infinity.  A  comet,  therefore;  which 
should  describe  an  elliptic  path,  however  long  its  axis,  must  have  visited 
the  sun  before,  and  must  again  return  (unless  disturbed)  in  some  ictcr- 
ininatc  period, — but  should  its  orbit  be  of  the  hyperbolic  character,  when 
once  it  had  passed  its  perihelion,  it  could  never  more  return  within  tho 
sphere  of  our  observation,  but  must  run  off  to  visit  other  systems,  or  be 
lost  in  tho  immensity  of  space.  A  very  few  comets  have  been  ascertained 
to  move  in  hyperbolas',  but  many  more  in  ellipses.  These  latter,  in  so 
far  as  their  orbits  can  remain  unaltered  by  the  attractions  of  the  planets, 
must  bo  regarded  as  permanent  members  of  our  system. 

(505.)  We  must  now  say  a  few  words  on  tho  actual  dimensions  of 
comets.  The  calculation  of  the  diameters  of  their  heads,  and  the  lengths 
and  breadths  of  their  tails,  offers  not  the  slightest  difliculty  when  once 
the  elements  of  their  orbits  are  known,  for  by  these  we  know  their  real 
distances  from  the  earth  at  any  time,  and  the  true  direction  of  the  tail, 
which  we  see  only  foreshortened.  Now  calculations  instituted  on  these 
principles  lead  to  the  surprising  faot,  that  the  comets  are  by  far  the  most 
voluminous  bodies  in  our  system.  The  following  are  the  dimensions  of 
some  of  those  which  have  boon  made  the  subjects  of  such  inquiry. 

'For  example,  that  of  1723,  calculated  by  Burckhardt ;  that  of  1771,  by  both  Burck 
hardt  and  Encke ;  and  the  second  coroet  of  1818,  by  Rosenberg  and  Schwabe. 


•  •^  "My 

» 


» 


C 

•A' 


*r\ 

».••,.  n-, 


g*H<iHil— 


■•^O' 

'•-M**^ 


302 


OUTLINES   OF  ASTRONOMY. 


(566.)  The  tail  of  the  great  comet  of  1680,  immediately  after  its  peri- 
helion passage,  was  found  by  Newton  to  have  no  less  than  20000000  of 
leagues  in  length,  and  to  have  occupied  only  two  days  in  its  emission 
from  the  comet's  body !  a  decisive  proof  this  of  its  being  darted  forth  by 
some  active  force,  the  origin  of  which,  to  judge  from  the  direction  of  the 
tail,  must  be  sought  in  the  sun  itself.  Its  greatest  length  amounted  to 
41000000  leagues,  a  length  much  exceeding  the  whole  interval  between 
the  sun  and  earth.  The  tail  of  the  comet  of  1769  extended  16000000 
leagues,  and  that  of  the  great  comet  of  1811,  36000000.  The  portion 
of  the  head  of  this  last,  comprised  within  the  transparent  atmospheric  en- 
velope which  separated  it  from  the  tail,  was  180000  leagues  in  diameter. 
It  is  hardly  conceivable,  that  matter  once  projected  to  such  enormous  dis- 
tances should  ever  be  collected  again  by  the  feeble  attraction  of  such  a 
body  as  a  comet — a  consideration  which  accounts  for  the  surmised  pro- 
gressive diminution  of  the  tails  of  such  as  have  been  frequently  observed. 

(567.)  The  most  remarkable  of  those  comets  which  have  been  ascer- 
tained to  move  in  elliptic  orbits  is  that  of  Halley,  so  called  from  the  cele- 
brated Edmund  Halley,  who,  on  calculating  its  elements  from  its  perihelion 
passage  in  1682,  when  it^appeared  in  great  splendour,  with  a  tail  30°  in 
lengtl),  was  led  to  conclude  its  identity  with  the  great  comets  of  1531  and 
1607,  whose  elements  he  had  also  ascertained.  The  intervals  of  these 
successive  apparitions  being  75  and  76  years,  Halley  was  encouraged  to 
predict  its  reappearance  about  the  year  1759.  So  remarkable  a  predic- 
tion could  not  fail  to  attract  the  attention  of  all  astronomers,  and,  as  the 
time  approached,  it  became  extremely  interesting  to  know  whether  the 
attractions  of  the  larger  planets  might  not  materially  interfere  with  its 
orbitual  motion.  The  computation  of  their  influence  from  the  Newtonian 
law  of  gravity,  a  most  difficult  and  intricate  piece  of  calculation,  was 
undertaken  and  accomplished  by  Clairaut,  who  found  that  the  action  of 
Saturn  would  retard  its  return  by  100  days,  and  that  of  Jupiter  by  no 
less  than  518,  making  in  all  618  days,  by  which  the  expected  return 
would  happen  later  than  on  the  supposition  of  its  retaining  an  unaltered 
period, — ^and  that,  in  short,  the  time  of  the  expected  perihelion  passage 
would  take  place  within  a  month,  one  way  or  other,  of  ths  middle  of 
April,  1759. — It  actually  happened  on  the  12th  of  March  in  that  year. 
Its  next  return  was  calculated  by  several  eminent  geometers',  and  fixed 
successively  for  the  4th,  the  7th,  the  11th,  and  the  26th  of  November, 
1835 ;  the  two  latter  determinations  appearing  entitled  to  the  higher  de- 
gree of  confidence,  owing  partly  to  the  more  complete  discussion  bestowed 
on  the  observations  of  1682  and  1759,  and  partly  to  the  continually  im- 

'  Darnoiseau,  Fontecoulant,  Rosenberger,  and  Lehmann. 


HALLEY  S  COMET. 


303 


proving  state  of  our  knowledge  of  the  methods  of  estimating  the  dis- 
turbing effect  of  the  several  planets.  The  last  of  these  predictions,  that 
of  M.  Lehmann,  was  published  on  the  25th  of  July.  On  the  5th  of 
August  the  comet  first  became  visible  in  the  clear  atmosphere  of  Rome 
as  an  exceedingly  faint  telescopic  nebula,  within  a  degree  of  its  place  as 
predicted  by  M.  Rosenberger  for  that  day.  On  or  about  the  20th  of 
August  it  became  generally  visible,  and,  pursuing  very  nearly  its  calcu- 
lated path  among  the  stars,  passed  its  perihelion  on  the  16th  of  November; 
after  which,  its  course  carrying  it  south,  it  ceased  to  be  visible  in  Europe, 
though  it  continued  to  be  conspicuously  so  in  the  southern  hemisphere 
throughout  February,  March,  and  April,  1836,  disappearing  finally  on  the 
5th  of  May. 

(568.)  Although  the  appearance  of  this  celebrated  comet  at  its  last 
apparition  was  not  such  as  might  be  reasonably  considered  likely  to  excite 
lively  sensations  of  terror,  even  in  superstitious  ages,  yet,  having  been  an 
object  of  the  most  diligent  attention  in  all  parts  of  the  world  to  astrono- 
mers, furnished  with  telescopes  very  far  surpassing  in  power  those  which 
Lad  been  applied  to  it  at  its  former  appearance  in  1759,  and  indeed  to  any 
of  the  greater  comets  on  record,  the  opportunity  thus  afforded  of  studying 
its  physical  structure,  and  the  extraordinary  phsenomena  which  it  pre- 
sented when  so  examined,  have  rendered  this  a  memorable  epoch  in  cometic 
history.  Its  first  appearance,  while  yet  very  remote  from  the  sun,  was 
that  of  a  small  round  or  somewhat  oval  nebula,  quite  destitute  of  tail,  and 
having  a  minute  point  of  more  concentrated  light  excentrically  situated 
within  it.  It  was  not  before  the  2d  of  October  that  the  tail  began  to  be 
developed,  and  thenceforward  increased  pretty  rapidly,  being  already  4° 
or  5°  long  on  the  5th.  It  attained  its  greatest  apparent  length  (about 
20°)  on  the  15th  of  October.  From  that  time,  though  not  yet  arrived 
at  its  perihelion,  it  decreased  with  such  rapidity,  that  already  on  the  29th 
it  was  only  3°,  and  on  November  the  5th  2  J°  in  length.  There  is  every 
reason  to  believe  that  before  the  perihelion,  the  tail  had  altogether  dis- 
appeared, as,  though  it  continued  to  be  observed  at  Pulkowa  up  to  the 
very  day  of  its  perihelion  passage,  no  mention  whatever  is  made  of  any' 
tail  being  then  seen. 

(569.)  By  far  the  most  striking  phaenomena,  however,  observed  in  this 
part  of  its  career,  were  those  which,  commencing  simultaneously  with  the 
growth  of  the  tail,  connected  themselves  evidently  with  the  production  of 
that  appendage  and  its  projection  from  the  head.  On  the  2d  of  October 
(the  very  day  of  the  first  observed  commencement  of  the  tail)  the  nucleus, 
which  had  been  faint  and  small,  was  observed  suddenly  to  have  become 
much  brighter,  and  to  be  in  the  act  of  throwing  out  a  jet  or  stream  of 


'l*Mtt«Ma 


^"tfa-mnrg 


I 


804 


OUTLINES   OF  ASTRONOMY. 


light  from  its  anterior  part,  or  that  turned  towards  the  sun.  This  ejection 
after  ceasing  awhile  was  resumed,  and  with  much  greater  apparent  vio- 
lence, on  the  8th,  and  continued,  with  occasional  intermittences,  so  long 
as  the  tail  itself  continued  visible.  Both  the  form  of  this  luminous  ejec- 
tion, and  the  direction  in  which  it  issued  from  the  nucleus,  meanwhile 
underwent  singular  and  capricious  alterations,  the  different  phases  suc- 
ceeding each  other  with  such  rapidity  that  on  no  two  successive  nights 
were  the  appearances  alike.  At  one  time  the  emitted  jet  was  single,  and 
confined  within  narrow  limits  of  divergence  from  the  nucleus.  At  others 
it  presented  a  fan-shaped  or  swallow-tailed  form,  analogous  to  that  of  a 
gas-flame  issuing  from  a  flattened  orifice :  while  at  others  again  two,  three, 
or  even  more  jets  were  darted  forth  in  different  directions.'  (See  figures 
a,  h,  c,  dy  plate  I.,  fig.  4,  which  represent,  highly  magnified,  the  appear- 
ances of  the  nucleus  with  its  jets  of  light,  on  the  8th,  9th,  10th,  and  12th 
of  October,  and  in  which  the  direction  of  the  anterior  portion  of  the  head, 
or  that  fronting  the  sun,  is  supposed  alike  in  all,  viz.  towards  the  upper 
part  of  the  engraving.  In  these  representations  the  head  itself  is  omitted, 
the  scale  of  the  figures  not  permitting  its  introduction :  e  represents  the 
nucleus  and  head  as  seen  October  9th  on  a  less  scale.)  The  direction  of 
the  principal  jet  was  observed  meanwhile  to  oscillate  to  and  fro  on  either 
side  of  a  line  directed  to  the  sun  in  the  manner  of  a  compass-needle  when 
thrown  into  vibration  and  oscillating  about  a  mean  position,  the  change 
of  direction  being  conspicuous  even  from  hour  to  hour.  These  jets, 
though  very  bright  at  their  point  of  emanation  from  the  nucleus,  faded 
rapidly  away,  and  became  diffused  as  they  expanded  into  the  coma,  at  the 
same  time  curving  backwards  as  streams  of  steam  or  smoke  would  do,  if 
thrown  out  from  narrow  orifices,  more  or  less  obliquely  in  opposition  to  a 
powerful  wind,  against  which  they  were  unable  to  make  way,  and  ulti- 
mately yielding  to  its  force,  so  as  to  be  drifted  back  and  confounded  in  a 
vaporous  train,  following  the  general  direction  of  the  current.' 

(570.)  Reflecting  on  these  phsenomena,  and  carefully  considering  the 
evidence  afforded  by  the  numerous  and  elaborately  executed  drawings 
which  have  been  placed  on  record  by  observers,  it  seems  impossible  to 
avoid  the  following  conclusions.    1st.  That  the  matter  of  the  nucleus  of 


'  See  the  exquisite  lithographic  representations  of  these  phenomena  by  Bessel. 
Astron.  Nachr .  No.  302,  and  the  fine  series  by  Schwabe  in  No.  297  of  that  collec- 
tion, as  also  the  magnificent  drawings  of  Struve,  from  which  our  figures  a,  6,  c,  d,  are 
copies. 

'  On  this  point  Schwabe's  and  Bessel's  drawings  are  very  express  and  unequiv- 
ocal. Struve's  attention  seems  to  have  been  more  especially  directed  to  the  scrutiny 
of  the  nucleus. 


halley's  comet. 


805 


ires  a,  b,  c,  d,  are 


a  comet  is  powerfully  excited  and  dilated  into  a  vaporous  state  by  the 
action  of  the  sun's  rays,  escaping  in  streams  and  jets  at  those  points  of  its 
surface  which  oppose  the  least  resistance,  and  in  all  probability  throwing 
that  surface  or  the  nucleus  itself  into  irregular  motions  by  its  reaction  in 
the  act  of  so  escaping,  and  thus  altering  its  direction.  i 

2dly.  That  this  process  chiefly  takes  place  in  that  portion  of  the 
nucleus  which  is  turned  towards  the  sun ;  the  vapour  escaping  chiefly  in 
that  direction. 

3dly.  That  when  so  emitted,  it  is  prevented  from  proceeding  in  the 
direction  originally  impressed  upon  it,  by  some  force  directed  from  the 
sun,  drifting  it  back  and  carrying  it  out  to  vast  distances  behind  the 
nucleus,  forming  the  tail  or  so  much  of  the  tail  as  can  be  considered  as 
consisting  of  material  substance. 

4thly.  That  this  force,  whatever  its  nature,  acts  unequally  on  the  ma- 
terials of  the  comet,  the  greater  portion  remaining  unvaporized,  and  a 
considerable  part  of  the  vapour  actually  produced,  remaining  in  its  neigh- 
bourhood, forming  the  head  and  coma. 

5thly.  That  the  force  thus  acting  on  the  materials  of  the  tail  cannot 
possibly  be  identical  with  the  ordinary  gravitation  of  matter,  being  centri- 
fugal or  repulsive,  as  respects  the  sun,  and  of  an  energy  very  far  exceeding 
the  gravitating  force  towards  that  luminary.  This  will  be  evident  if  we 
consider  the  enormous  velocity  with  which  the  matter  of  the  tail  is  carried 
backwards,  in  opposition  both  to  the  motion  which  it  had  as  part  of  the 
nucleus,  and  to  that  which  it  acquired  in  the  act  of  its  emission,  both 
which  motions  have  to  be  destroyed  in  the  first  instance,  before  any  move- 
ment in  the  contrary  direction  can  be  impressed. 

6thly.  That  unless  the  matter  of  the  tail  thus  repelled  from  the  sun  be 
retained  by  a  peculiar  and  highly  energetic  attraction  to  the  nucleus,  dif> 
fering  from  and  exceptional  to  the  ordinary  power  of  gravitation,  it  must 
leave  the  nucleus  altogether ;  being  in  efiiect  carried  far  beyond  the  coer- 
cive power  of  so  feeble  a  gravitating  force  as  would  correspond  to  the 
minute  mass  of  the  nucleus ;  and  it  is  therefore  very  conceivable  that  a 
comet  may  lose,  at  every  approach  to  the  sun,  a  portion  of  that  peculiar 
matter,  whatever  it  be,  on  which  the  production  of  its  tail  depends,  the 
remainder  being  of  course  less  excitable  by  the  solar  action,  and  more 
impassive  to  his  rays,  and  therefore,  pro  tanto,  more  nearly  approximating 
to  the  nature  of  the  planetary  bodies. 

(571.)  After  the  perihelion  passage,  the  comet  was  lost  sight  of  for 
upwar(^s  of  two  months,  and  at  its  reappearance  (on  the  24th  of  January 
1836)  presented  itself  under  quite  a  diflerent  aspect,  having  in  the  in- 
terval evidently  undergone  some  great  physical  change  which  had  operated 
20 


'•^i»  1^ 


irvTi 


if;.*  "^-'^wll 

l*«fi»  •  "fern,* 
£"•.11  :.'i*»«« 


t 

i 


806 


OUTLINES  OP  ASTRONOMY. 


an  entire  transformation  in  its  appearance.  It  no  longer  presented  any 
vestige  of  tail,  but  appeared  to  the  naked  eye  as  a  hazy  star  of  about  the 
fourth  or  fifth  magnitude,  and  in  powerful  telescopes  as  a  small,  round, 
well'defined  disc,  rather  more  than  2'  in  diameter,  surrounded  with  a 
nebulous  chevelure  or  coma  of  much  greater  extent.  Within  the  disc, 
and  somewhat  excentrically  situated,  a  minute  but  bright  nucleus  appeared, 
from  which  extended  towards  the  posterior  edge  of  the  disc  (or  that  remote 
from  the  sun)  a  short  vivid  luminous  ray.  (See  fig.  4  of  pi.  I.)  As  the 
comet  receded  from  the  sun,  the  coma  speedily  disappeared,  as  if  absorbed 
into  the  disc,  which,  on  the  other  hand,  increased  continually  in  dimen- 
sions, and  that  with  such  rapidity,  that  in  the  week  elapsed  from  January 
25th  to  February  1st,  (calculating  from  micrometrical  measures,  and  from 
the  known  distance  of  the  comet  from  the  earth  on  those  days)  the  actual 
volume  or  real  solid  content  of  the  illuminated  space  had  dilated  in  the 
ratio  of  upwards  of  40  to  1.  And  so  it  continued  to  swell  out  with  un- 
diminished rapidity,  until  from  this  cause  alone  it  ceased  to  be  visible,  the 
illumination  becoming  fainter  as  the  magnitude  increased ;  till  at  length 
the  outline  became  undistinguishable  from  simple  want  of  light  to  trace 
it.  While  this  increase  of  dimension  proceeded,  the  form  of  the  disc 
passed,  by  gradual  and  successive  additions  to  its  length  in  the  direction 
opposite  to  the  sun,  to  that  of  a  paraboloid,  as  represented  in  g,  fig.  4, 
plate  I.,  the  anterior  curved  portion  preserving  its  planetary  sharpness, 
but  the  base  being  faint  and  ill-defined.  It  is  evident  that  had  this  pro- 
cess continued  with  sufficient  light  to  render  the  result  visible,  a  tail  would 
have  been  ultimately  reproduced;  but  the  increase  of  dimension  being 
accompanied  with  diminution  of  brightness,  a  short,  imperfect,  and  as  it 
were  rudimentary  tail  only  was  formed,  visible  us  such  for  a  few  nights  to 
the  naked  eye,  or  in  a  low  magnifying  telescope,  and  that  only  when  the 
comet  itself  had  begun  to  fade  away  by  reason  of  its  increasing  distance. 
(572.)  While  the  parabolic  envelope  was  thus  continually  dilating  and 
growing  fainter,  the  nucleus  underwent  little  change,  but  the  ray  proceed- 
ing from  it  increased  in  length  and  comparative  brightness,  preserving  all 
the  time  its  direction  along  the  axis  of  the  paraboloid,  and  offering  none 
of  those  irregular  and  capricious  phaenomena  which  characterized  the  jets 
of  light  emitted  anteriorly,  previous  to  the  perihelion.  If  the  office  of 
those  jets  was  to  feed  the  tail,  the  converse  office  of  conducting  back  its 
successively  condensing  matter  to  the  nucleus  would  seem  to  be  that  of 
the  ray  now  in  question.  By  degrees  this  also  faded,  and  the  last  appear- 
ance presented  by  the  comet  was  that  which  it  off^ired  at  its  first  appear- 
ance  in  August ;  viz.  that  of  a  small  round  nebula  with  a  bright  point  in  | 
or  near  the  centre. 


OTHER  PERIODICAL   COMETS. 


SOT 


(573.)  Besides  the  comet  of  Halley,  several  other  of  the  great  comets 
recorded  in  history  have  been  surmised  with  more  or  less  probability  to 
return  periodically,  and  therefore  to  move  in  elongated  ellipses  around  the 
sun.  Such  is  the  great  comet  of  1680,  whose  period  is  estimated  at  575 
years,  and  which  is  considered,  with  the  highest  appearance  of  probability, 
to  be  identical  with  a  magnificent  comet  observed  at  Constantinople  and 
in  Pales  vie,  and  referred  by  contemporary  historians,  both  European  and 
Chinese,  to  the  year  A.  D.  1105 ;  with  that  of  A.  D.  575,  which  was  seen 
at  noon-day  close  to  the  sun ;  with  the  comet  of  43  b.  c,  already  spoken 
of  as  having  appeared  after  the  death  of  Csesar,  and  which  was  also 
observed  in  the  day-time ;  and  finally  with  two  other  comets,  mention  of 
which  occurs  in  the  Sibylline  Oracles,  and  in  a  passage  of  Homer,  and 
which  are  referred,  as  well  as  the  obscurity  of  chronology  and  the  indica- 
tions themselves  will  allow,  to  the  years  618  and  1194  b.  o.  It  is  to  the 
assumed  near  approach  of  this  comet  to  the  earth  about  the  time  of  the 
Deluge,  that  Whiston  ascribed  that  overwhelming  tide  wave  to  whose 
agency  his  wild  fancy  ascribed  that  great  catastrophe — a  speculation,  it  is 
needless  to  remark,  purely  visionary. 

(574.)  Another  great  comet,  whose  return  in  the  year  actually  current 
(1848)  has  been  considered  by  more  than  one  eminent  authority  in  this 
department  of  astronomy '  highly  probable,  is  that  of  1556,  to  the  terror 
of  whose  aspect  some  historians  have  attributed  the  abdication  of  the 
Emperor  Charles  Y.  This  comet  is  supposed  to  be  identical  with  that 
of  1264,  mentioned  by  many  historians  as  a  great  comet,  and  observed 
also  in  China,  —  the  conclusion  in  this  case  resting  upon  the  coincidence 
of  elements  calculated  on  the  observations,  such  as  they  are,  which  have 
been  recorded.  On  the  subject  of  this  coincidence  Mr.  Hind  has  recently 
entered  into  many  elaborate  calculations,  the  result  of  which  is  strongly 
iu  favour  of  the  supposed  identity.  This  probability  is  farther  increased 
by  the  fact  of  a  comet  with  a  tail  of  40°  and  a  head  bright  enough  to  be 
visible  after  sunrise  having  appeared  in  A.  d.  975;  and  of  two  others 
having  been  recorded  by  the  Chinese  annalists  in  A.  D.  395  and  104.  It 
is  true  that  if  these  be  the  same,  the  mean  period  would  be  somewhat 
short  of  292  years.  But  the  effect  of  planetary  perturbation  mijht 
reconcile  even  greater  difiierences,  and  though  up  to  the  time  of  our 
writing  no  such  comet  has  yet  been  observed,  at  least  another  year  must 
elapse  before  its  return  can  be  pronounced  hopeless.  „ 

(675.)  In  1661,  1532,  1402,  1145,  891,  and  243  great  comets 
appeared — that  of  1402  being  bright  enough  to  be  seen  at  noon-day.  A 
period  of  129  years  would  conciliate  all  these  appearances,  and  should 

'  Fingrc,  Cotnetographic,  i.  411.    Lolande,  Astr.  3185. 


«l         ~" 


nfTm 


808 


OUTLINES   OF  ASTRONOMY. 


I 


have  brought  back  the  comet  in  1789  or  1790  (other  circuro stances 
agreeing.)  That  no  such  comet  was  observed  about  that  time  is  no  proof 
that  it  did  not  return,  since,  owing  to  the  situation  of  its  orbit,  had  the 
perihelion  passage  taken  place  in  July  it  might  have  escaped  observation. 
Mcchain,  indeed,  from  an  elaborate  discussion  of  the  observations  of  1532 
and  1661,  came  to  the  conclusion  that  these  comets  were  not  the  same ; 
but  the  elements  assigned  by  Olbers  to  the  earlier  of  them,  differ  so 
widely  from  those  of  Meehain  for  the  same  comet  on  the  one  hand,  and 
agree  so  well  with  those  of  the  last  named  astronomer  for  the  other,' 
that  we  are  perhaps  justified  in  regarding  the  question  as  not  yet  set  at 
rest. 

(57G.)  We  come  now,  however,  to  a  class  of  comets  of  short  period, 
respecting  whose  return  there  is  no  doubt,  inasmuch  as  two  at  least  of 
them  have  been  identified  as  having  performed  successive  revolutions 
round  the  sun;  have  had  their  return  predicted  already  several  times; 
and  have  on  each  occasion  scrupulously  kept  to  their  appointments.  Tlie 
first  of  these  is  the  comet  of  Encke,  so  called  from  Professor  Encke  of 
Berlin,  who  first  ascertained  its  periodical  return.  It  revolves  in  an 
ellipse  of  great  excenlricity  (though  not  comparable  to  that  of  Halley's,) 
the  plane  of  which  is  inclined  at  an  angle  of  about  13°  22'  to  the  plane 
of  the  ecliptic,  and  in  the  short  period  of  1211  days,  or  about  3]  years. 
This  remarkable  discovery  was  made  on  the  occasion  of  its  fourth  recorded 
appearance,  in  1819.  From  an  ellipse  then  calculated  by  Encke,  its 
return  in  1822  was  predicted  by  him,  and  observed  at  Paramatta,  in  New 
South  Wales,  by  M.  Riimker,  being  invisible  in  Europe :  since  which  it 
has  been  re-predicted  and  re-observed  in  all  the  principal  observatories, 
both  in  the  northern  and  southern  hemispheres,  as  a  phenomenon  of 
regular  occurrence. 

(577.)  On  comparing  the  intervals  between  the  successive  perihelion 
passages  of  this  comet,  after  allowing  in  the  most  careful  and  exact  manner 
for  all  the  disturbances  due  to  the  actions  of  the  planets,  a  very  singular 
fact  has  come  to  light,  viz.  that  the  periods  are  continually  diminishing, 
or,  in  other  words,  the  mean  distance  from  the  sun,  or  the  major  axis  of 
the  ellipse,  dwindling  by  slov/  and  regular  degrees  at  the  rate  of  about 
0*-ll  per  revolution.  This  is  evidently  the  effect  which  would  be  pro- 
duced by  a  resistance  experienced  by  the  comet  from  a  very  rare  ethereal 
medium  pervading  the  regions  la  which  it  moves ;  for  such  resistance,  by 
diminishing  its  actual  velocity,  would  diminish  also  its  centrifugal  force, 
and  thus  give  the  sun  more  power  over  it  to  draw  it  nearer.  Accordingly 
this  is  the  solution  proposed  by  Encke,  and  at  present  generally  received. 

'  See  Schumacher's  Catal.  Astron.  Abhandl.  i. 


DOUBLE   COMET   OF  BIELA. 


309 


for  the  other,' 
s  not  yet  set  at 


It  will,  therefore,  probably  fall  ultimately  into  the  sun,  should  it  not  first 
be  dissipated  altogether, — a  thing  no  way  improbable,  when  the  lightness 
of  its  materials  is  considered. 

(578.)  By  measuring  the  apparent  magnitude  of  this  comet  at  different 
distances  from  the  sun,  and  thence,  from  a  knowledge  of  its  actual  dis- 
tance from  the  earth  at  the  time,  coDcluding  its  real  volume,  it  has  been 
ascertained  to  contract  in  bulk  as  it  approaches  to,  and  to  expand  as  it 
recedes  from,  that  luminary.  M.  Yalz,  who  was  the  first  to  notice  this 
fact,  accounts  for  it  by  supposing  it  to  undergo  a  real  compression  or  con- 
densation of  volume  arising  from  the  pressure  of  an  aethereal  medium  which 
be  conceives  to  grow  more  dense  in  the  sun's  neighbourhood.  But  such 
an  hypothesis  is  evidently  inadmissible,  since  it  would  require  us  to  assume 
the  exterior  of  the  comet  to  be  in  the  nature  of  a  skin  or  bag  impervious 
to  the  compressing  medium.  The  phenomenon  is  analogous  to  the  increase 
of  dimension  above  described  as  observed  in  the  comet  of  Halley  when  in 
the  act  of  receding  from  the  sun,  and  is  doubtless  referable  to  a  similar 
cause,  viz.  the  alternate  conversion  of  evaporable  matter  into  the  states  of 
visible  cloud  and  invisible  gas  by  the  alternating  action  of  cold  and  heat. 
Tills  comet  has  no  tail,  but  offers  to  the  view  only  a  small  ill-defined 
nucleus,  excentrically  situated  within  a  more  or  less  elongated  oval  mass 
of  vapours,  being  nearest  to  that  vertex  which  is  towards  the  sun. 

(579.)  Another  comet  of  short  period  is  that  of  Biela,  so  called  from 
M.  Biela,  of  Josephstadt,  who  first  arrived  at  this  interesting  conclusion 
on  the  occasion  of  its  appearance  in  1826.  It  is  considered  to  be  identi- 
cal with  comets  which  appeared  in  1772, 1805,  &c.,  and  describes  its  very 
oxcentric  ellipse  about  the  sun  in  2410  days  or  about  6f  years ;  and  in  a 
plane  inclined  12°  34'  to  the  ecliptic.  It  appeared  again  according  to  the 
prediction  in  1832,  and  in  1846.  Its  orbit,  by  a  remarkable  coincidence, 
very  nearly  intersects  that  of  the  earth ;  and  had  the  latter  at  the  time  of 
its  passage  in  1832,  been  a  mon.a  in  advance  of  its  actual  place,  it  would 
have  passed  through  the  comet, — a  singular  rencontre,  perhaps  not  un- 
attended with  danger.' 

'  Should  calculation  establish  the  fact  of  a  resistance  experienced  also  by  this  comet, 
the  subject  of  periodical  comets  will  assume  an  extraordinary  degree  of  interest.  It 
cannot  be  doubted  that  many  more  will  be  discovered,  and  by  their  resistance  questions 
will  come  to  be  decided,  such  as  the  followitTg : — What  is  the  law  of  density  of  the  re- 
sisting medium  which  surrounds  the  sun  ?  Is  it  at  rest  or  in  motion  ?  If  the  latter,  in 
wliat  direction  does  it  move  ?  Circularly  round  the  sun,  or  traversing  space  ?  If  cir- 
cularly, in  what  plane  ?  It  is  obvious  that  a  circular  or  vorticose  motion  of  the  ether 
would  accelerate  some  comelt  and  retard  others,  according  as  their  revolution  was,  rela- 
tive to  such  motion,  direct  or  retrograde.  Supposing  the  neighbourhood  of  the  sun  to 
be  filled  with  a  material  fluid,  it  is  not  conceivable  that  the  circulation  of  the  planets  in 


■k 


Rr«  -tout*' 


f 


810 


OUTLINES  OF  ASTRONOMT. 


H 

I.;,    I 


l- 


(580.)  This  comet  is  small  and  hardly  visible  to  the  naked  eye,  even 
when  brightest.  Nevertheless,  as  if  to  make  up  for  its  seeming  insignifi. 
cance  by  the  interest  attaching  to  it  in  a  physical  point  of  view,  it  exhi. 
bited  at  its  last  appearance,  in  1846,  a  phaenomenon  which  struck  every 
astronomer  with  amazement,  as  a  thing  without  previous  example  in  the 
history  of  our  system.'  It  was  actually  seen  to  separate  itself  into  two  dis- 
tinct comets,  which,  after  thus  parting  company,  continued  to  journey  along 
amicably  through  an  arc  of  upwards  of  70°  of  their  apparent  orbit,  keeping 
all  the  while  within  the  same  field  of  view  of  the  telescope  pointed  towards 
them.  The  first  indication  of  something  unusual  being  about  to  take 
place,  might  be,  perhaps,  referred  to  the  19th  of  December,  1845,  when 
the  comet  appeared  pear-shaped,  the  nebulosity  being  unduly  elongated  in 
the  north  following  direction.'  But  on  the  13th  of  January,  at  Wash* 
ington  in  America,  and  on  the  15th  and  subsequently  in  every  part  of 
Europe,  it  was  distinctly  seen  to  have  become  double ;  a  very  small  and 
faint  cometio  body,  having  a  nucleus  of  its  own,  being  observed  appended 
to  it,  at  a  distance  of  about  2'  (in  arc)  from  its  centre,  and  in  a  direction 
forming  an  angle  of  about  328°  with  the  meridian,  running  northwards 
from  the  principal  or  original  comet  (see  art.  204).  From  this  time  tbe 
separation  of  the  two  comets  went  on  progressively,  though  slowly.  On 
the  30th  of  January,  the  apparent  distance  of  the  nucleus  had  increased 
to  3',  on  the  7th  of  February  to  4',  and  on  the  13th  to  5',  and  so  on, 
until  on  the  5th  of  March  the  two  comets  were  separated  by  an  interval 
of  9'  19",  the  apparent  direction  of  the  line  of  junction  all  the  while 
varying  but  little  with  respect  to  the  parallel.' 

(581.)  During  this  separation  very  remarkable  changes  were  observed 
to  be  going  on  both  in  the  original  comet  and  its  companion.    Both  had 

it  for  ages  should  not  have  impressed  upon  it  some  degree  of  rotation  in  their  own 
direction.  And  this  may  preserve  them  from  the  extreme  eflects  of  accumulated 
resistance. — Author. 

'  Perhaps  not  quite  so.  To  say  nothing  of  a  singular  surmise  of  Kepler,  that  two 
great  comets  seen  at  once  in  1618,  might  be  a  single  comet  separated  into  two,  the  fol- 
lowing passage  of  Helvelius  cited  by  M.  Littrow  (Nachr.  564)  does  really  seem  to 
refer  to  some  phsenomenon  bearing  at  least  a  certain  analogy  to  it.  "  In  ipso  disco," 
he  says  (Cometographia,  p.  326)  '*  quatuor  vel  quinque  corpuscula  qu»dam  sive  nu- 
cleos  reliquo  corpore  aliquanto  densiores  ostendebat." 

'  According  to  Mr.  Hind's  observation.    But  there  can  be  little  dr«ubt  that  by  a  mis- 
take of  the  most  common  occurrence,  wHen'no  measure  of  the  position  is  taken,  north] 
following  is  an  error  of  entry  or  printing  for  north  preceding  (n  f  for  n  p).    In  fact,  an  | 
elongation  from  north  following  to  south  preceding  would  agree  with  the  regular  direc- 
tion of  the  tail  and  would  occasion  no  remark. 

*  By  far  the  greater  portion  of  this  increase  of  apparent  distance  was  due  to  the  | 
comet's  increased  proximity  to  the  earth.    The  real  increase  reduced  to  a  distance  ='  I 
of  tbe  comet  was  at  the  rate  of  about  3"  per  diem. 


DOUBLE  COMET   OV  BIELA. 


811 


nuclei,  both  had  short  tails,  parallel  in  direotion,  and  nearly  perp  "loular 
to  the  line  of  junction,  but  vrhereas  at  its  first  observation  on  January 
13tb,  the  now  comet  was  extremely  small  and  faint  in  comparison  with 
the  old,  the  difference  both  in  point  of  light  and  apparent  magnitude  di- 
minished.  On  the  10th  of  February,  they  were  nearly  equal,  although 
the  day  before  the  moonlight  had  effaced  the  new  one,  leaving  the  other 
bright  enough  to  be  well  observed.  On  the  14th  and  16th,  however,  the 
new  comet  had  gained  a  decided  superiority  of  light  over  the  old,  pre- 
senting at  the  same  time  a  sharp  and  starlike  nucleus,  compared  by  Lieut. 
Maury  to  a  diamond  spark.  But  this  state  of  things  was  not  to  continue. 
Already,  on  the  IS^h,  the  old  comet  had  regained  its  superiority,  being 
nearly  twice  as  bright  as  its  companion,  and  offering  an  unusually  bright 
and  starlike  nucleus.  From  this  period  the  new  companion  began  to  fade 
away,  but  continued  visible  up  to  the  15th  of  March.  On  the  24th  the 
comet  was  again  single,  and  on  the  22d  of  April  both  had  disappeared. 

(582.)  While  this  singular  interchange  of  light  was  going  forwards, 
indications  of  some  sort  of  communication  between  the  comets  were  exhi- 
bited. The  new  or  companion  comet,  besides  its  tail,  extending  in  a 
direction  parallel  to  that  of  the  other,  threw  out  a  faint  arc  of  light,  which 
extended  as  a  kind  of  bridge  from  the  one  to  the  other;  and  after  the 
restoration  of  the  original  comet  to  its  former  preeminence,  it,  on  its  part, 
threw  forth  additional  rays,  so  as  to  present  (on  the  22d  and  28d  Febru- 
ary) the  appearance  of  a  comet  with  three  faint  tails,  forming  angles  of 
about  120°  with  each  other,  one  of  which  extended  towards  its  com- 
panion.' , 

(583.)  Professor  Plantamour,  director  of  the  observatory  of  Geneva, 
having  investigated  the  orbits  of  both  these  comets  as  separate  and  inde- 
pendent bodies,  from  the  extensive  and  careful  series  of  observations 
made  upon  them,  has  arrived  at  the  conclusion  that  the  increase  of  dis- 
tance between  the  two  nuclei,  at  least  during  the  interval  from  February 
10/A  to  March  22df  was  simply  apparent,  being  due  to  the  variation  of 
distance  from  the  earth,  and  to  the  angle  under  which  their  line  of  junc- 
tion presented  itself  to  the  visual  ray ;  the  real  distance  during  all  that 
interval  (neglecting  small  fractions)  having  been  on  an  average  about 
thirty-nine  times  the  semi-diameter  of  the  earth,  or  less  than  two-thirds 
the  distance  of  the  moon  from  its  centre.  From  this  it  would  appear, 
that  already,  at  this  distance,  the  two  bodies  had  ceased  to  exercise  any 


<c:s 


!*«i:S 


,>»< 


■•4*«, 


•■■i««»i»wi|B 


'  These  last-mentioned  particulars  rest  on  the  testimony  of  Lieutenant  Maury  of 
Washington,  who  had  the  advantage  of  using  a  nine-inch  object-glass  of  Munich 
manufacture.    It  does  not  appear  that  any  large  telescope  was  turned  upon  it  in  Eu 
rope  on  the  dates  in  question. 


312 


OUTLINES  OF  ASTRONOMY. 


perceptible  amount  of  perturbative  gravitation  on  each  other;  as,  indeed, 
from  the  probable  minuteness  of  cometary  masses  we  might  reasonably 
expect.  Calculating  upon  the  elements  assigned  by  him',  we  find  16<'-4 
for  the  interval  of  their  next  perihelion  passages.  And  it  will  be,  there- 
fore, necessary  at  their  next  reappearance,  to  look  out  for  each  comet  as  a 
separate  and  independent  body,  computing  its  place  from  these  elements 
as  if  the  other  had  no  existence.  Nevertheless,  as  it  is  still  perfectly 
possible  that  some  link  of  connection  may  subsist  between  them,  (if,  in- 
deed, by  some  unknown  process  the  companion  has  not  been  actually 
reabsorbed,)  it  will  not  be  advisable  to  rely  on  this  calculation  to  the 
neglect  of  a  most  vigilant  search  throughout  the  whole  neighbourhood  of 
the  more  conspicuous  one,  lest  the  opportunity  should  be  lost  of  pursuing 
to  its  conclusion  the  history  of  this  strange  occurrenct. 

(584.)  A  third  comet  of  short  period  has  still  more  "ecently  been  added 
to  our  list  by  M.  Faye,  of  the  observatory  of  Paris,  -ivho  detected  it  on 
the  22d  of  November  1843.  A  very  few  observations  sufficed  to  show 
that  no  parabola  would  satisfy  the  conditions  of  its  motion,  and  that  to 
represent  them  completely,  it  was  necessary  to  assign  to  it  an  elliptic  orbit 
of  very  moderate  excentricity.  The  calculations  of  M.  Nioolai,  subse- 
quently revised  and  slightly  corrected  by  M.  Leverrier,  have  shown  that 
an  almost  perfect  representation  of  itn  motions  during  the  whole  period 
of  its  visibility  would  be  afforded  by  assuming  it  to  revolve  in  a  period  of 
2717'''68  (or  somewhat  less  than  7i  years)  in  an  ellipse  whose  excen- 
tricity is  0*55596,  and  inclination  to  the  ecliptic  11°  22'  31";  and  taking 
this  for  a  basis  of  further  calculation,  and  by  means  of  these  data  and  the 
other  elements  of  the  orbit  estimating  the  effect  of  planetary  perturbation 
during  the  revolution  now  in  progress,  he  has  fixed  its  next  return  to  the 
perihelion  for  the  3d  of  April  1851,  with  a  probable  error  one  way  or 
other  not  exceeding  one  or  two  days. 

(585.)  The  effect  of  planetary  perturbation  on  the  motion  of  comets 
has  been  more  than  once  alluded  to  in  what  has  been  above  said.  With- 
out going  minutely  into  this  part  of  the  subject,  which  will  be  better  un- 
derstood after  the  perusal  of  a  subsequent  chapter,  it  must  be  obvious, 
that  as  the  orbits  of  comets  are  very  excentric,  and  inclined  in  all  sorts  of 

1  Original  Comet.  Companioiii. 

Perihehon  passage,  1846,  Feb.  1 1  00476 1 1  07 1 1 1  Geneva  h.  t. 

Long,  seniiaxis  major 0*5471002 0-5451271 

Perihelion  distance 9932701 1 99326965 

Angle  of  excentricity  or  whose 

Bine=e 49°  12' 2"'5 49°  6' 14"-4         '    ,►"... 

Inclination 12    34  53  -3 12   34  H  '3 

Node  S2 245    54  38-8 245   56     1  7 

Perihelion 109     2201 109     2  39-6 

Mean  equinox  of  1846,  '0. 


COMETS   OF  LEXELL  AND   DE  VICO. 


818 


angles  to  the  ecliptic,  they  must  in  many  instances,  if  not  actually  inter- 
sect, at  least  pass  very  near  to  the  orbits  of  some  of  the  planets.  We 
hove  already  seen,  for  instance,  that  the  orbit  of  Biela's  comet  so  nearly 
intersects  that  of  the  earth,  that  an  actual  collision  is  not  impossible,  and 
indeed  (supposing  neither  orbit  variable)  must  in  all  likelihood  happen  in 
the  lapse  of  some  millions  of  years.  Neither  are  instances  wanting  of 
comets  having  actually  approached  the  earth  within  comparatively  short 
distances,  as  that  of  1770,  which  on  the  1st  of  July  of  that  year  was 
witin  little  more  than  seven  times  the  moon's  distance.  The  same  eomot 
in  1707  passed  Jupiter  at  a  distance  only  one  58th  of  the  radius  of  that 
planet's  orbit,  and  it  has  been  rendered  extremely  probable  that  it  is  to 
the  disturbance  its  former  orbit  underwent  during  that  appulso  that  we 
owe  its  appearance  within  our  own  range  of  vision.  This  exceedingly  re- 
markable comet  was  found  by  Lcxell  to  describe  an  elliptic  orbit  with  an 
excentricity  of  0*7858,  with  a  periodic  time  of  about  five  years  and  a 
half,  and  in  a  plane  only  1°  84'  inclined  to  the  ecliptic,  having  passed  its 
perihelion  on  the  13th  of  August  1770.  Its  return  of  course  was  eagerly 
expected,  but  in  vain,  for  the  comet  has  never  been  seen  since.  Its  ob- 
servation on  its  first  return  in  1776  was  rendered  impossible  by  the  relar 
tive  situations  of  the  perihelion  and  of  the  earth  at  the  time,  and  before 
another  revolution  could  be  accomplished  (as  has  since  been  ascertained,) 
about  the  23d  of  August  1770,  by  a  singular  coincidence  it  again 


VIZ 


approached  Jupiter  within  one  491st  part  of  its  distance  from  the  sun, 
being  nearer  to  that  planet  by  one-fifth  than  its  fourth  satellite.  -  No 
wonder,  therefore,  that  the  planet's  attraction  (which  at  that  distance 
would  exceed  that  of  the  sun  in  the  proportion  of  at  least  200  to  1) 
should  completely  alter  the  orbit  and  deflect  it  into  a  curve,  not  one  of 
whose  elements  would  have  the  least  resemblance  to  those  of  the  ellipse 
of  Lexell.  It  is  worthy  of  notice  that  by  this  rencontre  with  the  system 
of  Jupiter's  satellites,  none  of  their  motions  suffered  any  perceptible 
derangement,  —  a  sufficient  proof  of  the  smallness  of  its  mass.  Jupiter 
indeed,  seems,  by  some  strange  fatality,  to  be  constantly  in  the  way  of 
comets,  and  to  serve  as  a  perpetual  stumbling-block  to  them. 

(586.)  On  the  22nd  of  August,  1844,  Signer  Do  Vico,  director  of  the 
observatory  of  the  CoUegio  Romano,  discovered  a  comet,  the  motions  of 
which,  a  very  few  observations  sufficed  to  show,  deviated  remarkably  from 
a  parabolic  orbit.  It  passed  its  perihelion  on  the  2nd  of  September,  and 
continued  to  be  observed  until  the  7th  of  December.  Elliptic  elements 
of  this  comet,  agreeing  remarkably  well  with  each  other,  were  accordingly 
calculated  by  several  astronomers  j  from  which  it  appears  that  the  period 
of  revolution  is  about  1900  days,  or  5  J  (5-4357)  years,  which  (supposing 


C''^'*^ 
•«.-»»)' 
^'■■■^f,'^-^ 


>«V««Mi 


814 


OUTLINES  OF  ASTRONOMY. 


I  ^ 


I;        '    !■.») 


its  orbit  undigturbed  in  the  interim)  would  bring  it  back  to  the  perihelion 
on  or  about  the  18th  of  January,  1850.  As  the  aaaemblage  and  com- 
parison of  these  elements  thus  computed  independently,  will  serve  bettor, 
perhaps,  than  any  other  example,  to  aflford  the  student  an  idea  of  the 
degree  of  arithmetical  certainty  capable  of  being  attained  in  this  branch 
of  astronomy,  difficult  and  complex  as  the  calculations  themselves  are,  and 
liable  to  error  as  individual  observations  ^  a  body  so  ill-defined  as  the 
smaller  comets  are  for  the  most  part ;  we  shall  present  thom  in  a  tabular 
form,  as  on  the  next  page :  the  elements  being  as  usual ;  the  time  of  peri- 
helion passage,  longitude  of  the  perihelion,  that  of  the  ascending  node, 
the  inclination  to  the  ecliptic,  semiaxis  and  excentrioity  of  the  orbit,  and 
the  periodic  time. 

This  comet,  when  brightest,  was  visible  to  the  naked  eye,  and  had  a 
small  tail.  It  is  especially  interesting  to  astronomers  from  the  circum- 
stance of  its  having  been  rendered  exceedingly  probable  by  the  researches 
of  M.  Leverrier,  that  it  is  identical  with  one  which  appeared  in  1678  with 
some  of  its  elements  considerably  changed  by  perturbation.  This  comet 
is  further  remarkable,  from  having  been  concluded  by  Messrs.  Laugier 
and  Mauvais,  to  be  identical  with  the  comet  of  1585  observed  by  Tycbo 
Brahe,  and  possibly  also  with  those  of  1748,  1766,  and  1819. 

(587.)  Elliptic  elements  have  in  like  manner  been  assigned  to  the 
comet  discovered  by  M.  Brorsen,  on  the  26th  of  February,  1846,  which, 
like  that  last  mentioned,  speedily  after  its  discovery  began  to  show  evident 
symptoms  of  deviation  from  a  parabola.  These  elements,  with  the  names 
of  their  respective  calculators,  are  as  follow.  The  dates  are  for  February 
1846,  Greenwich  time. 


Computed  by 

Brunnow. 

Hind. 

Van  WUlingen 
and  De  Ilaac. 

Perihelion  Dasaftare 

25"'-  37794 

116°  28'  .S4"-0 

102     39    36-  5 

30     55      6-  5 

3-15021 

0-79363 

2042 

25-'-  33109 

116°  28'  17"-S 

102    45    20-  9 

30    49     3-  6 

3-12292 

0-79771 

2016 

25-«-  02227 

116°  23'  62"-9 

103    31    25-  7 

30    30    30-  2 

2-87052 

0-77313 

1776 

Lonar.  of  Perihelion. 

Long,  of  SI,.,, 

Inclination 

Semiaxis 

£xoentricity 

Period  (davs) 

. _                 

-   '• '*■!-.'.'       %<■,'.'■( 


r,.    J  " 


COMET  OF  DB  VIOO. 


815 


the  perihelion 
luge  and  com- 
ill  serve  bettor, 
an  idea  of  the 
in  this  branch 
iselvcs  are,  and 
-defined  as  the 
3m  in  a  tabular 
lie  time  of  pi^ri- 
scending  node, 
:  the  orbit,  and 


Tan  WIlUnKen 
and  De  Uaac. 


i 


M 
H 


4 


■ 


u 
at 

a 

o 
o 


o 


e 


9t 

O 


^  R  i   s 

T*   «P   S 


s 


130    — 

•I"   w 
•o 

h 


at) 


>.f 


o 


«0 


M 


»«    40 

•"•   «6   PS 
<o   (lb   1^ 


®      w. 


>n 


lO 


e 

eo 


o 


«e  to 

at  t- 

*  '♦'  2  S  «» 

^   U^   o  «   p^ 

CO  o 


w 


CO 

i 


o 


»l 


1-^    « 


cu 

00 


2  5 


S3 


ll 

N 


•A 


«e 


M 


e< 


s 

lA 


64 

00 

>n  lo   00 

oo  tH   a* 

«  «P  s 

CO  e 


K» 


o 


1 1  r 


A   00 

S8  S 


N 


eo 
oo 
2  S  o» 

O    «p    ,-( 
CO   s 


eo 


N 


a 
o 


a 

;2 

'u 
« 


O 
« 

B 
•& 

a 
o 


9 


a 
o 

'i 

.9 


do  ^ 
S  « 
3  5 


'53 

a 
« 

M 


I 

I 

Pi 


f 


rf'l 


'  r 


316 


OUTLINES   OF  ASTRONOMY. 


I'!-:    -l 


i  6 
■)   ''■ 


2 ''  - 


tl 


;li 


This  comet  is  faint,  and  presents  nothing  remarkable  in  its  appearance. 
Its  chief  interest  arises  from  the  great  similarity  of  its  parabolic  elements 
to  those  of  the  comet  of  1532,  the  place  of  the  perihelion  and  node,  and 
the  inclination  of  the  orbit,  being  almost  identical. 

(588.)  Elliptic  eleir^ents  have  also  been  calculated  by  M.  D' Arrest,  for 
a  comet  discovered  by  M.  Peters,  on  the  26th  of  June,  1846,  which  go 
to  assign  it  a  place  among  the  comets  of  short  period,  viz.  5804*-3,  or 
very  nearly  16  years.  The  excentricity  of  the  orbit  is  0*75672,  its  semi- 
axis  6-32066,  and  the  inclination  of  its  plane  to  that  of  the  ecliptic  31°  2' 
14".     This  comet  passed  its  perihelion  on  the  1st  of  June,  1846. 

(589.)  By  far  the  most  remarkable  comet,  however,  which  has  been 
seen  during  the  present  century,  is  that  which  appeared  in  the  spring  of 
1843,  and  whose  tail  became  visible  in  the  twilight  of  the  17th  of  March 
in  England  as  a  great  beam  of  nebulous'  light,  extending  from  a  point 
above  the  western  horizon,  through  the  stars  of  Eridanus  and  Lepus, 
under  the  belt  of  Orion.  This  situation  was  low  and  unfavourable ;  and 
it  was  not  till  the  19th  that  the  head  was  seen,  and  then  only  as  a  faint 
and  ill-defined  nebula,  very  rapidly  fading  on  subsequent  nights.  In 
more  southern  latitudes,  however,  not  only  the  tail  was  seen,  as  a  mag- 
nificent train  of  light  extending  50°  or  60°  in  length  j  but  the  head  and 
nucleus  appeared  with  extraordinary  splendour,  exciting  in  every  country 
where  it  was  seen  the  greatest  astonishment  and  admiration.  Indeed,  all 
descriptions  agree  in  representing  it  as  a  stupendous  spectacle,  such  as  in 
superstitious  ages  would  not  fail  to  have  carried  terror  into  every  bosom. 
In  tropical  latitudes  in  the  northern  hemisphere,  the  tail  appeared  on  the 
3d  of  ]\Iarch,  and  in  Van  Diemen's  Land,  so  early  as  the  1st,  the  comet 
having  passed  its  perihelion  on  the  27th  of  February.  Already  on  the 
3d  the  head  was  so  far  disengaged  from  the  immediate  vicinity  of  the  sun, 
as  to  appear  for  a  short  time  above  the  horizon  after  sunset.  On  this  day 
when  viewed  through  a  46-inch  achromatic  telescope  it  presented  a  plan- 
etary disc,  from  which  rays  emerged  in  the  direction  of  the  tail.  The  tail 
was  double,  consisting  of  two  principal  lateral  streamers,  making  a  very 
small  angle  with  each  other,  and  divided  by  a  comparatively  dark  line,  of 
the  estimated  length  of  25°,  prolonged,  however,  on  the  north  side  by  a 
divergent  streamer,  making  an  angle  of  5°  or  6°  with  the  general  direc- 
tion of  the  axis,  and  traceable  as  far  as  65°  from  the  head.  A  similar 
though  fainter  lateral  prolongation  appeared  on  the  south  side.  A  fine 
drawing  of  it  of  this  date  by  C.  P.  Smyth,  Esq.,  of  the  Royal  Observatory, 
C.  Gr.  H.,  represents  it  as  highly  symmetrical,  and  gives  the  idea  of  a 
vivid  cone  of  light,  with  a  dark  axis,  and  nearly  rectilinear  sides,  inclosed 
in  a  fainter  cone,  the  sides  of  which  curve  slightly  outwards.    The  light 


GREAT   COMET   OF   1843. 


31T 


its  appearance. 

iholk  elements 

and  node,  and 

:.  D' Arrest,  for 
.846,  which  go 
nz.  5804*-3,  or 
'5672,  its  semi- 
s  ecliptic  31°  2' 
1, 1846. 

which  has  been 
n  the  spring  of 
!  17th  of  March 
jg  from  a  point 
Qus  and  Lepu3, 
ifavourable;  and 
Q  only  as  a  faint 
lent  nights.     In 
seen,  as  a  raag- 
mt  the  head  and 
in  every  country 
ion.    Indeed,  all 
Btacle,  such  as  in 
nto  every  bosom, 
appeared  on  the 
le  1st,  the  comet 
Already  on  the 
Icinity  of  the  sun, 
jet.     On  this  day 
presented  a  plan- 
16  tail.     The  tail 
I,  making  a  very 
rely  dark  line,  of 
north  side  by  a 
;he  general  direc- 
lead.    A  similar 
Xh  side.     A  fine 
»yal  Observatory, 
[es  the  idea  of  a 
|ar  sides,  inclosed 
irds.    The  Ught 


of  the  nucleus  at  this  period  is  compared  to  that  of  a  star  of  the  first  or 
second  magnitude;  and  on  the  11th,  of  the  third;  from  Avhich  time  it 
degraded  in  light  so  rapidly,  that  on  the  19th  it  was  invisible  to  the  naked 
eye,  the  tail  all  the  while  continuing  brilliantly  visible,  though  much 
more  so  at  a  distance  from  the  nucleus,  with  which,  indeed,  its  connexion 
was  not  then  obvious  to  the  unassisted  sight  —  a  singular  feature  in  the 
hi-story  of  this  body.  The  tail,  subsequent  to  the  3d,  was,  generally 
speaking,  a  single  straight  or  slightly  curved  broad  band  of  light,  but  on 
the  11th  it  is  recorded  by  Mr,  Clerihew,  who  observed  it  at  Calcutta,  to 
have  shot  forth  a  lateral  tail  nearly  twice  as  long  as  the  regular  one,  but 
fainter,  and  making  an  angle  of  about  18°  with  its  direction  on  the 
southern  side.  The  projection  of  this  ray  (which  was  not  seen  either 
before  or  after  the  day  in  question)  to  so  enormous  a  length,  (nearly 
100°)  in  a  single  day  conveys  an  impression  of  the  intensity  of  the  forces 
acting  to  produce  such  a  velocity  of  material  transfer  through  space,  such 
as  no  other  natural  phaenomenon  is  capable  of  exciting.  It  is  clear  that 
if  we  have  to  deal  here  with  matter,  such  as  we  conceive  it,  viz.  possessing 
inertia — at  all,  it  must  be  under  the  dominion  of  forces  incomparably 
more  energetic  than  gravitation. 

(590.)  There  is  abundant  evidence  of  the  comet  in  question  having 
been  seen  in  full  daylight,  and  in  the  sun's  immediate  vicinity.  It  was 
so  seen  on  the  28th  of  February,  the  day  after  its  perihelion  passage,  by 
every  person  on  board  the  H.  E.  I.  C.  S.  Owen  Glendower,  then  off  the 
Cape,  as  a  short,  dagger-like  object,  close  to  the  sun,  a  little  before  sunset. 
On  the  same  day,  at  S^  6"  p.  M.,  and  consequently  in  full  sunshine,  the 
distance  of  the  nucleus  from  the  sun  was  actually  measured  with  a  sex- 
tant by  Mr.  Clarke,  of  Portland,  United  States,  the  distance,  centre  from 
centre,  being  then  only  3°  50'  43".  He  describes  it  in  the  following 
terms :  "  The  nucleus,  and  also  every  part  of  the  tail,  were  as  well  defined 
as  the  moon  on  a  clear  day.  The  nucleus  and  tail  bore  the  same  appear- 
ance, and  resembled  a  perfectly  pure  white  cloud,  without  any  variation, 
except  a  slight  change  near  the  head,  just  sufficient  to  distinguish  the 
nucleus  from  the  tail  at  that  point."  The  denseness  of  the  nucleus  was 
so  considerable,  that  Mr.  Clarke  had  no  doubt  it  might  have  been  visible 
upon  the  sun's  disc,  bad  it  passed  between  that  and  the  observer.  The 
length  of  the  visible  tail  resulting  from  these  measures  was  59',  or  not  far 
from  double  the  apparent  diameter  of  the  sun ;  and  as  we  shall  presently 
see  that  on  the  day  in  question  the  distance  from  the  earth  of  the  sun  and 
comet  must  have  been  very  nearly  equal,  this  gives  us  about  1700000 
miles  for  the  linear  dimensions  of  this,  the  densest  portion  of  that  ap- 


^^- 


|^•l■M'..::«B•| 


818 


OUTLINES  OF  ASTRONOMY. 


pendage,  making  no  allowance  for  the  foreshortening,  which  at  that  time 
was  very  considerable. 

(591.)  The  elements  of  this  comet  are  among  the  most  remarkable  of 
any  recorded.  They  have  been  calculated  by  several  eminent  astrouomers, 
among  whose  results  we  shall  specify  only  those  which  agree  best ;  the 
earlier  attempts  to  compute  its  path  having  been  rendered  uncertain  by 
the  difBculty  attending  exact  observations  of  it  in  the  first  part  of  its 
visible  career.  The  following  are  those  which  seem  entitled  to  most 
confidence: 


1 

Encke. 

Plantamour. 

Knorre. 

Nicolai. 

Peters. 

Perihcl.  pase.,  1843, 
Veb..  mean  time  at 
Greenwich 

27<>  45096 

279°  y  30" 

4  15     5 

36  12  38 

0-00522 

Retrograde. 

27<i42935 
278°  18'    3" 

0    51     4 
35      8   66 

000581 
Retrograde. 

27''.39638 
278°  28'  26" 

1    43     3 
35    35  29 

0-00579 
Retrograde. 

27<'43023 
278°  36'  33" 

1    37  65 
35    36  29 

0-00558 
Retrograde. 

271-41319 

279°  59'    7" 

3    55   17 

35    15   42 

0-00428 
Retrograde. 

Long,  of  periliel 

Lonir.  of  V 

Perihel.  dist 

Motion 

(592.)  What  renders  these  elements  so  remarkable  is  the  smallness  of 
the  perihelion  distance.  Of  all  comets  which  have  been  recorded  this  has 
made  the  nearest  approach  to  the  sun.  The  sun's  radius  being  the  sine 
of  his  apparent  semi-diameter  (16'  1"  '5)  to  a  radius  equal  to  the  earth's 
mean  distance=l,  is  represented  on  that  scale  by  0-00466,  which  falls 
short  of  0-00584,  the  perihelion  distance  found  by  taking  a  mean  of  all 
the  foregoing  results,  by  only  0-00067,  or  about  one  seventh  of  its  whole 
magnitude.  The  comet,  therefore,  approached  the  luminous  surface  of 
the  sun  within  about  the  seventh  part  of  the  sun's  radius  I  It  is  worth 
while  to  consider  what  is  implied  in  such  a  fact.  In  the  first  place,  the 
intensity  both  of  the  light  and  radiant  heat  of  the  sun  at  difierent  diis- 
tances  from  that  luminary  increase  proportionally  to  the  Fpherical  area  of 
the  portion  of  the  visible  hemisphere  covered  by  the  sun's  disc.  This 
disc,  in  the  case  of  the  earth,  at  its  mean  distance  has  an  angular  dia- 
meter of  32'  3".  At  our  comet  in  perihelio  the  apparent  angular  dia- 
meter of  the  sun  was  no  less  than  121°  32'.  The  ratio  of  the  spherical 
surfaces  thus  occupied  (as  appears  from  spherical  geometry)  is  that  of  thn 
squares  of  the  sines  of  the  fourth  parts  of  these  angles  to  each  other,  or 
that  of  1  :  47042.  And  in  this  proportion  are  to  each  other  the  amounts 
of  light  and  heat  thrown  by  the  sun  on  an  equal  area  of  exposed  surface 
on  our  earth  and  at  the  comet  in  equal  instants  of  time.  Let  any  one 
imagine  the  eficct  of  so  fierce  a  glare  as  that  of  47000  suns  such  as  we 
experience  the  warmth  of,  on  the  materials  of  which  the  earth's  surface 
is  composed.    To  form  some  practical  idea  of  it  we  may  compare  it  with 


1 


QREAT  COMET 


1848. 


319 


t  at  that  time 


what  is  recorded  of  Parker's  great  lens,  whoso  diameter  was  32^  inches 
and  focal  length  six  feet  eight  inches.  The  effect  of  this,  supposing  all 
the  light  and  heat  transmitted,  and  the  focal  concentration  perfect,  (both 
conditions  very  imperfectly  satisfied,)  would  be  to  enlarge  the  sun's 
effective  angular  diameter  to  23°  26',  which,  compared  on  the  same 
principle  with  a  sun  of  32'  in  diameter,  would  give  a  multiplier  of  only 
1915  instead  of  47000.  The  heat  to  which  the  comet  was  subjected 
therefore  surpassed  that  in  the  focus  of  the  lens  in  question,  on  the 
lowest  calculation,  in  the  proportion  of  24^  to  1.  Yet  that  lens  melted 
cornelian,  agate,  and  rock  crystal ! 

(593.)  To  this  extremity  of  heat  however  the  comet  was  exposed  but 
for  a  short  time.  Its  actual  velocity  in  perihelio  was  no  less  than  366 
miles  per  second,  and  the  whole  of  that  segment  of  its  orbit  above  (i.  e. 
north  of)  the  plane  of  the  ecliptic,  and  in  which,  as  ^ill  appear  from  a 
consideration  of  the  elements,  the  perihelion  was  situated,  was  described 
in  little  more  than  two  hours ;  such  being  the  whole  duration  of  the  time 
from  the  ascending  to  the  descending  node,  or  in  which  the  comet  had 
north  latitude.  Arrived  at  the  descending  node,  its  distance  from  the 
sun  would  be  already  doubled,  and  the  radiation  reduced  to  one  fourth 
of  its  maximum  amount.  The  comet  of  1680,  whose  perihelion  distance 
was  00062,  and  which  therefore  approached  the  sun's  surface  within  one 
third  part  of  his  radius  (more  than  double  the  distance  of  the  comet  now 
in  question)  was  computed  by  Newton  to  have  been  subjected  to  au 
intensity  of  heat  2000  times  that  of  red-hot  iron, — a  term  of  comparison 
indeed  of  a  very  vague  description,  and  which  modern  therraotics  do  not 
recognize  as  affording  a  legitimate  measure  of  radiant  heat.' 

(594.)  Although  some  of  the  observations  of  this  comet  were  vague 
and  inaccurate,  yet  there  seem  good  grounds  for  believing  that  its  whole 
course  cannot  be  reconciled  with  a  pan^bolic  orbit,  and  that  it  really 
describes  an  ellipse.  Previous  to  any  calculation,  it  was  remarked  that 
in  the  year  1668  the  tail  of  an  immense  comet  was  seen  in  Lisbon,  at 
Bologna,  in  Brazil,  and  elsewhere,  occupying  nearly  the  same  situation 
among  the  stars,  and  at  the  same  season  of  the  year,  viz.  on  the  5th  of 
March  and  the  following  days.    Its  brightness  was  such  that  its  reflected 

'  A  transit  of  thia  comet  over  the  sun's  disc  must  probably  have  taken  place  shortly 
after  its  passage  through  its  decending  node.  It  is  greatly  to  be  regretted  that  so 
interesting  a  phenomenon  should  have  passed  unobserved.  Whether  it  be  possible 
that  some  offset  of  its  tail,  darted  off  so  late  as  the  7th  of  March,  when  the  comet 
was  already  far  south  of  the  ecliptic,  should  have  crossed  that  plane  and  been  seen 
near  the  Pleiades,  may  be  doubted,  (lertain  it  is,  that  on  the  evening  of  that  day,  a 
decidedly  cometic  ray  was  seen  in  the  immediate  neighbourhood  of  those  stais  by  Mr. 
Nasmyth.  (Ast.  Soc.  Notices,  vol.  v.  p.  270.) 


^es 


«* 
? 


iiii^w 


J**     


820 


OUTLINES  OF  ASTRONOMY. 


f. 

■■.,    Hi 

.  i 

1  ' 

.ft 


!4 
* 

» 
ft 


trace  was  easily  distinguished  on  the  sea.  The  head,  when  it  at  length 
came  in  sight,  was  comparatively  faint  and  scarce  discernible.  No  precise 
observations  were  made  of  this  comet,  but  the  singular  coincidence  of 
situation,  season  of  the  year,  and  physical  resemblance,  excited  a  strong 
suspicion  of  the  identity  of  the  two  bodies,  implying  a  period  of  175 
years  within  a  day  or  two  more  or  less.  This  suspicion  has  been  con- 
verted almost  into  a  certainty  by  a  careful  examination  of  what  is  recorded 
of  the  older  comet.  Locating  on  a  celestial  chart  the  situation  of  the 
head,  concluded  from  the  direction  and  appearance  of  the  tail,  when  only 
that  was  seen,  and  its  visible  place,  when  mentioned,  according  to  the 
descriptions  given,  it  has  been  found  practicable  to  derive  a  rough  orbit 
from  the  course  thus  laid  down :  and  this  agrees  in  all  its  features  so  well 
with  that  of  the  modern  comet  as  nearly  to  remove  all  doubt  on  the 
Bubject.  Comets,  moreover,  are  recorded  to  have  been  seen  in  a.  d.  268, 
442-3,  791,  968,  1143,  1317,  1494,  which  may  have  been  returns  of 
this,  since  the  period  above-mentioned  would  bring  round  its  appearance 
to  the  years  268,  443,  618,  793,  968,  1143,  1318,  and  1493,  and  a 
certain  latitude  must  always  be  allowed  for  unknown  perturbations. 

(595.)  But  this  is  not  the  only  comet  on  record  whose  identity  with 
the  comet  of  '43  has  been  maintained.  In  1689  a  comet  bearing  a  con- 
siderable resemblance  to  it  was  observed  from  the  8th  to  the  23d  of  De- 
cember, and  from  the  few  and  rudely  observed  places  recorded,  its  elements 
had  been  calculated  by  Pingr6,  one  of  the  most  diligent  inquirers  into  this 
part  of  astronomy.'  From  these  it  appears  that  the  perihelion  distance 
of  that  conibb  was  very  remarkably  small,  and  a  sufficient  though  indeed 
rough  coincidence  in  the  places  of  the  perihelion  and  node  tended  to 
corroborate  the  suspicion.  But  the  inclination  (69°)  assigned  to  it  by 
Pingr^  appeared  conclusive  against  it.  On  recomputing  the  elements, 
however,  from  his  data,  Professor  Pierce  has  assigned  to  that  comet  an 
inclination  widely  differing  from  Pingre's,  viz.  30°  4"*,  and  quite  within 
reasonable  limits  of  resemblance.  But  how  does  this  agree  with  the 
longer  period  of  175  years  before  assigned  ?     To  reconcile  this  we  must 

*  Author  of  the  "  Cometographie,"  a  work  indispensable  to  all  who  would  study 
this  interesting  department  of  the  science. 

'United  States  Gazette,  May  29,  1843.  Considering  that  all  the  observations  lie 
near  the  descending  node  of  the  orbit,  the  proximity  of  the  comet  at  that  time  to  the 
sun,  and  the  loose  nature  of  the  recorded  observations,  no  doubt  almost  any  given  in- 
clination might  be  deduced  from  thetii.  The  true  test  in  such  cases  is  not  to  ascend 
from  the  old  incorrect  data  to  elements,  but  to  descend  from  known  anu  certain  ele- 
ments to  the  older  data,  and  ascertain  whether  the  recorded  phaenomena  can  be  repre- 
sented by  them  (perturbations  included)  within  fair  hmits  of  interpretation.  Such  is 
the  course  pursued  by  Clausen. 


GREAT   COMET   OF  1843. 


821 


n  it  at  length 
e.  No  precise 
loincidence  of 
icited  a  strong 
period  of  175 
has  been  con- 
hat  is  recorded 
ituation  of  the 
tail,  when  only 
(cording  to  the 
e  a  rough  orbit 
features  so  well 
1  doubt  on  the 
en  in  A.  D.  268, 
been  returns  of 
d  its  appearance 
od  1493,  and  a 
lurbations. 
ose  identity  with 
et  bearing  a  con- 
)  the  23d  of  De- 
•ded,  its  elements 

iquirers  into  this 
fvihelion  distance 

t  though  indeed 
node  tended  to 

ssigned  to  it  by 

(t  the  elements, 
that  comet  an 

and  quite  within 
agree  with  the 

icile  this  we  must 

III  who  would  study 

I  the  observations  lie 
Jet  at  that  time  to  ihc 
lalmoBt  any  given  in- 
\ea  is  not  to  o^jcend 
Iwu  ana  certain  ele- 
lomena  can  be  repre- 
Irpretaiion.    Such  is 


suppose  that  these  175  years  comprise  at  least  eight  returns  of  the  comet, 
and  that  in  effect  a  mean  period  of  21''-875  must  be  allowed  for  its  return. 
Now  it  is  worth  remarking  that  this  period  calculated  backwards  from 
1843 -ISO  will  bring  us  upon  a  series  of  years  remarkable  for  the  appear- 
ance of  great  comets,  many  of  which,  as  well  as  the  imperfect  descriptions 
wc  have  of  their  appearance  and  situation  in  the  heavens,  offer  at  least  no 
obvious  contradiction  to  the  supposition  of  their  identity  with  this.  Be- 
sides those  already  mentioned  as  indicated  by  the  period  of  175  years,  we 
may  specify  as  probable  or  possible  intermediate  returns,  those  of  the 
comets  of  1733?',  1G89  above-mentioned,  1559?,  1537S  1515»,  1471, 
142G,  1405-6,  1383,  1361, 1340^  1296, 1274, 1230^  1208, 1098, 1056, 
1034,  1012",  990  ?^  925?,  858??,  684«,  552,  5309,  421,  245  or  :U7'», 
180",  158,  Should  this  view  of  the  subject  be  the  true  one,  we  may  ex- 
pect its  return  about  the  end  of  1864  or  beginning  of  1865,  in  which 
event  it  will  bo  observable  in  the  Southern  Hemisphere  both  before  and 
after  its  perihelion  passage". 

(500.)  M.  Clausen,  from  the  assemblage  of  all  the  observations  of  this 
comet  known  to  him,  has  calculated  elliptic  elements  which  give  the  extra- 
ordinarily short  period  of  638  years.  And  in  effect  it  has  been  suggested 
that  a  still  further  subdivision  of  the  period  of  21-875  into  three  of 
7-292  years,  would  reconcile  this  with  other  remarkable  comets.  This 
seems  going  too  far ;  but  at  all  events  the  possibility  of  representing  its 
motions  by  so  short  an  ellipse  will  easily  reconcile  us  to  the  admission  of 
a  period  of  21  years.  That  it  should  only  be  visible  in  certain  apparitions, 
and  not  in  others,  is  sufficiently  explained  by  the  situation  of  its  orbit. 
(597.)  We  have  been  somewhat  diffuse  on  the  subject  of  this  comet, 

'  P.  Passage  1733-781.  This  great  southern  comet  of  May  17th  seems  too  early  in 
tlie  year. 

'P.  P.  153f)-906.    In  January  1537,  a  comet  was  seen  in  Pisces. 

'  P.  P.  1513031.  A  comet  predicted  the  death  of  Ferdinand  the  Catholic.  He  died 
Jan.  23,  1515. 

'  P.  P.  1340  031.    Evidently  a  southern  comet,  and  a  very  probable  appearance. 

'  P.  P.  1230-656,  was  perhaps  a  return  of  Halley's. 

'  P.  P.  1011-906.  In  1012,  a  very  great  comet  in  the  southern  part  of  the  heavens. 
"  Son  oclat  blessait  les  ycux."  (Pingre  Cometographie,  from  whom  all  these  recorded 
appearances  are  taken.) 

'  P.  P.  990031.     •'  Comete  fort  epouvantable,"  some  year  between  989  and  998. 

'  P.  P.  683-781.   In  684,  appeared  two  or  three  comets.    Dates  begin  to  be  obscure. 

°Two  distinct  comets  (one  probably  the  comet  of  Csesar  and  1680)  appeared  in  530 
and  531,  the  former  observed  in  China,  the  latter  in  Europe. 

"  P.  P.  246-281 ;  both  southern  comets  of  the  Chinese  annals.  The  year  of  one  or 
I  oiher  may  be  wrong. 

"  P.  P.  180-656.  Nov.  6,  a.d.  180.    A  southern  comet  of  the  Chinese  annals. 

"Clausen,  Astron.  Nachr.  No.  485. 

21 


*  kit- ■-*»**' 


I 


322 


OUTLINES   OF  ASTRONOMY. 


r 


Ik 

» 


for  the  sake  of  showing  the  degree  and  kind  of  interest  which  attaches  to 
cornetic  astronomy  in  the  present  state  of  the  science.     In  fact  there  is  no 
branch  of  astronomy  more  replete  with  interest,  and  we  may  add  more 
eagerly  pursued  at  present,  inasmuch  as  the  hold  which  exact  calculation 
gives  us  on  it  may  be  regarded  as  completely  established ;  so  that  whatever 
may  be  concluded  as  to  the  motions  of  any  comet  which  shall  hencefor- 
ward come  to  be  observed,  will  be  concluded  on  sure  grounds  and  with 
numerical  precisioL ;  while  the  improvements  which  have  been  introduced 
into  the  calculation  of  comctary  perturbation,  and  the  daily  increasing 
familiarity  of  numerous  astronomers  with  computations  of  this  nature, 
enable  us  to  trace  their  past  and  future  history  with  a  certainty,  which  at 
the  commencement  of  the  present  century  could  hardly  have  been  looked 
upon  as  attainable.    Every  comet  newly  discovered  is  at  once  subjected  to 
the  ordeal  of  a  most  rigorous  inquiry.     Its  elements,  roughly  calculrted 
withm  acfew  days  of  its  appearance,  are  gradually  approximated  to  as  ob- 
servations accumulate,  by  a  multitude  of  ardent  and  expert  computists. 
On  the  least  indication  of  a  deviation  from  a  parabolic  orbit,  its  elliptic 
elements  become  a  subject  of  universal  and  lively  interest  and  discussion. 
Old  records  are  ransacked,  with  all  the  advantage  of  improved  data  and 
methods,  so  as  to  rescue  from  oblivion  the  orbits  of  ancient  comets  which 
present  any  similarity  to  that  of  the  new  visitor.    The  disturbances  under- 
gone in  the  interval  by  the  action  of  the  planets  are  investigated,  and  the 
past,  thus  brought  into  unbroken  connexion  with  the  present,  is  made  to 
afford  substantial  ground  for  prediction  of  the  future.     A  great  impulse, 
meanwhile,  has  been  given  of  late  years  to  the  discovery  of  comets,  by 
the  establishment  in  1840',  by  his  late  Majesty  the  King  of  Denmark, 
of  a  prize  medal,  to  be  awarded  for  every  such  discovery,  to  the  first  ob- 
server, (the  influence  of  which  may  be  most  unequivocally  traced  in  the 
great  number  of  these  bodies  which  every  successive  year  sees  added  to 
our  list,)  and  by  the  circulation  of  notices,  by  special  letter*,  of  every  such 
discovery  (accompanied,  when  possible,  by  an  ephemeris),  to  all  observers 
who  have  shown  that  they  take  an  interest  in  the  inquiry,  so  as  to  ensure 
the  full  and  complete  observation  of  the  new  comet,  so  long  as  it  reinaiy 
within  the  reach  of  our  telescopes. 

(598.)  It  is  by  no  means  merely  as  a  subject  of  antiquarian  interest,  or 
on  account  of  the  brilliant  spe'^acle  which  comets  occasionally  afford,  that 
astronomers  attach  a  high  degree  of  itrportance  to  all  that  regards  them. 
Apart  even  from  the  singularity  and  mystery  which  appertains  to  their 

'  See  the  announcement  of  this  institution  in  Astron.  Nachr.  No.  'f.OO. 
*By  Prof.  Schumacher,  Director  of  the  Royal  Observatory  of  Ahona. 


phyf 
calci 
the  ] 
thei 
trace 
has  a 
filling 
cases 
ciusic 
in  pa! 
matio: 
be  oti 
Jfercu 
more  j 
deterni 
in  the 
their  n 
the  ear 
(599 
the  grei 
profoun 
their  ta 
borrow] 
physica 
the  aetl 
trato  th 
nary  aci 
such  es 
course  I 
is  the  qi 
for  cons 
round  tl 
defiance 
tion,  ext 
near  the 
in  the  la 
It  seems 
material 
[such  a  tfl 
'tJie  lum( 
degree  d 


.|,r'    -1    -"I 


I 


INTEREST  ATTACHED   TO   COMETARY  ASTRONOMY. 


823 


cU  attaches  to 
act  tlierc  is  no 
nay  add  more 
act  calculation 
3  that  whatever 
shall  hencefor- 
mnds  and  with 
seen  introduced 
laily  increasing 
of  this  nature, 
ainty,  which  at 
avc  been  looked 
noe  subjected  to 
ughly  calculcted 
Limatcd  to  as  ob- 
Lpert  computists. 
orbit,  its  elliptic 
it  and  discussion, 
iproved  data  and 
ent  comets  which 
sturbances  under- 
2stigated,  and  the 
■esent,  is  made  to 
A  great  impulse, 
cry  of  comets,  by 
[ing  of  Denmark, 
ry,  to  the  first  ob- 
ally  traced  in  tbe 
^ear  sees  added  to 
,terS  of  every  sucli 
s),  to  all  observers 
ry,  so  as  to  ensure 
long  88  it  remaitis 

marian  interest,  or 
ionally  afford,  thai 
that  regards  them. 
appertains  to  theii 

chr.  No.  -^.00. 
ory  of  Altona. 


physical  constitution,  they  have  bucome,  through  the  medium  of  exact 
calculation,  unexp3cted  instruments  of  inquiry  into  points  connected  with 
the  planetary  system  itself,  of  no  small  importance.  Wc  have  seen  that 
the  movements  of  the  comet  of  Encke,  thus  minutely  and  perseveringly 
traced  by  the  eminent  astronomer  whose  name  is  used  to  distinguish  it, 
has  afforded  ground  for  believing  in  the  presence  of  a  resisting  medium 
filling  the  whole  of  our  system.  Similar  inquiries,  prosecuted  in  the 
cases  of  other  periodical  comets,  will  extend,  confirm,  or  modify  our  con- 
clusions on  this  head.  The  perturbations,  too,  which  comets  experience 
in  passing  near  any  of  the  planets,  may  afford,  and  have  afforded,  infor- 
mation as  to  the  magnitude  of  the  disturbing  masses,  which  could  not  well 
be  otherwise  obtained.  Thus  the  approach  of  this  comet  to  the  planet 
Mercury  in  1838  afforded  an  estimation  of  the  mass  of  that  planet,  the 
more  precious,  by  reason  of  the  great  uncertainty  under  which  all  previous 
determinations  of  that  element  laboured.  Its  approach  to  the  same  planet 
in  the  present  year  (1848)  will  be  still  nearer.  On  the  22d  of  November 
their  mutual  distance  will  be  only  fifteen  times  the  moon's  distance  from 
the  earth. 

(599.)  It  is,  however,  in  a  physical  point  of  view  that  these  bodies  offer 
the  greatest  stimulus  to  our  curiosity.     There  is,  beyond  question,  some 
profound  secret  and  mystery  of  nature  concerned  in  the  phaenomenon  of 
their  tails.     Perhaps  h  is  not  too  much  to  hope  that  future  observation, 
borrowing  every  aid  from  rational  speculation,  grounded  on  the  progress  of 
physical  scieno  generally,  (especially  those  branches  of  it  which  relate  to 
the  aethereal  or  imponderable  elements),  may  ere  long  enable  us  to  pene- 
trate this  mystery,  and  to  declare  whether  it  is  really  matter,  in  the  ordi- 
nary acceptation  of  the  term,  which  is  projected  from  their  heads  with 
such  extravagant  velocity,  and  if  not  impelled,  at  least  directed  in  its 
course  by  a  reference  to  the  sun,  as  its  point  of  avoidance.     In  no  respect 
is  the  question  as  to  the  materiality  of  the  tail  more  forcibly  pressed  on  us 
for  consideration,  than  in  that  of  the  enormous  sweep  which  it  makes 
round  the  sun  in  perihelio,  in  the  manner  of  a  straight  and  rigid  rod,  in 
i  defiance  of  the  law  of  gravitation,  nay,  even  of  the  received  laws  of  mo- 
I  tion,  extending  (as  we  have  seen  in  the  comets  of  1680  and  1843)  from 
I  near  the  sun's  surface  to  the  earth's  orbit,  yet  whirled  round  unbroken ; 
in  the  latter  case  through  an  angle  of  180°  in  little  more  than  two  hours. 
It  seems  utterly  incredible  that  in  such  a  case  it  is  one  and  the  same 
material  object  which  is  thus  brandished.     If  there  could  be  conceived 
[such  a  thing  as  a  negative  shadow,  a  momentary  impression  made  upon 
[the  luminiferous  aether  behind  the  comet,  this  would  represent  in  some 
[degree  the  conception  such  a  phseuomenon  irresistibly  calls  up.     But  this 


*':  -no  ■ :  \<t 


.        ^      -^ 

■"■"V*^ 


'■■X  .-iRysa 


'  Iftiiit.*; 


MM*: 


■i"  ■■; 


324 


OUTLINES   OF  ASTRONOMY. 


is  not  all.  Even  such  an  extraordinary  excitement  of  the  aother,  conceive 
it  as  we  will,  will  afford  no  account  of  the  projection  of  lateral  streamers ; 
of  the  effusion  of  light  from  the  nucleus  of  a  comet  towards  the  sun  j  and 
its  subsequent  rejection  ;  of  the  irregular  and  capricious  mode  in  which 
that  effusion  has  been  seen  to  take  place ;  none  of  the  clear  indications  of 
alternate  evaporation  and  condensation  going  on  in  the  immense  regions  of 
space  occupied  by  the  tail  and  coma,  —  none,  in  short,  of  innumerable 
other  facts  which  link  themselves  with  almost  equally  irresistible  cogency 
to  our  ordinary  notions  of  matter  and  force. 

(600.)  The  great  number  of  comets  which  appear  to  move  in  parabolic 
orbits,  or  orbits  at  least  undistlnguishable  from  parabolas  during  their  de- 
scription of  that  comparatively  small  part  within  the  range  of  their  visi- 
bility to  us,  has  given  rise  to  an  impression  that  they  are  bodies  extraneous 
to  our  system,  wandering  through  space,  and  merely  yielding  a  local  and 
temporary  obedience  to  its  laws  during  their  sojourn.  What  truth  there 
may  bo  in  this  view,  we  may  never  have  satisfactory  grounds  for  deciding. 
On  such  an  hypothesis,  our  elliptic  comets  owe  their  permanent  denizen- 
ship  within  the  sphere  of  the  sun's  predominant  attraction  to  tho  action 
of  one  or  other  of  the  planets  near  which  they  may  have  passed,  in  such 
a  manner  as  to  diminish  their  velocity,  and  render  it  compatible  with 
elliptic  motion.'  A  similar  cause  acting  the  other  ..ay,  might  with  equal 
probability,  give  rise  to  a  hyperbolic  motion.  But  whereas  in  the  former 
case,  the  comet  would  remain  in  the  system,  and  might  make  an  indefiaitc 
number  of  revolutions,  in  the  latter  it  would  return  no  more.  This  ma; 
possibly  be  the  cause  of  the  exceedingly  rare  occurrence  of  a  hyperbolic 
comet  as  compared  with  elliptic  ones. 

(601.)  All  the  planets  without  exception,  and  almost  all  the  satellites, 
circulate  in  one  durection.  Retrograde  comets,  however,  are  of  very  com- 
mon occurrence,  which  certainly  would  go  to  assign  them  an  exterior  or 
at  least  an  independent  origin.  Laplace,  from  a  consideration  of  all  the 
cometary  orbits  known  in  the  earlier  part  of  the  present  century,  con- 
cluded that  the  mean  or  average  situation  of  the  planes  of  all  the  cometar; 
orbits,  with  respect  to  the  ecliptic,  was  so  nearly  that  of  perpendicularity, 
as  to  afford  no  presumr  don  of  any  cause  biassing  their  directions  in  this 
respect.  Yet  we  think  it  worth  noticing,  that  among  the  comets  which 
are  as  yet  known  to  describe  elliptic  orbits,  not  one  whose  inclination  is 
under  17°  is  retrograde ;  and  that  out  of  thirty-six  comets  which  have 
had  elliptic  elements  assigned  to  them,  whether  of  great  or  small  exceu- 
tricities,  and  without  any  limit  of  inclination,  only  five  are  retrograded, 

'  The  velocity  in  an  ellipse  is  always  less  than  in  a  parabola,  at  equal  distances  from  | 
the  sun ;  in  an  hyperbola  always  greater. 


GENERAL  REMARKS. 


825 


ithcr,  conceive 
ral  streamers  j 

the  sun ;  and 
node  in  Viluch 

indications  of 
;nse  regions  of 
)f  innumerable 
istible  cogency 

)ve  in  parabolic 
during  their  de- 
ge  of  their  visi- 
odies  extraneous 
ling  a  local  and 
hat  truth  there 
nds  for  deciding, 
rmanent  denizen- 
on  to  tho  action 
3  passed,  in  sucli 
compatible  with 
might  with  equal 
■eas  in  tho  former 
lake  an  indefinite 
ore.     This  maj 
of  a  hyperbolic 

all  the  satellites, 
are  of  very  com- 
km  an  exterior  or 
Lration  of  all  the 
lent  century,  con- 
If  all  the  cometarj 
perpendicularity, 
>  directions  in  this 
Ithe  comets  which 
lose  inclination  is 
omets  which  have 
at  or  small  excen-  j 
are  retrograded, 

1  equal  distances  from 


and  of  these  only  two,  viz.  Ilalley's  and  the  great  comet  of  1843,  can  be 
regarded  as  satisfactorily  mad.^  out.     Finally,  of  tho  125  comets  whose 
elements  are  given  in  tho  ^.d^^ection  of  Schumacher  and  Olbers,  up  to 
1823,  the  number  of  retrograde  comets  under  10°  of  inclination  is  only 
2  out  of  9,  and  under  20°,  7  out  of  23.     A  plane  of  motion,  therefore, 
nearly  coincident  with  the  ecliptic,  and  a  periodical  return,  are  circum- 
stances eminently  favourable  to  direct  revolution  in  the  cometary  as  they 
arc  decisive  among  the  planetary  orbits.    [Here  also  we  may  notice  a  very 
curious  remark  of  Mr.  Hind,  (Ast.  Nachr.  No.  724,)  respecting  periodic 
comets,  viz.,  that,  so  far  as  at  present  known,  they  divide  themselves  for 
the  most  part  into  two  families,  —  the  one  having  periods  of  about  75 
years,  corresponding  to  a  mean  distance  about  that  of  Uranus ;  the  other 
corresponding  more  nearly  with  tboso  of  the  asteroids,  and  with  a  mean 
distance  between  those  small  planets  and  Jupiter.     The  former  group 
consists  of  four  members,  Halley's  comet  revolving  in  76  years,  one  dis- 
covered by  Olbers  in  74,  De  Vice's  4th  comet  in  78,  and  Brorsen's  3d  in 
75,  respectively.     Examples  of  the  latter  group  are  to  be  seen  in  the 
table,  p.  552,  at  the  end  of  this  volume.     It  may  be  added,  also,  that 
one  or  two  of  the  asteroids  are  described  as  having  a  faint  nebulous  enve- 
lope about  them,  indicating  somewhat  of  a  cometio  nature.] 


?:6^ 


.  Af-  ■■  ■•.'•'■ 


V. 


826 


OUTLINES  OF  ASTRONOMY. 


PART  II. 


■^: 


OF  THE   LUNAR   AND   PLANETARY   PERTURBATIONS. 


"  Magnus  ab  integro  eteclorutn  nascitur  ordo." — Viro.  Pollio. 


m 


• 


CHAPTER  XII. 

SUBJECT  PROPOUNDED. — PROBLEM  OP  THREE  BODIES. — SUPERPOSITION 
OP  SMALL  MOTIONS.  —  ESTIMATION  OP  THE  DISTURBING  FORCE.— 
ITS  GEOMETRICAL  REPRESENTATION.  —  NUMERICAL  ESTIMATION  IN- 
PARTICULAR  CASES.  —  RESOLUTION  INTO  RECTANGULAR  COMPO- 
NENTS. —  RADIAL,  TRANSVERSAL,  AND  ORTHOGONAL  DISTURBING 
FORCES.  —  NORMAL  AND  TANGENTIAL.  —  THEIR  CHARACTERISTIC 
EFFECTS. — EFFECTS  OF  THE  ORTHOGONAL  FORCE. — MOTION  OP  THE 
NODES. —  CONDITIONS  OF  THEIR  ADVANCE  AND  RECESS. —  CASES  OF 
AN  EXTERIOR  PLANET  DISTURBED  BY  AN  INTERIOR. — THE  BEVERSK 
CASE. —  IN  EVERY  CASE  THE  NODE  OP  THE  DISTURBED  ORBIT  RE- 
CEDES ON  THE  PLANE  OP  THE  DISTURBING  ON  AN  AVERAGE. - 
COMBINED  EFFECT  OP  MANY  SUCH  DISTURBANCES. — MOTION  OP  THE 
moon's  nodes.  —  CHANGE  OP  INCLINATION.  —  CONDITIONS  OF  ITS 
INCREASE  AND  DIMINUTION. — AVERAGE  EFFECT  IN  A  WHOLE  RE- 
VOLUTION.—  COMPENSATION   IN   A   COMPLETE  REVOLUTION   OF  THE  | 

NODES. — Lagrange's  theorem  of  the  stability  of  the  incli 

NATIONS  OF  THE  PLANETARY  ORT  ITS. —  CHANGE  OP  OBLIQUITY  OF  I 
the  ecliptic. — PRECESSION  OF  THE  EQUINOXES  EXPLAINED.-] 
NUTATION.  —  PRINCIPLE  OF  FORCED   VIBRATIONS. 


(60?  )  In  the  progress  of  this  work,  we  have  more  than  once  called  the 
reaucr's  attention  to  the  existence  of  inequalities  in  the  lunar  and  plane- 
tary motions  not  included  in  the  expression  of  Kepler's  laws,  but  in  some  I 
sort  supplementary  to  them,  and  of  an  order  so  far  subordinate  to  those  j 
leading  features  of  the  celestial  movements,  as  to  require,  for  their  deteei 
tion,  ni(;er  observations,  and  longer  continued  comparison  between  facts 


PERTURBATIONS. 


827 


and  tliwurics,  than  suffice  for  the  cstnbliHhnicnt  and  verification  of  tho 
elliptic  theory.  These  inequalities  uro  known,  in  physical  astronomy,  by 
the  name  of  perturbation*.  They  arise,  in  tho  case  of  tho  primary 
planets,  from  the  mutual  gravitations  of  these  planets  towards  each  other, 
which  derange  their  elliptic  motions  round  the  sun;  and  in  that  of  tho 
secondaries,  partly  from  tho  mutual  gravitation  of  tho  secondaries  of  the 
same  system  similarly  deranging  their  elliptic  motions  round  their  common 
primary,  and  partly  from  the  unequal  attraction  of  tho  sun  and  planets  on 
them  and  on  their  primary.  Thoi^e  perturbations,  although  small,  and,  in 
most  instances,  insensible  in  short  intervals  of  time,  yet,  when  accumu- 
lated, as  some  of  them  may  become,  in  the  lapse  of  ages,  alter  very 
greatly  the  original  elliptic  relations,  so  us  to  render  the  same  elements  of 
the  planetary  orbits,  which  at  one  epoch  represented  perfectly  well  their 
movements,  inadequate  and  unsatisfactory  after  long  intervals  of  time. 

(603.)  When  Newton  first  reasoned  his  way  from  tho  broad  features 
of  the  celestial  motions,  up  to  the  law  of  universal  gravitation,  as  affect- 
ing all  matter,  and  rendering  every  particle  in  the  universe  subject  to  the 
influence  of  every  other,  he  was  not  unaware  of  the  modifications  which 
'^^his  generalization  would  induce  upon  the  results  of  a  more  partial  and 
liaiitcd  application  of  the  same  law  to  the  revolutions  of  the  planets  about 
the  sun,  and  the  satellites  about  their  primaries,  as  their  only  centres  of 
attraction.  So  far  from  it,  his  extraordinary  sagacity  enabled  him  to  per- 
ceive very  distinctly  how  several  of  the  most  important  of  the  lunor 
inequalities  take  their  origin,  in  this  more  general  way  of  conceiving  the 
agency  of  the  attractive  power,  especially  the  retrograde  motion  of  the 
nodes,  and  the  direct  revolution  of  the  apsides  of  her  orbit.  And  if  he 
did  not  extend  his  investigations  to  the  mutual  perturbations  of  the  planets, 
it  was  not  for  want  of  perceiving  that  such  perturbations  must  exist,  and 
might  go  the  length  of  producing  great  derangements  from  the  actual  state 
of  the  systom,  but  was  owing  to  the  then  undeveloped  state  of  the  prac- 
tical part  of  astronomy,  which  had  not  yet  attained  the  precision  requisite 
to  make  such  an  attempt  inviting,  or  indeed  feasible.  What  Newton  left 
undone,  however,  his  successors  have  accomplished ;  and,  at  this  day,  it 
is  hardly  too  much  to  assert  that  there  is  not  a  single  perturbation,  great 
or  small,  which  observation  has  become  precise  enough  clearly  to  detect 
and  place  in  evidence,  which  has  not  been  traced  up  to  its  origin  in  the 
mutual  gravitation  of  the  parts  of  our  system,  and  minutely  accounted 
for,  in  its  numerical  amount  and  value,  by  strict  calculation  on  Newton's 
principles. 

(604.)  Calculations  of  this  nature  require  a  very  high  analysis  for  their 
successful  performance,  such  as  is  fur  beyond  the  scope  and  object  of  this 


55*^' 


"S^ 


i  > 


328 


OUTLINES   OF  ASTRONOMY. 


s 

:; 

■•l 


work  to  attempt  exhibiting.  The  reuder  who  would  master  them  must 
prepare  himself  for  the  undertaking  by  an  extensive  course  of  prepara- 
tory study,  and  umst  nseend  by  steps  which  wo  must  not  here  even  digress 
to  point  out.  It  will  bo  our  object,  in  this  chapter,  however,  to  give  some 
general  insight  into  the  nature  and  manner  of  operation  of  the  acting  forces, 
and  to  point  out  what  arc  the  circumstances  which,  in  some  cases,  give  them 
a  high  degree  of  efficiency — a  sort  of  purvhuitc  on  the  balance  of  the  sys- 
tem ;  while,  in  others,  with  no  less  amount  of  intonsity,  their  effective 
agency  in  producing  extensive  and  lasting  changes  is  compensated  or  ren- 
dered abortive ;  as  well  as  to  explain  the  nature  of  those  admirable  results 
respecting  the  stability  of  our  system,  to  which  the  researches  of  geome- 
ters have  conducted  them ;  and  which,  under  the  form  of  mathematical 
theorems  of  great  simplicity  and  elegance,  involve  the  history  of  the  past 
and  future  state  of  the  planetary  orbits  during  ages,  of  which,  contem- 
plating the  subject  in  this  point  of  view,  we  neither  perceive  the  begin- 
ning nor  the  end. 

(005.)  Were  there  no  other  bodies  in  the  universe  but  the  sun  and  one 
planet,  the  latter  would  describe  an  exact  ellipse  about  the  former  (or  both 
round  their  common  centre  of  gravity),  and  continue  to  perform  its  revo- 
lutions in  one  and  the  same  orbit  for  ever ;  but  the  moment  we  add  to 
our  combination  a  third  body,  the  attraction  of  this  will  draw  both  the 
former  bodies  out  of  their  mutual  orbits,  and,  by  acting  on  them  un- 
equally, will  disturb  their  relation  to  each  other,  and  put  an  end  to  the 
rigorous  and  mathematical  exactness  of  their  elliptic  motions,  not  only 
about  a  fixed  point  in  space,  but  about  one  another.  From  this  way  of 
propounding  the  subject,  we  see  that  it  is  not  the  whole  attraction  of  the 
newly-introduced  body  which  produces  perturbation,  but  the  difference  of 
its  attractions  on  the  two  originally  present. 

(606.)  Compared  to  the  sun,  all  the  planets  are  of  extreme  minuteness; 
the  mass  of  Jupiter,  the  greatest  (»f  them  all,  being  not  mors  than  about 
one  1100th  part  that  of  the  sun.  Their  attractions  on  each  other,  there- 
fore, are  all  very  feeble,  compared  with  the  presiding  central  power,  and 
the  effects  of  their  disturbing  forces  are  proportionally  minute.  In  the 
case  of  the  secondaries,  the  chief  agent  by  which  their  motions  are 
deranged  is  the  sun  itself,  whose  mass  is  indeed  great,  but  whose  disturb- 
ing influence  is  immensely  diminished  by  their  near  proximity  to  their 
primaries,  compared  to  their  distances  from  the  sun,  which  renders  the 
difference  of  attractions  on  both  extremely  small,  compared  to  the  whole 
amount.  In  this  case  the  greatest  part  of  the  sun's  attraction,  viz.  that 
which  is  common  to  both,  is  exerted  to  retain  both  primary  and  secondary 
in  their  common  orbit  about  itself,  and  prevent  their  parting  company. 


SUPERPOSITION    OF   SMALL   MOTIONS. 


329 


Only  the  Bnmll  overplus  of  force  on  one  as  conipftrcd  with  the  other  acta 
as  a  disturbing  power.  The  nieuii  value  of  this  overplus,  in  the  case  of 
the  moon  disturbed  by  the  sun,  is  calculated  by  Newton  to  amount  to 
no  higlier  a  fructicm  than  nj^'ooo  of  gravity  at  the  earth's  surface,  or  j\^ 
of  the  principal  force  which  retains  the  moon  in  its  orbit. 

(007.)  From  this  extreme  minuteness  of  the  intensities  of  the  disturb- 
ing, compared  to  the  principal  forces,  and  the  consequent  smallness  of 
their  momciihirt/  effects,  it  happens  that  wo  can  estimate  each  of  theso 
cfit'cts  separately,  as  if  the  others  did  not  take  place,  without  fear  of 
inducing  error  in  our  conclusions  beyond  the  limits  necessarily  incident 
to  a  first  appro.\imation.  It  is  a  principle  in  mechanics,  immediately 
flowing  from  the  primary  relations  between  forces  and  the  motions  they 
produce,  that  when  a  number  of  very  minute  forces  act  at  once  on  a 
system,  their  joint  effect  is  the  sum  or  aggregate  of  their  separate  effects, 
at  least  within  such  limits,  that  the  original  relation  of  the  parts  of  the 
fiystcm  shall  not  have  been  materially  changed  by  their  action.  Such 
effects  supervening  on  the  greater  movements  due  to  the  action  of  the 
primary  forces  may  be  con)pared  to  the  small  ripplings  caused  by  a 
thousand  varying  breezes  on  the  broad  and  regular  swell  of  a  deep  and 
rolling  ocean,  which  run  on  as  if  the  surface  were  a  plane,  and  cross  in  all 
directions  without  interfering,  each  as  if  the  other  had  no  existence.  It 
is  only  when  their  effects  become  accumulated  in  lapse  of  time,  so  as  to 
alter  the  primary  rclatiutiK  or  data  of  the  system,  that  it  becomes  neces- 
sary to  have  especial  regard  to  the  changes  correspondingly  introduced 
into  the  estimation  of  their  momentary  efficiency,  by  which  the  rate  of  the 
subsequent  changes  is  affected,  and  periods  or  cycles  of  immense  length 
take  their  orig^in.  From  this  consideration  arise  some  of  the  most  curious 
theories  of  jthysicul  astronomy. 

(608.)  Hence  it  is  evident,  that  in  estimating  tho  disturbing  influence 
of  several  bodies  forming  a  system,  in  which  one  has  a  remarkable  pre- 
ponderance over  all  the  rest,  we  need  not  embarrass  ourselves  with  combi- 
nations of  the  disturbing  powers  one  auioug  another,  unless  where 
immensely  long  periods  are  concerned ;  such  us  consist  of  many  hundreds 
of  revolutions  of  the  bodies  in  question  about  their  common  centre.  So 
that,  in  effect,  so  far  as  we  propose  to  go  into  its  consideration,  the 
problem  of  the  investigation  of  the  perturbations  of  a  system,  however 
numerous,  constituted  as  ours  is,  reduces  itself  to  that  of  a  system  of  three 
bodies:  a  predominant  central  body,  a  disturbing,  and  a  disturbed;  the 
two  latter  of  which  may  exchange  denominations,  according  as  the  motions 
of  the  one  or  the  other  are  the  subject  of  inquiry. 

(609.)  Both  the  intensity  and  direction  of  the  disturbing  force  are 


5m 


•H 


iST- 


*>3 


'"**«R!r^ 


i'«i 


'JW* 


I  'PWJI 


830 


OUTLINES   OF  ASTRONOMY. 


"fci 


continually  varying,  according  to  the  relative  situation  of  the  disturbing 
and  disturbed  body  with  respect  to  the  sun.  If  the  attraction  of  the  dis- 
turbing body  M,  on  the  central  body  S,  and  the  disturbed  body  P,  (by 
which  designations,  for  brevity,  we  shall  hereafter  indicate  them,)  were 
equal,  and  acted  in  parallel  lines,  whatever  might  otherwise  be  its  law  of 
variation,  there  would  be  no  deviation  caused  in  the  elliptic  motion  of  P 
about  S,  or  of  each  about  the  other.  The  case  would  be  strictly  that  of 
art.  454 ;  the  attraction  of  M,  so  circumstanced,  being  at  every  moment 
exactly  analogous  in  its  effects  to  terrestrial  gravity,  which  acts  in  parallel 
lines,  and  is  equally  intense  on  all  bodies,  great  and  small.  But  this  is 
not  the  case  of  nature.  Whatever  is  stated^in  the  subsequent  article  to 
that  last  cited,  of  the  disturbing  effect  of  the  sun  and  moon,  is,  mutatis 
mtitandisf  applicable  to  every  case  of  perturbation ;  and  it  must  be  now 
our  business  to  enter,  somewhat  more  in  detail,  into  the  general  heads  of 
the  subject  there  merely  hinted  at. 

(610.)  To  obtain  clear  ideas  of  the  manner  in  which  the  disturbing 
force  produces  its  various  effects,  we  must  ascertain  at  any  given  motueut, 
and  in  any  relative  situations  of  the  three  bodies,  its  direction  and  inten- 
sity as  compared  with  the  gravitation  of  P  towards  S,  in  virtue  of  which 
latter  force  alone  P  would  describe  an  ellipse  about  S  regarded  as  fixed, 
or  rather  P  and  S  about  their  common  centre  of  gravity  in  virtue  of  their 
mutual  gravitation  to  each  other.  In  the  treatment  of  the  problem  of 
three  bodies,  it  is  convenient,  and  tends  to  clearness  of  apprehension,  to 
regard  one  of  them  as  fixed,  and  refer  the  motions  of  the  others  to  it  as 
to  a  relative  centre.  In  the  case  of  t^to  planets  disturbing  each  other's 
motions,  the  sun  is  naturally  chosen  as  this  fixed  centre ;  but  in  that  of 
satellites  disturbing  each  other,  or  disturbed  by  the  sun,  the  centre  of 
their  primary  is  taken  as  their  point  of  reference,  and  the  sun  itself  is 
regarded  in  the  light  of  a  very  distant  and  massive  satellite  revolving 
about  the  primary  in  a  relative  orbit,  equal  and  similar  to  that  which  the 
primary  describes  absoluteh/  round  the  sun.  Thus  the  generality  of  our 
language  is  preserved,  and  when,  referring  to  any  particular  central  body, 
v^e  speak  of  an  exterior  and  an  interior  planet,  we  include  the  cases  in 
which  the  former  is  the  sun  and  the  latter  a  satellite ;  as,  for  example,  in 
the  Lunar  theory.  It  is  a  principle  in  dynamics,  that  the  relative  motions 
of  a  system  of  bodies  inter  se  are  no  way  altered  by  impressing  on  all  of 
them  a  common  motion  or  motions,  or  a  conmion  force  or  forces  accelera- 
ting or  retarding  them  all  equally  in  common  directions,  i,  e.  in  parallel 
lines.  Suppose,  therefore,  we  apply  to  all  the  three  bodies,  S,  P,  and  M, 
alike,  forces  equal  to  those  with  which  M  and  P  attract  S,  but  in  opposite 
directions.    Then  will  the  relative  motions  both  of  M  and  P  about  S  be 


T 


ESTIMATION  OP  THE  DISTURBING  FORCE. 


831 


unaltered ;  but  8,  being  now  urged  by  equal  ftnd  opposite  forces  to  and 
from  both  M  and  P,  will  remain  at  rest.  Let  us  now  consider  how  either 
of  the  other  bodies,  as  P,  stands  affected  by  these  newly-introduced  forces, 
in  addition  to  those  which  before  acted  on  it.  It  is  clear  that  now  P  will 
be  simultaneously  acted  on  by  four  forces ;  firstly,  the  attraction  o/"  S  in 
the  direction  P  S ;  secondly,  an  additional  force,  in  the  same  direction, 
equal  to  its  attraction  on  S ;  thirdly,  the  attraction  of  M  in  the  direction 
P  M ;  and  fourthly,  a  force  parallel  to  M  S,  -and  equal  to  M's  attraction 
OH  S.  Of  these,  the  two  first,  following  the  same  law  of  the  inverse 
square  of  the  distance  S  P,  may  be  regarded  as  one  force,  precisely  as  if 
the  sum  of  the  masses  of  8  and  P  were  collected  in  S ;  and  in  virtue  of 
their  joint  action,  P  will  describe  an  ellipse  about  S,  except  in  so  far  as 
that  elliptic  motion  is  disturbed  by  the  other  two  forces.  Thus  we  see 
that  in  this  view  of  the  subject  the  relative  disturbing  force  acting  on  P 
is  no  longer  the  mere  single  attraction  of  M,  but  a  force  resulting  from 
the  composition  of  that  attraction  with  M's  attraction  on  S  transferred  to 
P  in  a  contrary  direction. 

(611.)  Let  C  P  A  be  part  of  the  relative  orbit  of  the  disturbed,  and  M  B 
of  the  disturbing  body,  their  planes  intersecting  in  the  line  of  nodes  SAB, 


<c 


'.i*» 


■'•»Bvw»l»Jg 


(fr-T-'^v 


3 


and  having  to  each  other  the  inclination  expressed  by  the  spherical  angle 
P  Art.  In  M  P,  produced  if  required,  take  M  N  :  M  S  : :  M  S»  :  M  P«. 
Then,  if  S  M'  be  taken  to  represent,  in  quantity  and  direction,  the  accele- 

'  The  render  will  he  careful  to  observe  the  order  of  the  letters,  where  forces  nre 
represented  by  lines.  M  S  represents  a  force  acting  from  M  towards  S,  S  M  from  S 
towards  M. 


."! 


832 


OUTLINES  OF  ASTRONOMY. 


i 


rative  attraction  of  M  on*S,  M  S  will  represent  in  quantity  and  direction 
the  new  force  applied  to  P,  parallel  to  that  line,  and  N  M  will  represent 
on  the  same  scale  the  accclerative  attraction  of  M  on  P.  Consequently, 
the  disturbing  force  acting  on  P  will  be  the  resultant  of  two  forces  applied 
at  P,  represented  respectively  by  N  M  and  M  S,  which  by  the  laws  of 
dynamics  are  equivalent  to  a  single  force  represented  in  guantitif  and 
direction  by  N  S,  but  having  V  for  its  point  of  application. 

(612.)  The  line  N  S,  is.  easily  calculated  by  trigonometry,  when  the 
relative  situations  and  real  distances  of  the  bodies  are  known ;  and  the 
force  expressed  by  that  line  is  directly  comparable  with  the  attractive 
forces  of  S  on  P  by  the  following  proportions,  in  which  M,  S,  represent 
the  masses  of  those  bodies  which  are  supposed  to  be  known,  and  to  which, 
at  equal  distances,  their  attractions  are  proportional :  — 

Disturbing  force  :  M's  attraction  on  S  : :  N  S  :  S  M ; 

M's  attraction  on  S  :  S's  attraction  on  M  : :  M  :  S ; 

S's  attraction  on  M  :  S's  attraction  on  P  : :  S  P* :  S  M* :  by  com- 
pounding which  proportions  we  collect  as  follows :  — 

Disturbing  force  :  S's  attraction  on  P  : :  M  .  N  S  .  S  F  :  S  .  S  M". 

A  few  numerical  examples  are  subjoined,  exhibiting  the  results  of  this 
calculation  in  particular  cases,  chosen  so  as  to  exemplify  its  application 
under  very  various  circumstances,  throughout  the  planetary  system.  In 
each  case  the  numbers  set  down  express  the  proportion  in  which  the  central 
force  retaining  the  disturbed  body  in  its  elliptic  orbit  exceeds  the  disturb- 
ing force,  to  the  nearest  whole  number.  The  calculation  is  made  for  three 
positions  of  the  disturbing  body — viz.  at  its  greatest,  its  least,  and  its  mean 
distance  from  the  disturbed. 


Disturbing  body. 

Disturbed  body. 

Ratio  at  the 
greatest  distance 

Ratio  at  the 

mean  distance 

:  1. 

Ratio  at  the 

least  distance 

:  1. 

The  Sun 

The  Moon 

90 

354 

95683 

255208 

57420 

526 

6433 

20248 

179 

312 

147575 

210245 

56592 

526 

6937 

21579 

89 

128 

53268 

26833 

5519 

626 

1033 

3065 

Jupiter 

Saturn 

Jupiter 

The  Earth 

The  Earth 

Uranus 

Venus  

Neptune 

Mercury 

Nentune... 

Jupiter 

Ceres 

Saturn  

Jupiter 

(613.)  If  the  orbit  of  the  disturbing  body  be  circular,  S  M  is  invariable. 
In  this  case,  N  S  will  continue  to  represent  the  disturbing  force  on  the 
same  invariable  scale,  whatever  may  be  the  configuration  of  the  three 
bodies  with  respect  to  each  other.    If  the  orbit  of  M  be  but  little  elliptic, 


ESTIMATION  OF  THE   DISTURBING  FORCE. 


833 


ad  direction 
ill  represent 
jnsequently, 
)rces  applied 
the  laws  of 
ijuantity  and 

y,  when  the 
itn'f  and  the 
;he  attractive 
,  S,  represent 
and  to  which, 


M' :  by  com- 

:  S  .  S  M». 
results  of  this 
its  application 
f  system.  In 
ich  the  central 
Is  the  disturb- 
made  for  three 
and  its  mean 


Ratio  at  the 

least  distance 

:  1. 


89 

128 

53268 

26833 

5519 

526 

1033 

3065 


is  invariable, 
force  on  the 
of  the  three 
little  elliptic, 


the  same  will  be  nearly  the  case.  In  what  follows  throughout  this  ohiipter, 
except  where  the  contrary  is  expressly  mentioned,  we  shall  neglect  the 
exccntricity  of  the  disturbing  orbit. 

(614.)  If  P  be  nearer  to  M  than  S  is,  M  N  is  greater  than  M  P,  and 
N  lies  in  M  P  prolonged,  and  therefore  on  the  opposite  side  of  the  plane 
of  P's  orbit  from  that  on  which  M  is  situated.  The  force  N  S  therefore 
urges  P  towards  M's  plane,  and  towards  a  point  X,  situated  between  S 
and  M,  in  the  line  S  M.  If  the  distance  M  P  be  equal  to  M  S  as  when 
P  is  situated,  suppose,  at  D  or  E,  M  N  is  also  equal  to  M  P  or  M  S,  so 
that  N  coincides  with  P,  and  therefore  X  with  S,  the  disturbing  forces  being 
in  these  cases  directed  towards  the  central  body.  But  if  M  P  be  greater 
than  MS,  M  N  is  less  than  M  P,  and  N  lies  between  M  and  P,  or  on  the 
same  side  of  the  plane  of  P's  orbit  that  M  is  situated  on.  The  force  N 
S,  therefore,  applied  at  P,  urges  P  towards  the  contrary  side  of  that  plane 
towards  a  point  in  the  line  M  S  produced,  so  that  X  now  shifts  to  the 
farther  side  of  S.  In  all  cases,  the  disturbing  force  is  wholly  effective  in 
♦      ;  1  ne  M  P  S,  in  which  the  three  bodies  lie. 


It  is  very  important  for  the  student  to  fix  distinctly  and  bear  constantly 
in  his  mind  these  relations  of  the  disturbing  agency  considered  as  a  simjle 
nnresolved  forces  since  their  recollection  will  preserve  him  from  many 
mistakes  in  conceiving  the  mutual  actions  of  the  planets,  &c.  on  each 
other.  For  fivnmplc,  in  the  figures  here  referred  to,  that  of  Art.  611 
corresponds  to  the  case  of  a  nearer  disturbed  by  a  more  distant  body,  as 
the  earth  by  Jupiter,  or  the  moon  by  the  Sun  j  and  that  of  the  present 
article  to  the  converse  case :  as,  for  instance,  of  Mars  disturbed  by  the 
earth.    Now,  in  this  latter  class  of  cases,  whenever  M  P  is  greater  than 


imni     ♦ 


•!<».««»»; 


'■i 


t 


834 


OUTLINES   OF  ASTRONOMY. 


Vi, 


t 
I 
i 

i 


M  S,  or  S  P,  greater  than  2  S  M,  N  lies  on  tho  same  side  of  the  plane 
of  P's  orbit  with  M,  so  that  N  S,  the  disturbing  force,  contrary  to  what 
might  at  first  be  supposed,  always  urges  the  disturbed  planet  out  of  the 
'ane  of  its  orbit  towards  the  opposite  side  to  that  on  which  the  disturbing 
jjlanet  lies.  It  will  tend  greatly  to  give  clearness  and  definiteness  to  his 
ideas  on  the  subject,  if  he  will  trace  out  on  various  suppositions  as  to  the 
relative  magnitude  of  the  disturbing  and  disturbed  orbits  (supposed  to  lie 
in  one  plane)  the  form  of  the  oval  about  M  considered  as  a  fixed  point,  in 
which  the  point  N  lies  when  P  makes  a  complete  revoluuon  round  S. 

(615.)  Although  it  is  necessary  for  obtaining  in  the  first  instance  t 
clear  conception  of  the  action  of  the  disturbing  force,  to  consider  it  in  this 
way  as  a  single  force  having  a  definite  direction  in  space  and  a  determinate 
intensity,  yet  as  that  direction  is  continually  varying  with  the  position  of 
N  S,  both  with  respect  to  the  radii  S  P,  S  M,  the  distance  I  M,  and  the 
direction  of  P's  motion,  it  would  be  impossible,  by  so  considering  it,  to 
attain  clear  views  of  its  dynamical  effect  after  any  considerable  lapse  of 
time,  and  it  therefore  becomes  necessary  to  resolve  it  into  other  equivalent 
forces  acting  in  such  directions  as  shall  admit  of  distinct  and  separate 
consideration.  Now  this  may  be  done  in  several  difierent  modes.  First, 
we  may  resolve  it  into  three  forces  acting  in  fixed  directions  in  space 
rectangular  to  one  another,  and  by  estimating  its  effect  in  each  of  these 
three  directions  separately,  conclude  the  total  or  joint  effect.  This  is  the 
mode  of  procedure  which  aff"ord3  the  readiest  and  most  advantageous 
handle  to  the  problem  of  perturbations  when  taken  up  in  all  its  generality, 
and  is  accordingly  that  resorted  to  by  geometers  of  the  modern  school  ia 
all  their  profound  resenrches  on  the  subject.  Another  mode  consists  in 
resolving  it  also  into  three  rectangular  components,  not,  however,  in  fixed 
directions,  but  in  variable  ones,  viz.  in  the  directions  of  the  lines  N  Q, 
Q  L,  and  L  S,  of  which  L  S  is  in  the  direction  of  tho  radius  vector  S  P, 
Q  L  in  a  direction  perpendicular  to  it,  and  in  the  plane  in  which  S  P  and 
a  tangent  to  P's  orbit  at  P  both  lie ;  and  lastly,  N  Q  in  a  direction  per- 
pendicular to  the  plane  in  which  P  is  at  the  instant  moving  about  8 
The  first  of  these  resolved  portions  we  may  term  the  radial  componeni 
of  the  disturbing  force,  or  simply  the  radial  disturbing  force;  the  second  the 
transversal ;  and  the  third  the  orthogonaV  When  the  disturbed  orbit  is 
one  of  small  exccntvicity,  the  transversal  component  acts  nearly  in  the 
direction  of  the  tangent  to  P's  orbit  at  P,  and  is  therefore  confounded  wUh 
that  resolved  component  which  we  shall  presently  describe  (art.  618)  under 

'  This  is  a  term  coined  fur  the  occasion.    The  want  of  some  appellation  for  this  com- 
ponent of  the  disturbing  force  is  often  felt. 


RESOLUTION   OF  THE   DISTUEBING  FORCIi!. 


335 


of  the  plane 
trary  to  what 
it  out  of  the 
he  disturbing 
litenesd  to  his 
ions  as  to  the 
'pposed  to  lie 
fixed  point,  in 
round  S. 
rst  instance  i. 
aider  it  in  this 
L  a  determinate 
he  position  of 
I  M,  and  the 
asidering  it,  to 
srable  lapse  of 
ther  equivalent 
t  and  separate 
modes.     First, 
ctions  in  space 
each  of  these 
This  is  the 
t  advantageous 
its  generality, 
odern  school  in 
ode  consists  in 
owever,  in  fixed 
the  lines  N  Q, 
ius  vector  S  P, 
which  S  P  and 
a  direction  per- 
oving  about  8 
dial  componeni 
;  the  second  the 
isturbed  orbit  is 
nearly  in  the 
lonfounded  w'th 
art.  618)  under 

lation  for  this  com- 


the  name  of  the  tangential  force.     This  is  the  mode  of  resolving  the 
disturbing  force  followed  by  Newton  and  his  immediate  successors. 

(616.)  The  immediate  actions  oi  these  components  of  the  disturbing 
force  are  evidently  independent  of  each  other,  being  rectangular  in  their 
directions ;  and  they  affect  the  movement  of  the  disturbed  body  in  modes 
perfectly  distinct  and  sharacteristic.  Thus,  the  radial  component,  being 
directed  to  or  from  the  central  body,  has  no  tendency  to  disturb  either 
the  plane  of  P's  orbit,  or  the  equable  description  of  areas  by  P  about  S, 
since  the  law  of  areas  proportional  to  the  times  is  not  a  character  of  the 
force  of  gravity  only,  but  holds  good  equally,  whatever  be  the  force  which 
retains  a  body  in  an  orbit,  provided  only  its  direction  is  al»yays  towards  a 
fixed  centre.'  Inasmuch,  however,  as  its  law  of  variation  is  not  conform- 
able to  the  simple  law  of  gravity,  it  alters  the  elliptic  form  of  P's  orbit, 
by  directly  aflFecting  both  its  curvature  and  velocity  at  every  point.  In 
virtue,  therefore,  of  the  action  of  this  disturbing  force,  the  orbit  deviates 
from  the  elliptic  form  by  the  approach  or  recess  of  P  to  or  from  S,  so  that 
the  eflPect  of  the  perturbations  produced  by  this  part  of  the  disturbing 
force  falls  wholly  on  the  radius  vector  of  the  disturbed  orbit. 

(617.)  The  transversal  disturbing  force  represented  by  QL,  on  the 
otlier  hand,  has  no  direct  action  to  draw  P  to  or  from  S.  It:,  ^hole  effi- 
ciency is  directed  to  accelerate  or  retard  P's  motion  in  a  direction  at  right 
angles  to  S  P.  Now  the  area  momentarily  descr.bed  by  P  about  S,  is, 
ceteris  paribus,  directly  as  the  velocity  of  P  in  a  direction  perpendicular 
to  S  P.  Whatever  force,  therefore,  increases  this  transverse  velocity  of 
P,  accelerates  the  description  of  areas,  and  vice  versd.  With  the  area 
ASP  is  directly  connected,  by  the  nature  of  the  ellipse,  the  angle  ASP 
described  or  to  be  described  by  P  from  a  fixed  line  in  the  plane  of  the 
orbit,  so  that  any  change  in  the  rate  o"  -lescription  of  areas  ultimately 
resolves  itself  into  a  change  in  the  amount  of  angular  motion  nbout  S, 
and  givjs  rise  to  a  departure  from  the  elliptic  laws.  Hence  arise  what 
are  called  in  the  peiturbational  theory  equations  (i.  e.  changes  or  fluctua- 
tions to  and  fro  about  an  average  quantity)  of  the  mean  motion  of  the 
disturbed  body.  '    '     - 

(618.)  There  is  yet  another  mode  of  resolving  the  disturbing  force  into 
rectangular  components,  which,  though  not  so  well  adapted  to  the  compu- 
tation of  results,  in  reducing  to  numerical  calculation  the  motions  of  the 
disturbed  body,  is  fitted  to  afford  %  clearer  insight  into  the  nature  of  the 
modifications  which  the  form,  magnitude,  and  situation  of  its  orbit  un- 
dergo in  virtue  of  its  action,  and  which  we  shall  therefore  employ  in 
preference.     It  consists  in  estimating  the  components  of  the  disturbing 

'  Newton,  i.  I. 


■11' 


."»;?^'-'^x 


JM 


*t.' 


i 

'■'*«f8fr 


fi- 


886 


OUTLINES   OF  ASTRONOMY. 


I 
I 

i 
* 
I 


I 
I 


force,  which  lie  in  the  plane  of  the  orbit,  not  in  the  direction  wo  hftvj 
termed  radial  and  transversal,  i.  e.  in  that  of  the  radius  vector  PS  and 
perpendicular  to  it,  but  in  the  direction  of  a  tangent  to  the  orbit  at  P, 
and  in  that  of  a  normal  to  the  curve,  and  at  right  angles  to  the  tangent, 
r  which  reason  these  components  may  be  called  the  tangential  and 
'■  tncl  disturbing  forces.  When  'he  orbit  of  the  disturbed  body  is  cir- 
cular, or  nearly  so,  this  mode  of  resolution  coincides  with  or  differs  but 
little  from  the  former,  but,  when  the  ellipticity  is  considerable,  these 
directions  may  deviate  from  the  radial  and  transversal  directions  to  ap^ 
extent.  As  in  the  Newtonian  mode  of  resolution,  the  effect  of  the  one 
component  falls  wholly  upon  the  approach  and  recess  of  the  body  P  to 
the  central  body  S,  and  of  the  other  wholly  on  the  rate  of  description  of 
areas  by  P  round  S,  so  in  this  which  we  are  now  considering,  the  direct 
effect  )i  the  one  component  (the  normal)  falls  wholly  on  the  curvature  of  the 
orbit  at  the  point  of  its  action,  increasing  that  curvature  when  the  normal 
force  acts  inwards,  or  towards  the  concavity  of  the  orbit,  and  diminishing 
it  when  in  the  opposite  direction ;  while,  on  the  other  hand,  the  tangential 
component  is  directly  effective  on  the  velocity  of  the  disturbed  body,  in- 
creasing or  diminishing  it  according  as  its  direction  conspires  with  or 
opposes  its  motion.  It  is  evident  enough  that  where  the  object  is  to  trace 
sinjply  the  changes  produced  by  the  disturbing  force,  in  angle  and  distance 
from  the  central  body,  the  former  mode  of  resolution  must  have  the 
advantage  in  perspicuity  of  view  and  applicability  to  calculation.  It  is 
less  obvious,  but  will  abundantly  appear  in  the  sequel  that  the  latter  offers 
peculiar  advantages  in  exhibiting  to  the  eye  and  the  reason  the  momen- 
tary influence  of  the  disturbing  force  on  the  elements  of  the  orbit  itself, 

(519.)  Neither  of  the  last  mentioned  pairs  of  the  resolved  portions  of 
the  disturbing  force  tends  to  draw  P  out  of  the  plane  of  its  orbit  PSA. 
But  the  remaining  or  orthogonal  portion  N  Q  acts  directly  and  solely  to 
produce  that  effect.  In  consequence,  under  the  influence  of  this  force,  P 
must  quit  that  plane,  and  (the  same  cause  continuing  in  action)  must 
describe  a  curve  of  double  curvature  as  it  ia  called,  no  two  consecutive 
portions  of  which  lie  in  the  same  plane  passing  through  S.  The  effect 
of  this  is  to  produce  a  continual  variation  in  those  elements  of  the  orbit 
of  P  on  which  the  situation  of  its  plane  in  space  depends ;  i.  e.  on  its 
inclination  to  a  fixed  plane,  and  the  position  in  such  a  plane  of  the  node 
or  line  of  its  intersection  therewith.  As  this,  among  all  the  various 
effects  of  perturbation,  is  that  which  is  at  once  the  most  simple  in  its 
conception,  and  the  easiest  to  follow  into  its  remoter  consequences,  we 
shall  begin  with  its  explanation. 

(G20.)  Suppose  that  up  to  P  (Art.  611,  614,)  the  body  were  describing 


EFFECTS  OF  THE  ORTHOQONAL  FORCE. 


83T 


jtion  ^0  hMi 
jctor  PS  and 
iie  orbit  at  P, 
0  the  tangent, 
ingential  and 
ed  body  is  cir- 
or  diffors  but 
dcrable,  these 
Bctions  to  ar^ 
Feet  of  the  one 
the  body  P  to 
description  of 
ring,  the  direct 
jurvatareof  the 
hen  the  normal 
nd  diminishing 
1,  the  tangential 
turbed  body,  in- 
nspires  with  or 
)bject  is  to  trace 
\ak  and  distance 
must  have  the 
culation.     It  is 
the  latter  offers 
on  the  moiuen- 
le  orbit  itself, 
ved  portions  of 
its  orbit  PSA. 
;ly  and  solely  to 
of  this  force,  P 
in  action)  must 
two  consecutive 
S.     The  effect 
nts  of  the  orbit 
ids ;  i-  e-  on  its 
ane  of  the  node 
all   the  various 
»st  simple  in  its 
sonsequcnces,  we 

were  describing 


an  undisturbed  orbit  C  P.  Then  at  P  it  would  be  moving  in  the  direotion 
of  a  tangent  P  R  to  the  ellipse  P  A,  which  prolonged  will  intersect  the 
plane  of  M's  orbit  somewhere  in  the  line  of  nodes,  as  at  R.  Now,  at  P, 
let  the  disturbing  force  parallel  to  N  Q  act  momentarily  on  P;  then  P 
will  bo  deflected  in  the  direction  of  that  force,  and  instead  of  the  arc  P  p, 
which  it  would  have  described  in  the  next  instant  if  undisturbed,  will 
describe  the  arc  P^  lying  in  the  state  of  things  represented  in  Art.  611, 
below,  and  in  Art.  614,  above,  Pjp  with  reference  to  the  plane  PSA. 
Thus,  by  this  action  of  the  disturbing  force,  the  plane  of  P's  orbit  will 
have  shifted  its  position  in  space  from  P  S  ^  (an  elementary  portion  of 
the  old  orbit)  to  P  S  y,  one  of  the  new.  Now  the  lines  of  nodes  SAB 
in  the  former  is  determined  by  prolonging  P  p  into  the  tangent  P  R, 
intersecting  the  plane  M  S  B  in  R,  and  joining  S  R.  And  in  like  manner, 
if  we  prolong  P  q  into  the  tangent  P  r,  meeting  the  same  plane  in  r,  and 
join  S  r,  this  will  be  the  new  line  of  nodes.  Thus  we  see  that,  under  the 
circumstances  expressed  in  the  form  **  figure,  the  momentary  action  of  the 
orthogonal  disturbing  force  will  havt.  jaused  the  line  of  nodes  to  retro- 
grade upon  the  plane  of  the  orbit  of  the  disturbing  body,  and  under 
those  represented  in  the  latter  to  advance.  And  it  is  evident  that  the 
action  of  the  other  resolved  portions  of  the  disturbing  force  will  not  in 
the  least  interfere  with  this  result,  for  neither  of  them  tends  either  to 
carry  P  out  of  its  former  plane  of  motion,  or  to  prevent  its  quitting  it. 
Their  influence  would  merely  go  to  transfer  the  points  of  intersection  of 
the  tangents  PporPq  from  R  or  r  to  R'  or  r',  points  nearer  to  or  far- 
ther from  S  than  R  r,  but  in  the  same  lines. 

(621.)  Supposing,  now,  M  to  lie  to  the  left  instead  of  the  right  side 
of  the  line  of  nodes  in  fig.  1.,  P  retaini.  g  its  situation,  and  M  P  being 
less  than  M  S,  so  that  X  shall  still  lie  between  M  and  S.  In  this  situation 
of  things  (or  configuration,  as  it  is  termed  of  the  three  bodies  with 
respect  to  each  other,)  N  will  lie  behvo  the  plane  ASP,  and  the  disturb- 
ing force  will  tend  to  raise  the  body  P  above  the  plane,  the  resolved 
orthogonal  portion  N  Q  in  this  case  acting  upwards.  The  disturbed  arc 
P  q  will  therefore  lie  above  P  p,  and  when  prolonged  to  meet  the  plane 
M  S  B,  will  intersect  it  in  a  point  in  advance  of*  R ;  so  that  in  this  con- 
figuration the  node  will  advance  upon  the  plane  of  the  orbit  of  M,  pro- 
vided always  that  the  latter  orbit  remains  fixed,  or,  at  least,  does  not  itself 
shift  its  position  in  such  a  direction  as  to  defeat  this  result. 

(622.)  Oenerally  speaking,  the  node  of  the  disturbed  orbit  will  recede 
I  «j)o»  any  plane  which  we  may  consider  as  fixed,  whenever  the  action  of 
the  orthogonal  disturbing  force  tends  to  bring  the  disturbed  body  nearer 
I  to  that  plane :  and  vice  versA.    This  will  be  evident  on  a  mere  inspection 
22 


•m,     ^ 


'•i 

•i 
■ 


jKCl^'T 


".*       •  .  i  ■  ■"  > 
,1,.,,  ■"'    VVJ,I 


'*&»: 


SU*- «:»*(. f 


li 


388 


OUTLINES   OF  ASTRONOMY. 


<•. ,  t, 


I 

18 


of  the  annexed  figure,  in  which  C  A  reprcsenta  a  semicircle  of  the  projec- 
tion of  the  fixed  plane  as  seen  from  S  on  the  sphere  of  the  heavens,  and 
0  P  A  that  of  the  plane  of  P's  undisturbed  orbit,  the  motion  of  P  being 
in  the  direction  of  the  arrow,  from  C  the  ascending,  to  A  the  descend- 
ing node.     It  is  at  once  seen,  by  prolonging  V  q^F  q'  into  arcs  of  great 


,  ^  -'  ■;  / 


circles,  P  r,  P  r,  (forwards  or  backwards,  as  the  case  may  be)  to  meet 
C  A,  that  the  node  will  have  retrograded  through  the  arc  A  r,  or  C  r, 
whenever  P  q  lies  between  C  P  A  and  C  A,  or  when  the  perturbing  force 
carries  P  towards  the  fixed  plane,  but  will  have  advanced  through  A  r'  or 
C  r'  whefi  P  q'  lies  above  G  P  A,  or  when  the  disturbing  impulse  has 
lifted  P  above  its  old  orbit  or  away  from  the  fixed  plane,  and  this  with- 
out any  reference  to  whether  the  undisturbed  orhitual  motion  o  V  at  the 
moment  is  carrying  it  towards  the  plane  C  A  or  from  it,  as  in  the  two 
cases  represented  in  the  figure. 

(628.)  Let  us  now  consider  the  mutual  disturbance  of  two  bodies  M 
and  P,  in  the  various  configurations  in  which  they  may  be  presented  to 
each  other  and  to  their  common  central  body.  And  first,  let  us  take  the 
case,  as  the  simplest,  where  the  disturbed  orbit  is  exterior  to  that  of  the 
disturbing  body  (as  in  fig.  art.  614),  and  the  distance  between  the  orbits 
greater  than  the  semiaxis  of  the  smaller.  First,  let  both  planets  lie  od 
the  same  side  of  the  line  of  nodes.  Then  (as  in  art.  620)  the  direc 
tion  of  the  whole  disturbing  force,  and  therefore  also  that  of  its  ortho- 
gonal component,  will  be  towards  the  opposite  side  of  the  plane  of  Fs 
orbit  from  that  on  which  M  lies.  Its  effect  therefore  will  be,  to  draw  P 
out  of  its  plane  in  a  direction  from  the  plane  of  M's  orbit,  so  that  in  this 
state  of  things  the  node  will  advance  on  the  latter  plane,  however  P  and 
M  may  be  situated  in  these  semicircumferenccs  of  their  respective  orbits. 
Suppose,  nes.t,  M  transferred  to  the  opposite  side  of  the  line  of  iiodes, 
then  will  the  direction  of  its  action  on  P,  with  respect  to  the  plane  of  P's 
orbit,  be  reversed,  and  P  in  quitting  that  plane  will  now  approach  to 
instead  of  receding  from  the  plane  of  M's  orbit,  so  that  its  node  will  nov 
recede  on  that  plane. 

(624.)  Thus,  while  M  and  P  revolve  about  S,  and  in  the  course  of  many 
revolutions  of  each  are  presented  to  each  other  and  to  S  in  all  possible 
configurations,  the  node  of  P's  orbit  will  always  advance  on  M's  when  I 


MOTION  OF  THE  NODES. 


889 


)f  the  projec- 
heavens,  and 
n  of  P  being 
the  descend- 
arca  of  great 


c    r 


ly  be)  to  meet 
irc  A  r,  or  C  r, 
lerturbing  force 
,hrougb  A  r'  or 
ig  impulse  has 
^  and  this  icith- 
Hon  0  V  attJm 
it,  as  in  the  two 

if  two  bodies  M 
be  presented  to 
t,  let  us  take  the 
or  to  that  of  the 
itween  the  orbits 
h  planets  lie  on 
,  620)  the  direc 
,bat  of  its  ortho- 
the  plane  of  Fa 
Jill  be,  to  draw  P 
bit,  80  that  in  this 
e,  however  P  and 
respective  orbits. 
the  line  of  iiodes, 
)  the  plane  of  I"8 
now  approach  to 
t  its  node  will  now 

the  course  of  many ! 
S  in  all  po£ 

nee  on  M's  when  I 


both  bodies  are  on  the  same  side  of  the  line  of  nodes,  and  recede  when 
on  the  opposite.  They  will,  therefore,  on  an  average,  advance  and  recede 
during  equal  times  (supposing  the  orbits  nearly  circular).  And,  there- 
fore, if  their  advance  were  at  each  instant  of  its  duration  equally  rapid 
with  their  recess  at  each  corresponding  instant  during  that  phase  of  the 
movement,  they  would  merely  oscillate  to  and  fro  about  a  mean  position, 
without  any  permanent  motion  in  either  direction.  But  this  is  not  the 
case.  The  rapidity  of  their  recess  in  every  position  favourable  to  recess 
is  greater  than  that  of  their  advance  in  the  corresponding  opposite  posi- 
tion.   To  show  this,  let  us  consider  any  two  configurations  in  which  M's 

H-  '      Fig.  79.  f . 


■'J'-*'.  ^5- 


phases  are  diametrically  opposite,  so  that  the  triangles  P  S  M,  P  S  M', 
shall  lie  in  one  plane,  having  any  inclination  to  P's  orbit,  according  to  the 
situation  of  P.  Produce  P  S,  and  draw  M  m,  M'm'  perpendicular  to  it, 
which  will  therefore  be  equal.  Take  M  N  :  M  S  : :  M  S' :  M  F,  and 
M'  N'  :  M'  S  : :  M'  S« :  M'  P» :  then,  if  the  orbits  be  nearly  circles,  and 
therefore  M  S  =  M'  S,  N'  M'  will  be  less  than  M  N ;  and  therefore 
(since  P  M'  is  greater  than  P  M)  P  N'  :  P  M'  in  a  greater  ratio  than 
P  N  :  P  M ;  and  consequently,  by  similar  triangles,  drawing  N  n,  N'  » 
perpendicular  to  P  S,  N'  w'  :  M'  m  in  a  greater  ratio  than  N  «  :  M  m,  r.nd 
therefore  N'  n'  is  greater  than  N  n.  Now  the  plane  P  M  M*  intersects 
Fs  orbit  in  P  S,  and  being  inclined  to  that  orbit  at  the  same  angle 
through  its  whole  extent,  if  from  N  and  N'  perpendiculars  be  conceived 
let  fall  on  that  orbit,  these  will  be  to  each  other  in  the  proportion  of  N  n, 
N'n';  and  therefore  the  perpendicular  from  N'  will  be  greater  than  that 
from  N.  Now  since  by  art.  611  N'  S  and  N  S  represent  in  quantity  a'^d 
direction  the  total  disturbing  forces  of  M'  and  M  on  P  respectively,  there- 
fore these  perpendiculars  express  (art.  615)  the  orthogonal  disturbing 


'  "«■  ■  .V*.. 


-%-^ 


,,^,  -•'  v.,4 

'■^■'••".■.•tfBJI 


840 


OUTLINES   07  ASTRONOMT. 


I 

CI: 

8' 


forces,  the  former  of  which  tends  (as  above  shown)  to  make  the  nodes 
recede,  and  the  latter  to  advance;  and  therefore  the  preponderance  in 
every  such  pair  of  situations  of  M  is  in  favour  of  a  retrograde  motion. 

(625.)  liCt  us  next  consider  the  case  where  the  distance  between  the 
orbits  is  less  than  the  semiazis  of  the  interior,  or  in  which  the  least  dis- 
tonce  of  M  from  P  is  less  than  M  S.    Take  any  situation  of  P  with 

Fig.  80. 


respect  to  the  line  of  nodes  AC.  Then  two  points  d  and  e,  distant  by 
less  than  120**,  can  be  taken  on  the  orbit  of  M  equidistant  from  P  with 
S.  Suppose  M  to  occupy  successively  every  possible  situation  in  its  orbit, 
P  retaining  its  place ;  —  then,  if  it  were  not  for  the  existence  of  the  arc 
de,  in  which  the  relations  of  art.  G24  are  reversed,  it  would  appear  by 
the  reasoning  of  that  article  that  the  motion  of  the  node  is  direct  when 
M  occupies  any  part  of  the  semiorbit  F  M  B,  and  retrograde  when  it  is  in 
the  opposite,  but  that  the  retrograde  motion  on  the  whole  would  predom- 
inate. Much  more  then  will  it  predominate  when  there  exists  an  arc 
dM.e  within  which  if  M  be  placed,  its  action  will  produce  a  retrograde 
instead  of  a  direct  motion. 

(626.)  This  supposes  that  the  are  de  lies  wholly  in  the  semicircle 
"EdB.  But  suppose  it  to  lie,  as  in  the  annexed  figure,  partly  within  and 
partly  without  that  circle.    The  greater  part  dB  necessarily  lies  within 


Fig.  81. 


"1  "■'-. 


it,  and  not  only  so,  but  within  that  portion,  the  point  of  M's  orbit  nearest 
to  P,  in  which,  therefore,  the  retrograding  force  has  its  maximum,  is  sit- 
uated. Although,  therefore,  in  the  portion  Be,  it  is  true,  the  retrograde 
tendency  otherwise  general  oyer  the  whole  of  tJiat  semicirolo  (Art.  624) 


MOTION   OF  THE   NODES. 


841 


:e  the  nodes 
onderaace  in 
le  motion, 
between  tbe 
the  least  dis* 
on  of  P  with 


,nd  e,  distant  by 
int  from  P  with 
tion  in  its  orbit, 
tence  of  the  arc 
rould  appear  by 
5  is  direct  wben 
ade  when  it  is  ia 
e  would  predom- 
re  exists  an  arc 
luce  a  retrograde 

n  the  semicircle 
)artly  within  and 
irily  lies  within 


will  be  reversed,  yet  the  effect  of  this  will  be  much  more  than  counter- 
balanced by  tbe  more  energetic  and  more  prolonged  retrograde  action  over 
dB;  and,  therefore,  in  tbis  <!U80  also,  on  the  average  of  every  possible 
situation  of  M,  tbe  motion  of  the  node  will  bo  retrograde. 

(627.)  Let  us  lastly  consider  an  interior  planet  disturbed  by  an  exte- 
rior.   Take  M D  and  M  E  (fig.  of  art.  Gil.)  each  equal  to  MS.     Then 
first,  when  P  is  between  D  and  the  node  A,  being  nearer  than  S  to  M, 
the  disturbing  force  acts  towards  M's  orbit  on  the  side  on  which  M  lies, 
and  the  node  recedes.     It  also  recedes  when  (M  retaining  the  same  situa- 
tion) P  is  in  any  part  of  the  arc  E  C  from  E  to  the  other  node,  because 
in  that  situation  the  direction  of  the  disturbing  force,  it  is  true,  is  re- 
versed, but  that  portion  of  P's  orbit  being  also  reversely  situated  with 
respect  to  the  plane  of  M's,  P  is  still  urged  towards  the  latter  plane,  but 
on  the  side  opposite  to  M.     Thus,  (M  holding  its  place)  whenever  P  is 
anywbcre  in  D  A  or  E  di  the  node  recedes.     On  the  other  hand,  it  ad- 
vances whenever  P  is  between  A  and  E  or  between  C  and  D,  because,  in 
these  arcs,  only  one  of  the  two  determining  elements  (viz.  the  direction 
of  the  disturbing  force  with  respect  to  the  plane  of  P's  orbit ;  and  the 
situation  of  tbe  one  plane  with  respect  to  the  other  ns  to  above  and  be- 
low) has  undergone  reversal.     Now  first,  whenever  M  is  anywhere  but  in 
tiic  line  of  nodes,  the  sum  of  the  arcs  D  A  and  E  C  exceeds  a  semicircle, 
and  that  the  more,  the  nearer  M  is  to  a  position  at  right  angles  to  the 
line  of  nodes.     Secondly,  the  arcs  favourable  to  the  recess  of  the  node 
comprehend  those  situations  in  which  tbe  orthogonal  disturbing  force  is 
most  powerful,  and  vice  versd.     This  is  evident,  because  as  P  approaches 
D  or  E,  this  component  decreases,  and  vanishes  at  those  points  (612.) 
The  movement  of  the  node  itself  also  vanishes  when  P  comes  to  the 
node,  for  although  in  this  position  the  disturbing  orthogonal  force  neither 
vanishes  nor  changes  its  direction,  yet,  since  at  the  instant  of  P's  passing 
the  node  (A)  the  recess  of  the  node  is  changed  into  an  advance,  it  must 
necessarily  at  that  point  be  stationary.'     Owing  to  both  these  causes, 
therefore,  (that  tbe  mode  recedes  during  a  longer  time  than  it  advances, 
and  that  a  more  energetic  force  acting  in  its  recess  causes  it  to  recede 
more  rapidly,)  the  retrograde  motion  will  preponderate  on  the  whole  in 
each  complete  synodic  revolution  of  P.     And  it  is  evident  that  the  rea- 
soning of  this  and  the  foregoing  articles,  is  no  way  vitiated  by  a  moderate 
amount  of  excentricity  in  either  orbit. 


fVTJ 


it 


M's  orbit  nearest 

maximum,  is  sit- 

jie,  the  retrograde 

licirclo  (Art.  624) 


It  would  seem,  at  first  sight,  as  if  a  change  per  $altum  took  place  here,  but  the 
I  continuity  of  the  node's  motion  will  be  apparent  from  an  inspection  of  the  annexed 
[figure,  where  bad  is  a  portion  of  P's  disturbed  path  near  the  node  A,  concave  towards 
9  plane  U  A.    The  momentary  place  of  the  moving  node  is  determined  by  the  inter- 


ta 


842 


OUTLINES  OF  ASTRONOMT. 


'  (628.)  It  is  therefore  a  geDoral  proposition,  that  on  the  average  of  each 
complete  synodic  revolution,  the  node  of  every  disturbed  planet  recedes 
upon  the  orbit  of  the  disturbing  one,  or  in  other  words,  that  in  every  puir 
of  orbits,  the  node  of  each  recedes  upon  the  other,  and  of  course  upon  any 
intermediate  plane  which  we  may  regard  as  fixed.  On  a  plane  not  inter- 
mediate between  them,  however,  the  node  of  one  orbit  will  advance,  and 
that  of  the  other  will  recede.    Suppose  for  instance,  C  A  C  to  be  a  piano 

Fig.  88. 


m 


. »» 

•'II 

V 

II 
■I 

j; 
•t 

e; 


%2 


intermediate  between  PP  an''  M  M  the  two  orbits.  K  pp  and  wim  be 
the  new  positions  of  the  orbits,  the  node  of  P  on  M  will  have  receded 
from  A  to  5,  that  of  M  on  F  from  A  to  4,  that  of  P  and  M  on  C  C  re- 
spectively from  A  to  1  and  from  A  to  2.  But  if  F  A  F  bo  a  plane  Dot 
intermediate,  the  node  of  M  on  that  plane  baa  receded  from  A  to  6,  but 
that  of  P  will  have  advanced  from  A  to  7.  If  the  fixed  plane  have  not 
a  common  intersection  with  those  of  both  orbits,  it  is  equally  easy  to  sec 
that  the  node  of  the  disturbed  orbit  may  either  recede  on  both  that  plane 
and  the  disturbing  orbit,  or  advance  on  the  one  and  recede  on  the  other, 
according  to  the  relative  situation  of  the  planes. 

(629.)  This  is  the  case  with  the  planetary  orbits.     They  do  not  all 

section  of  the  tangent  &e  with  A  G,  which  as  6  passes  through  a  to  d,  recedes  from  A 

Fig.  82. 


to  a,  rests  there  for  an  instant*  and  then  advances  again. 


MOTION   OF  THE   NODES. 


848 


reroge  of  each 
)laQot  rccodos 

I  in  every  pair 
urHe  upon  any 
llano  not  inter- 

II  advance,  and 
3  to  bo  a  plane 


•m 


pp  and  mm  be 
rill  have  receded 
id  M  on  C  C  re- 
bo  a  plane  not 
from  A  to  6,  but 
d  plane  have  not 
qually  easy  to  sec 
n  both  that  plane 
cede  on  the  other, 

They  do  not  all 

to  d,  recedes  from  A 


intersect  each  other  in  a  common  node.  Although  perfectly  true,  there* 
furu,  that  tlio  node  of  any  one  planot  would  recede  on  the  orbit  of  any  and 
each  other  by  the  individual  action  of  thiit  other,  yet,  when  all  act  to- 
gether, recess  on  one  piano  may  be  equivalent  to  advance  on  another,  so 
thut  the  motion  of  the  node  of  any  one  orbit  on  a  given  plane,  arising  from 
their  joint  action,  taking  into  account  the  different  situations  of  all  the 
planes,  becomes  a  curiously  complicated  phtcnomcnon  whose  law  cannot 
be  very  easily  expressed  in  words,  though  reducible  to  strict  ni  'ical 
statement,  being,  in  fact,  a  mere  geometrical  result  of  what  is  «bove 
shown. 

((130.)  The  nodes  of  all  the  planetary  orbit: >  on  the  true  ecliptic,  as  a 
matter  of  fact,  are  retrograde,  though  they  arc  not  all  so  on  a  fixed  plane, 
such  as  wo  may  conceive  to  exist  in  the  planetary  system,  and  to  be  a 
plane  of  reference  unaffected  by  their  mutual  ('■sturban'^es.  It  is.  how- 
cvor,  to  the  ecliptic,  that  we  are  under  the  necessity  of  referrir  their 
movements  from  our  station  in  the  sy.stoni;  and  if  we  would  tr  u  j'or  our 
ideas  to  a  fixed  plane,  it  becomes  necessary  to  take  account  of  the  varia- 
tion of  the  ecliptic  itself,  produced  by  the  joint  action  c :  v.il  the  planets. 

(08 1.)  Owing  to  the  smallncss  of  the  masses  of  the  planets,  and  their 
groat  distances  from  each  other,  the  revolutions  of  their  nodes  are  exees- 
gively  slow,  being  in  every  case  less  tlum  a  single  degree  por  century,  and 
in  most  cases  not  amounting  to  half  that  quantity.  It  is  otherwi.se  with 
the  mc.on,  and  that  owing  to  two  distinct  reasons.  First,  that  the  disturb- 
ing force  itself  arising  from  the  sun's  action,  (os  appears  from  the  table 
given  in  art.  012,)  bears  a  much  larger  proportion  to  the  earth's  central 
attraction  on  the  moon  than  in  the  case  of  any  planet  disturbed  by  any 
other.  And  secondly,  because  the  synodic  revolution  of  the  moon, 
within  which  the  average  is  struck  (and  always  on  the  side  of  recess),  is 
only  29  J  days,  a  period  much  shorter  tl  "'i  ^".lat  of  any  of  the  planets, 
and  vastly  so  than  that  of  several  among  them.  All  this  is  agreeable  to 
what  has  already  been  stated  (art.  407,  408,)  respecting  the  motion  of  the 
moon's  nodes,  and  it  is  hardly  necessary  to  mention  that,  when  calculated, 
as  it  has  been,  d  priori,  from  an  e:;act  estimation  of  all  the  acting  forces, 
the  result  is  found  to  coincide  with  perfect  precision  with  that  immediately 
derived  from  observation,  so  that  not  a  doubt  can  subsist  as  to  this  being 
the  real  process  by  which  so  remarkable  an  effect  is  produced. 

(032.)  So  far  as  the  physical  condition  of  each  planet  is  concerned,  it 
is  evident  that  the  position  of  their  nodes  can  be  of  little  importance.  It 
is  otherwise  with  the  mutual  inclinations  of  their  orbits  with  respect  to 
each  other,  and  to  fhe  equator  of  each.  A  variation  in  the  position  of  the 
ecliptic,  for  instance,  by  which  its  pole  should  shift  its  distance  from,  the 


''Wmrv 


••««."«« 


«» 


V 


844 


OUTLINES  OF  ASTRONOMY. 


I»< 


M 

11 


■iHt 


pole  of  the  equator,  would  disturb  our  seasons.  Should  the  plane  of  the 
earth's  orbis,  for  instapce,  ever  be  so  changed  as  to  bring  the  ecliptic  to 
coincide  with  the  equator,  we  should  have  perpetual  spring  over  all  the 
world ;  and  on  the  other  hand,  should  it  coincide  with  a  meridian,  the 
extremes  of  summer  and  winter  would  become  intolerable.  The  inquiry, 
then,  of  the  variations  of  inclination  of  the  planetary  orbits  inter  se,  is 
one  of  much  higher  practical  interest  than  those  of  their  nodes. 

(633,)  Referring  to  the  figures  of  art.  610,  et  seq.,  it  is  evident  that 
the  plane  S  Pg,  in  which  the  disturbed  body  moves  during  an  instant  of 
time  from  its  quitting  P,  is  differently  inclined  to  the  orbit  of  M,  or  to  a 
fixed  plane,  from  the  original  or  undisturbed  plane  P  Sj?.  The  difference 
of  absolute  position  of  these  two  planes  in  space  is  the  angle  between  the 
planes  P  S  R  and  P  S  r,  and  is  therefore  calculable  by  spherical  trigono- 
metry, when  the  angle  R  S  r  or  the  momentary  recess  of  the  node  is 
known,  and  also  the  inclination  of  the  planes  of  the  orbits  to  each  other. 
We  perceive,  then,  that  between  the  momentary  change  of  inclination, 
and  the  momentary  recess  of  the  node,  there  exists  an  intimate  relation, 
and  that  the  research  of  the  one  is  in  fact  bound  up  in  that  of  the  other. 
This  may  be,  perhaps,  made  clearer,  by  considering  the  orbit  of  P  to  be 
not  merely  an  imaginary  line,  but  an  actual  circle  or  elliptic  hoop  of  some 
rigid  material,  without  inertia,  on  which,  as  on  a  wire,  the  body  P  may 
slide  as  a  bead.  It  is  evident  that  the  position  of  this  hoop  will  be  deter- 
mined at  any  instant,  by  its  inclination  to  the  ground  plane  to  which  it 
is  referred,  and  by  the  place  of  its  intersection  therewith,  or  node.  It 
will  also  be  determined  by  the  momentary  direction  of  P's  motion,  which 
(having  no  inertia)  it  must  obey ;  and  any  change  by  which  P  should,  in 
the  next  instant,  alter  its  orbit,  would  be  equivalent  to  a  shifting,  bodily, 
of  the  whole  hoop,  changing  at  once  its  inclination  and  nodes. 

(634.)  One  immediate  conclusion  from  what  has  been  pointed  out 
above,  is  that  where  the  orbits,  as  in  the  case  of  the  planetary  system  and 
the  moon,  are  slightly  inclined  to  one  another,  the  momentary  variations 
of  the  inclination  are  of  an  order  much  inferior  in  magnitude  to  those  ia 
the  place  of  the  node.  This  is  evident  on  a  mere  inspection  of  our  figure, 
the  angle  R  P  r  being,  by  reason  of  the  small  inclination  of  the  planes 
S  P  R  and  R  S  r,  necessarily  much  smaller  than  the  angle  R  S  r.  In  pro- 
portion as  the  planes  of  the  orbits  are  brought  to  coincidence,  a  very  tri- 
fling angular  movement  of  Vp  about  P  S  as  an  axis  will  make  a  great 
variation  in  the  situation  of  the  point  r,  where  its  prolongation  intersects 
the  ground  plane. 

(635.)  Referring  to  the  figure  of  art.  622,  we  perceive  that  although 
the  motion  of  the  node  is  retrograde  whenever  the  momentary  disturbed 


CHANQE   OF   INCLINATION. 


345 


plane  of  the 
e  ecliptic  to 
over  all  the 
aaeridian,  the 
The  inquiry, 
s  inter  se,  is 

ies. 

\  evident  that 
au  instant  of 
of  M,  or  to  a 
The  difference 
le  between  the 
lerical  trigono- 
of  the  node  is 
I  to  each  other. 
of  inclination, 
timate  relation, 
it  of  the  other, 
irbit  of  P  to  be 
;ic  hoop  of  some 
he  body  P  may 
DP  will  be  detcr- 
lane  to  which  it 
lb,  or  node.    It 
's  motion,  which 
ich  P  should,  in 
shifting,  bodily, 
odes. 

een  pointed  out 
stary  system  and 
entary  variations 
itude  to  those  in 
ion  of  our  figure, 
in  of  the  planes 
leBSr.  Inpro- 
dence,  a  very  tri- 
rill  make  a  great 
igation  intersects 

ve  that  although 
nentary  disturbed 


arc  P  Q  lies  between  the  planes  C  A  and  C  G  A  of  the  two  orbits,  and 
vice  vcrsd,  indifferently  whether  P  be  in  the  act  of  receding  from  the 
plane  0  A,  as  in  the  quadrant  C  G,  or  of  approaching  to  it,  as  in  G  A, 
yet  the  same  identity  as  to  the  character  of  the  change  does  not  subsist 
in  respect  of  the  inclination.  The  inclination  of  the  disturbed  orbit  (i.  e. 
of  its  momentary  element)  Pj  or  Pg^,  is  measured  by  the  spherical  angle 
P  r  H  or  P  /  H.  Now  in  the  quadrant  C  G,  P  r  H  is  less,  and  Fr'K 
greater  than  P  C  H  j  but  in  G  A,  the  converse.  Hence  this  rule : — 1st, 
If  the  disturbing  force  urge  P  towards  the  plane  of  M's  orbit,  and  the 
undisturbed  motion  of  P  carry  it  also  towards  that  plane ;  and  2dly,  if  the 
disturbing  force  urge  P  from  that  plane,  while  P's  undisturbed  motion  also 
carries  it  from  it,  in  either  case  the  inclination  momentarily  increases  j  but 
if,  3dly,  the  disturbing  force  act  to,  and  P's  motion  carry  it  from  —  or  if 
the  force  act  from,  and  the  motion  carry  it  to,  that  plane,  the  inclination 
momentarily  diminishes.  Or  (including  all  the  cases  under  one  alternative) 
if  the  action  of  the  disturbing  force  and  the  undisturbed  motion  of  P  with 
reference  to  the  plane  of  M's  orbit  be  of  the  same  character,  the  inclina- 
tion increases ;  if  of  contrary  characters,  it  diminishes. 

(636.)  To  pass  from  the  momentary  changes  which  take  place  in  the 
relations  of  nature  to  the  accumulated  effects  produced  in  considerable 
lapses  of  time  by  the  continued  action  of  the  same  causes,  under  circum- 
stances varied  by  these  very  effects,  is  the  business  of  the  integral  calculus. 
Without  going  into  any  calculations,  however,  it  will  be  easy  for  us  to 
demonstrate  from  the  principles  above  laid  down,  the  leading  features  of 
thii5  part  of  the  planetary  theory,  viz.  the  periodic  nature  of  the  change 
of  the  inclinations  of  two  orbits  to  each  other,  the  re-establishment  of  their 
original  valuee,  and  the  consequent  oscillation  of  each  plane  about  a  certain 
mean  position.  As  in  explaining  the  motion  of  the  nodes,  we  will  com- 
mence,  as  the  simplest  case,  with  that  of  an  exterior  planet  disturbed  by 
an  interior  one  at  less  than  half  its  distance  from  the  central  body.  Let 
A  C  A'  be  the  great  circle  of  the  heavens  into  which  M's  orbit  seen  from 
S  is  projected,  extended  into  a  straight  line,  and  AgChA!  the  corre- 
sponding projection  of  the  orbit  of  P  so  seen.  Let  M  occupy  some  fixed 
situation,  suppose  in  the  semicircle  A  C,  and  let  P  describe  a  complete 
revolution  from  A  through  gChtxi  A'.  Then  while  it  is  between  A  and 
g  or  in  its  first  quadrant,  its  motion  is  from  the  plane  of  M's  orbit,  and 
at  the  same  time  the  orthogonal  force  acts  from  that  plane :  the  inclina- 
tion, therefore,  (art.  635)  increases.  In  the  second  quadrant  the  motion 
of  P  is  to,  but  the  force  continues  to  act  from,  the  plane,  and  the  inclinor 
tion  again  decreases.  A  similar  alternation  takes  place  in  its  course 
through  the  quadrants  Ch  and  hA.    Thus  the  plane  of  P's  orbit  oscil- 


linn 


c 


•1 


■-V:-*r( 


',;*-•"'       V.-,.) 


■  ■3Ht 


n 


i      I 


346 


OUTLINES  OP   ASTRONOMY. 


Fig.  84. 


rl 

If 

Ir 

u 


i; 


lates  to  and  fro  about  its  mean  position  twice  in  each  revolution  of  P. 
During  this  process  if  M  held  a  fixed  position  at  G,  the  forces  being 
symmetrically  alike  on  either  side,  the  extent  of  these  oscillations  would  be 
exactly  equal,  and  the  inclination  at  the  end  of  one  revolution  of  P  would 
revert  precisely  to  its  original  value.  But  if  M  be  elsewhere,  this  will 
not  be  the  case,  and  in  a  single  revolution  of  P,  only  a  partial  compensa- 
tion will  be  operated,  and  an  overplus  on  the  side,  suppose  of  diminution, 
will  remain  outstanding.  But  when  M"  comes  to  M',  a  point  equidistant 
from  G  on  the  other  side,  this  eflFect  will  be  precisely  reversed  (supposing 
the  orbits  circular).  On  the  average  of  both  situations,  therefore,  the 
effect  will  be  the  same  as  if  M  were  divided  into  two  equal  portions,  one 
placed  at  M  and  the  other  at  M',  which  will  annihilate  the  preponderance 
in  question  and  effect  a  perfect  restoration.  And  on  an  average  of  all 
possible  situations  of  M,  the  effect  will  in  like  manner  be  the  same  as  if 
its  mass  were  distributed  over  the  whole  circumference  of  its  orbit,  forming 
a  ring,  each  portion  of  which  will  exactly  destroy  the  effect  of  that  simi- 
larly situated  on  the  opposite  side  of  the  line  of  nodes. 

(673.)  The  reasoning  is  precisely  similar  for  the  more  complicated 
cases  of  arts.  (625)  and  (627.)  Suppose  that  owing  either  to  the 
proximity  of  the  two  orbits,  (in  the  case  of  an  exterior  disturbed  planet) 
or  to  the  disturbed  orbit  being  Interior  to  the  disturbing  one,  there  were 
a  larger  or  less  portion,  d  e,  of  P's  orbit  in  which  these  relations  were 
reversed.  Let  M  be  the  position  of  M'  corresponding  to  d  e,  then  taking 
G  M'=:=G-  M,  there  will  be  a  similar  portion  d'  d  bearing  precisely  the 
sam'  reversed  relation  to  M',  and  therefore,  tho  actions  of  M'  M,  will 
equally  neutralize  each  other  in  this  as  in  the  former  state  of  things. 

(638.)  To  operate  a  complete  and  rigorous  compensation,  however,  it 
is  necessary  that  M  should  be  presented  to  P  in  every  possible  conOgun- 
tion,  not  only  with  respect  to  P  itself,  but  to  the  line  of  nodes,  to  the 
position  of  which  line  the  whole  reasoning  bears  reference.  In  the  case 
of  the  moon  for  example,  the  disturbed  body  (the  moon)  revolves  in 
27''-322,  tho  disturbing  (the  sun)  in  365<-256,  and  the  lino  of  nodes  in 
6793''-391,  numbers  in  proportion  to  each  other  about  a?  1  to  13  and  249 
respectively.  Now  in  13  revolutions  of  P,  and  one  of  jNI,  if  the  node 
remained  fixed,  P  would  have  been  presented  to  31  so  nearly  in  every 


10 


CHANGE   OF  INCLINATION. 


347 


rolution  of  P. 
,  forces  being 
tions  would  be 
on  of  P  would 
rbere,  this  will 
tial  compensa- 
of  diminution, 
int  equidistant 
•sed  (supposing 
,  therefore,  tbc 
al  portions,  one 
B  preponderance 
1  average  of  all 
e  the  same  as  if 
ts  orbit,  forming 
;ct  of  that  sinii- 

lore  complicated 
y  either  to  the 
listurbed  planet) 

one,  there  were 
'se  relations  wore 

d  e,  then  taking 
ing  precisely  tbe 
ns  of  M'  M,  mW 
ite  of  things, 
lation,  however,  it 
possible  conBgura- 

of  nodes,  to  tbe 
jnce.  In  the  case 
;noon)  revolves  in 
le  line  of  nodes  in 
vs  1  to  13  and  249 
)f  ISI,  if  the  node 
0  nearly  in  every 


configuration  as  to  operate  an  almost  exact  compensation.  But  in  1 
revolution  of  M,  or  13  of  P,  the  node  itself  has  shifted  ^^\  or  about  j'g 
of  a  revolution,  in  a  direction  opposite  to  the  revolutions  of  M  and  P,  so 
that  although  P  has  been  brought  back  to  the  same  configuration  with 
respect  to  M,  both  are  j'g  of  a  revolution  in  advance  of  the  same  configu- 
ration as  respects  the  node.  The  compensation,  therefore,  will  not  be 
exact,  and  to  make  it  so,  this  process  must  be  gone  through  19  times,  at 
tbe  end  of  which  both  the  bodies  will  be  restored  to  the  same  relative 
position,  not  only  with  respect  to  each  other,  but  to  the  node.  The 
fractional  parts  of  entire  revolutions,  which  in  this  explanation  have  been 
neglected,  are  evidently  no  farther  influential  than  as  rendering  the  com- 
pensation thus  operated  in  a  revolution  of  the  node  slightly  inexact,  and 
thus  giving  rise  to  a  compound  period  of  greater  duration,  at  the  end  of 
which  a  compensation  almost  mathematically  rigorous,  will  have  been 
eflFected. 

(639.)  It  is  clear  then,  that  if  the  orbits  be  circles,  the  lapse  of  a  very 
moderate  number  of  revolutions  of  the  bodies  will  very  nearly,  and  that 
of  a  revolution  of  the  node  almost  exactly,  bring  about  a  perfect  restora- 
tion of  the  inclinations.  If,  however,  we  suppose  the  orbits  excentric,  it 
is  no  leas  evident,  owing  to  the  want  of  symmetry  in  the  distribution  of 
tbe  forces,  that  a  perfect  compensation  will  not  be  effected  either  in  one 
or  in  any  number  of  revolutions  of  P  and  M,  independent  of  the  motion 
of  the  node  itself,  as  there  will  always  be  some  configuration  more  favour- 
able to  either  an  increase  of  inclination  than  its  opposite  is  unfavourable. 
Thus  will  arise  a  change  of  inclination  which,  were  the  nodes  and  apsides 
of  the  orbits  fixed,  would  be  always  progressive  in  one  direction  until 
the  planes  were  brought  to  coincidence.  But,  1st,  half  a  revolution  of 
tbe  nodes  would  of  itself  reverse  the  direction  of  this  progression  by 
making  the  position  in  question  favour  the  opposite  movement  of  inclina- 
tion; aud,  2dly,  the  planetary  apsides  are  themselves  in  motion  with 
unequal  velocities,  and  thus  the  configuration  whose  influence  destroys 
tbe  balance,  is,  itself,  always  shifting  its  place  on  the  orbits.  The  varia- 
tions of  inclination  dependent  on  the  excentricities  are  therefore,  like  those 
independent  of  them,  periodical,  and  being,  moreover,  of  an  order  more 
minute  (by  reason  of  the  smallness  of  the  excentricities)  than  the  latter, 
it  is  evident  that  the  total  variation  of  tbe  planetary  inclinations  must 
fluctuate  within  very  narrow  limits.  Geometers  have  accordingly  demon- 
strated by  an  accurate  analysis  of  all  the  circumstances,  and  an  exact 
estimation  of  the  acting  forces,  that  such  is  the  case ;  and  this  is  what 
is  meant  by  asserting  the  stability  of  the  planetary  system  as  to  the 
mutual  inclinations  of  its  orbits.     By  the  researches  of  Lagrange  (of 


"'    ''^A   ■•V-H 


'"  -"VMII** 


'■mtss» 


n 


848 


OUTLINES  OP  ASTRONOMY. 


¥ 

•4 

t 


1: 


vrhose  analytical  conduct  it  is  impossible  here  to  give  any  idea,)  the 
following  elegant  theorem  has  been  demonstrated :  — 

"  J/  tfie  mass  of  every  planet  be  multiplied  hy  the  square  root  of  the 
major  axis  of  its  orbit,  and  the  product  by  the  square  of  the  tangent  of 
its  inclination  to  a  fixed  plane,  the  sum  of  all  these  products  will  be  con- 
stantly the  same  under  the  influence  of  their  mutual  attraci^'on."  If  the 
present  situation  of  the  plane  of  the  ecliptic  be  taken  for  that  fixed  plane 
(the  ecliptic  itself  being  variable  likb  the  other  orbits),  it  is  found  that 
this  sum  is  actually  very  small :  it  must,  therefore,  always  remain  so. 
This  remarkable  theorem  alone,  then,  would  guarantee  the  stability  of  the 
orbits  of  the  greater  planets ;  but  from  what  has  above  been  shown  of  thp 
tendency  of  each  planet  to  work  out  a  compensation  on  every  other,  it  is 
evident  that  the  minor  ones  are  not  excluded  from  this  beneficial  arrange- 
ment. 

(640.)  Meanwhile,  there  is  no  doubt  that  the  plane  of  the  ecliptic  docs 
actually  vary  by  the  actions  of  the  planets.  The  amount  of  this  variation 
is  about  48"  per  century,  and  has  long  been  recognized  by  astronomers, 
by  an  increase  of  the  latitudes  of  all  the  stars  in  cer'  .in  situations,  and 
their  diminution  in  the  opposite  regions.  Its  effect  is  to  bring  the  ocliptic 
by  so  much  per  annum  nearer  to  coincidence  with  the  equator ;  but  from 
what  we  have  above  seen,  this  diminution  of  the  obliquity  of  the  ecliptic 
will  not  go  on  beyond  certain  very  moderate  limits,  after  which  (although 
in  an  immense  period  of  ages,  being  «a  compound  cycle  resulting  from  the 
joint  action  of  all  the  planets,)  it  will  again  increase,  and  thus  oscillate 
backward  and  forward  about  a  mean  ^  osition,  the  extent  of  its  deviation 
to  one  side  and  the  other  being  less  than  1°  21'. 

(641.)  One  efiect  of  this  variation  of  the  plane  of  the  ecliptic, — that 
which  causes  its  nodes  on  a  fixed  plane  to  change, — is  mixed  up  with  the 
precession  of  the  equinoxes,  and  undistinguishable  from  it,  except  in 
theory.  This  last-mentioned  phsenomenon  is,  however,  due  to  another 
cause,  analogous,  it  is  true,  in  a  general  point  of  view,  to  those  above 
considered,  but  singularly  modified  by  the  circumstances  under  which  it 
is  produced.  We  shall  endeavour  to  render  these  modifications  intelli- 
gible, as  far  as  they  can  be  made  so  without  the  intervention  of  analytical 
formulae.  '  ^ 

(642.)  The  precession  of  the  equinoxes,  as  we  have  thown  in  art.  312, 
consists  in  a  continual  retrogradation  of  the  node  of  the  earth's  equator  on 
the  ecliptic;  and  is,  therefore,  obviously  an  effect  so  far  analogous  to  the 
general  pbaenomenon  of  the  retrogradation  of  the  nodes  of  the  orbits  on 
each  other.  The  immense  distance  of  the  planets,  however,  compared 
with  the  size  of  the  earth,  and  the  smallness  of  their  masses  compared  to 


PRECESSION  OF  THE  EQUINOXES. 


849 


'  idea,)  tbe 

root  of  the 
5  tangent  of 
will  he  corir 
ft."      If  the 
A  fixed  plane 
is  found  that 
3  remain  so. 
tability  of  the 

shown  of  thp 
ry  other,  it  is 
ficial  arrange- 

le  ecliptic  does 
:  this  variation 
y  astronomers, 
situations,  and 
ing  the  scliplic 
ator;  but  from 
of  the  ecliptic 
hich  (although 
lilting  from  the 
thus  oscillate 
of  its  deviation 

ecliptic,— that 
Led  up  with  the 
it,  except  in 
due  to  another 
to  those  above 
under  which  it 
fications  intelU- 
ion  of  analytical 

)wn  in  art.  312, 
rth's  equator  on 
inalogous  to  the 
of  the  orbits  on 
vever,  compared 
ises  compared  to 


that  of  the  sun,  puts  their  action  out  of  the  question  in  the  inquiry  of  its 
cause,  and  we  must,  therefore,  look  to  the  massive  though  distant  sun, 
and  to  our  near  though  minute  neighbour,  the  moon,  for  its  explanation. 
This  will,  accordingly,  be  found  in  their  disturbing  action  on  the  redun- 
dant matter  accumulated  on  the  equator  of  the  earth,  by  which  its  figure 
is  rendered  spheroidal,  combined  with  the  earth's  rotation  on  its  axis.  It 
is  to  the  sagacity  of  Newton  that  we  owe  the  discovery  of  this  'singular 
mode  of  action. 

((543,)  Suppose  in  our  figure  (art.  611,)  that  instead  of  one  body,  P, 
revolving  round  S,  there  were  a  succession  of  particles  not  coherent,  but 
forming  a  kind  of  fluid  ring,  free  to  change  its  form  by  any  force  applied. 
Then,  while  this  ring  revolved  round  S  in  its  own  plane,  under  the  dis 
turbing  influence  of  the  distant  body  M,  (which  now  represcL^s  the  moon 
or  the  sun,  as  P  does  one  of  the  particles  of  the  earth's  equator,)  two 
things  would  happen :  1st,  its  figure  would  be  bent  out  of  a  plane  into  an 
undulated  form,  those  parts  of  it  within  the  arcs  D  A  and  E  C  being  ren- 
dered more  inclined  to  the  plane  of  M's  orbit,  and  those  within  the  arcs 
AE,  CD,  less  so  than  they  would  otherwise  be;  2dly,  the  nodes  of  this 
ring,  regarded  as  a  whole,  without  respect  to  its  change  of  figure,  would 
retreat  upon  that  plane. 

(044.)  But  suppose  this  ring,  instead  of  consisting  of  "li^crete  mole- 
cules free  tu  move  independently,  to  be  rigid  and  incapable  of  such  flexure, 
like  the  hoop  we  have  supposed  in  art.  633,  but  having  inertia,  then  it  is 
I  /ident  that  the  effort  of  those  parts  of  it  which  tend  to  become,  more 
inclined  will  act  through  the  medium  of  the  ring  itself  (as  a  mechanical 
engine  or  lever)  to  counteract  the  efibrt  of  those  which  have  at  the  same 
instant  a  contrary  tendency.  In  so  far  only,  then,  as  there  exists  an  excess 
on  the  one  or  the  other  side  will  the  inclination  change,  an  average  being 
struck  at  every  moment,  of  the  ring's  motion;  just  as  was  shown  to 
happen  in  the  view  we  have  taken  of  the  inclinations,  in  every  complete 
revolution  of  a  single  disturbed  body,  under  the  influence  of  a  fixed  dis- 
turbing one. 

(645.)  Meanwhile,  however,  the  nodes  of  the  rigid  ring  will  retrograde, 
the  general  or  average  tendency  of  the  nodes  of  every  molecule  being  to 
do  so.  Here,  as  in  the  other  case,  a  struggle  will  take  place  by  the  coun- 
teracting efibrts  of  the  molecules  contrarily  disposed,  propagated  through 
the  solid  substance  of  the  ring;  and  thus  at  every  instant  of  time,  an 
average  will  be  struck,  which  being  identical  in  its  nature  with  that 
effected  in  the  complete  revolution  of  a  single  disturbed  body,  will,  in 
every  case,  be  in  favour  of  a  recess  of  the  node,  B&ve  only  when  the  dis- 


't-t^'i 


850 


OUTLINES  OP  ASTRONOMY. 


»■ 
in 
»»■ 


;5j 


turbing  body,  be  it  sun  or  mooD,  is  situated  in  the  plane  of  the  earth's 
equator. 

(046.)  This  reasoning  is  evidently  independent  of  any  consideration 
of  the  cause  which  maintains  the  rotation  of  tlm  riug;  whether  the  par- 
ticles be  small  i^jitellites  retained  in  circular  orbits  under  the  equilibrated 
action  of  attractiv^o  and  centrifugal  forces,  or  wlie^'i  r  (hey  b«  small  masses 
conceived  as  attached  to  a  set  of  imaginary  s^' tkes,  as  of  u  whtc '..  » r^nter- 
ing  in  S,  and  free  only  to  tliift  their  jilanes  ay  a  niotion  oi  iho^e  pokes 
perpendicular  to  the  plane  of  the  wheel  Th-j"  makes  no  difference  in 
the  (/eneral effect }  tliough  the  i'iiflferent  velocities  of  rotation,  which  may 
be  impressed  on  such  a  system,  may  and  will  huve  a  very  great  influence 
both  on  the  absolute  and  relative  mai;i!itudr.';  of  the  two  effects  v.i  ques- 
tion —  tho  motion  of  the  nodes  and  oiiauge  of  inclination.  This  will  be 
easily  understood,  if  wc  suppose  the  riug  rjcithmU  a  rotate.  >  'uotiou,  in  which 
cxtreaie  case  it  is  obvious  that  bo  long  as  M  remained  fixed  there  would 
talie  phv:e  no  roccss  of  nodes  at  all,  but  only  a  tendency  of  the  ring  to  tilt 
its  p^^'ic-  round  a  diameter  perpendicular  to  the  position  of  M,  bringing  it 
towards  the  line  S  M. 

(647.)  The  motion  of  sucb  a  ring,  then,  as  we  have  been  considering, 
would  imitate,  so  far  as  the  recess  of  the  Jtodes  goes,  the  precession  of  the 
eqiiinoxes,  only  that  its  nodes  would  retrograde  far  more  rapidly  than  the 
observed  precession,  which  is  excessively  slow.  But  now  conceive  this 
ring  to  be  loaded  with  a  spherical  mass  enormously  heavier  than  itself, 
placed  concentrically  within  it,  and  cohering  firmly  to  it,  but  indifferent, 
or  very  nearly  so,  to  any  such  cause  of  motion ;  and  suppose,  moreover, 
that,  instead  of  one  such  ring  there  are  a  vast  multitude  heaped  together 
around  the  equator  of  such  a  globe,  so  as  to  form  an  elliptical  protube- 
rance, enveloping  it  like  a  shell  on  all  sides,  but  whose  mass,  taken  toge- 
ther, should  form  but  u  very  minute  fraction  of  the  whole  spheroid.  We 
have  now  before  us  a  tolerable  representation  of  the  case  of  nature;'  and 
it  is  evident  that  the  rings,  having  to  drag  round  with  them  in  their  nodal 

'  That  a  perfect  sphere  would  be .  so  inert  and  indifferent  as  to  a  revolution  of  the 
nodes  of  its  equator  under  the  influence  of  a  distant  attracting  body  appears  from  this, 
—  that  the  direction  of  the  resultant  attraction  of  such  a  body,  or  of  that  single  force 
which,  opposed,  would  neutralize  and  destroy  its  whole  action,  is  necessarily  in  a  line 
paHsing  through  the  centre  of  the  sphere,  and,  therefore,  can  have  no  tendency  to  turn 
the  sphere  one  way  or  other.  It  may  be  objected  by  the  reader,  that  the  whole  sphere 
may  be  conceived  as  consisting  of  rings  parallel  to  its  equator,  of  every  possible  dia- 
meter, and  that,  therefore,  its  nodes  should  retrograde  even  without  a  protuberant 
equator.  The  inference  is  incorrect,  but  our  limits  will  not  allow  us  to  go  into  an  ex- 
position of  the  fallacy.  We  should,  however,  caution  him,,  generally,  that  no  dyna- 
mical subject  is  open  to  more  mistakes  of  this  kind,  which  nothing  but  the  closest 
attention,  in  every  varied  point  of  view,  will  detect. 


PRECESSION  AND  NUTATION   EXPLAINED. 


351 


the  earth's 

onsideratioQ 
,her  the  par- 
equiliibrated 
jmtiU  masses 
rhtcl  •  'inter- 
thc!?e    >^oke8 
diffeveace  in 
1,  which  may 
reat  influence 
k.M  V.  ques- 
This  will  be 
jtiou,  in  vhich 
jd  there  would 
the  ring  to  tilt 
M,  bringing  it 

len  considering, 
recession  of  the 
rapidly  than  the 
w  conceive  this 
acr  than  itself, 
but  indifferent, 
)po8e,  moreover, 
heaped  together 
liptical  protuhe- 
lass,  taken  toge- 
e  spheroid.    We 
of  nature;'  and 
im  in  their  nodal 

a  revolution  of  the 
y  appears  from  this, 
of  that  single  force 
necessarily  in  a  line 
no  tendency  to  turn 
lat  the  whole  sphere 

every  possible  dia- 
iihout  a  protuberant 

us  to  go  into  an  ex- 
rally,  that  no  dyna- 
thing  but  the  closest 


revolution  this  great  inert  mass,  will  have  their  velocity  of  retrogradation 
proportionally  diminished.  Thus,  then,  it  is  easy  to  conceive  how  a  mo- 
tion similar  to  the  precession  of  the  equinoxes,  and,  like  it,  characterized 
by  extreme  slowness,  will  arise  from  the  causes  in  action. 

(648.)  Now  a  recess  of  the  node  of  the  earth's  equator,  upon  a  given 
plane,  corresponds  to  a  conical  motion  of  its  axis  round  a  perpendicular  to 
that  plane.  But  in  the  case  before  us,  that  plane  is  not  the  ecliptic,  but 
the  moon's  orbit  for  the  time  being;  and  it  may  be  asked  how  we  are  to 
reconcile  this  with  what  is  stated  in  art.  317  respecting  the  nature  of  the 
motion  in  question.  To  this  we  reply,  that  the  nodes  of  the  lunar  orbit, 
being  in  a  state  of  continual  and  rapid  retrogradation,  while  its  inclination 
is  preserved  nearly  invariable,  the  point  in  the  sphere  of  the  heavens  round 
which  the  pole  of  the  earth's  equator  revolves  (with  that  extreme  slow- 
ness characteristic  of  the  precession)  is  itself  in  a  state  of  continual  circu- 
lation round  the  pole  of  the  ecliptic,  with  that  much  more  rapid  motion 
which  belongs  to  the  lunar  node.     A  gbnce  at  the  annexed  figure  will 


\ 


Fig.  85. 


H-  mif'i.  f-i    ''r\    ■ 

-■■■  T.i  >     - ' 


lod 


explain  this  better  than  words.  P  is  the  pole  of  the  ecliptic,  A  the  pole 
of  the  moon's  orbit,  moving  round  the  small  circle  A  B  C  D  in  19  years; 
a  the  pole  of  the  earth's  equator,  which  at  each  moment  of  its  progress 
has  a  direction  perpendicular  to  the  varying  position  of  the  line  A  a,  and 
a  velocity  depending  on  the  varying  intensity  of  the  acting  causes  during 
the  period  of  the  nodes.  This  velocity  however  being  extremely  small, 
when  A  comes  to  B,  C,  D,  E,  the  line  A  a  will  have  taken  up  the  posi- 
tions B  &,  C  c,  D  d,  E  6,  and  the  earth's  pole  a  will  thus,  in  one  tropical 
revolution  of  the  node,  have  arrived  at  c,  having  described  not  an  exactJ- 
circular  arc  a  e,  but  a  single  undulation  of  a  wave-shape  or  epicycloidal 
curve,  ab  c  d  Cf  with  a  velocity  alternately  greater  and  less  than  its  mean 


*"'trn4-.-.vil 


If'-^^ivv 


..  •'■'■•■■■■Mmj 


'■m.t. 


"'tt 


o 


n 


852 


OUTLINE?   OF  ASTRONOMT. 


,  J, 
»> 

4! 


I 


\* 
i» 
•  b 

It 


motion,  and  this  will  be  repeated  in  every  succeeding  revolation  of  the 
node. 

(649.)  Now  this  is  precisely  the  kind  of  motion  which,  as  we  have 
seen  in  art.  325,  the  pole  of  the  earth's  equator  really  has  round  the  pole 
of  the  ecliptic,  iu  consequence  of  the  joint  effects  of  precession  and  nuta- 
tion, which  are  thus  uranographically  represented.  If  we  superadd  to  the 
effect  of  lunar  precession  that  of  the  solar,  which  alone  would  cause  the 
pole  to  describe  a  circle  uniformly  about  P,  this  will  only  affect  the  undu- 
lations  of  our  waved  curve,  by  extending  them  in  length,  but  will  produce 
no  effect  on  the  depth  of  the  waves,  or  the  excursions  of  the  earth's  axis 
to  and  from  the  pole  of  the  ecliptic.  Thus  we  see  that  the  two  phenomena 
of  nutation  and  precession  are  intimately  connected,  or  rather  both  of 
them  essential  constituent  parts  of  one  and  the  same  phenomenon.  It  is 
hardly  necessary  to  state  that  a  rigorous  analysis  of  this  great  problem,  by 
an  exact  estimation  of  all  the  acting  forces  and  summation  of  their  dy- 
namical effects,  leads  to  the  precise  value  of  the  co-efficients  of  precession 
and  nutation,  which  observation  assigns  to  them.  The  solar  and  lunar 
portions  of  the  precession  of  the  equinoxes,  that  is  to  say,  those  portions 
which  are  uniform,  are  to  each  other  in  the  proportion  of  about  2  to  5. 

(650.)  In  the  nutation  of  the  earth's  axis  we  have  an  example  (the 
first  of  its  kind  which  has  occurred  to  us),  of  a  periodical  movement  in 
one  part  of  the  system,  giving  rise  to  a  motion  having  the  same  precise 
period  in  another.  The  motion  of  the  moon's  nodes  is  here,  we  sec, 
represented,  though  under  a  very  different  form,  yet  in  the  same  exact 
periodic  time,  by  a  movement  of  a  peculiar  oscillatory  kind  impressed  on 
the  solid  mass  of  the  earth.  We  must  not  let  the  opportunity  pass  of 
generalizing  the  principle  involved  in  this  result,  as  it  is  one  which  we 
shall  find  again  and  again  exemplified  in  every  part  of  physical  astronomy, 
nay,  in  every  department  of  natural  science.  It  may  be  stated  as  <<  the 
principle  of  forced  oscillations;  or  of  forced  vibrations/'  and  thus  gene- 
rally announced : — 

If  one  part  of  any  system  connected  either  hy  material  tics,  or  by  the 
mutual  attractums  of  its  membc''^,  be  continually  maintained  by  any 
cause,  whether  inherent  in  the  constitution  of  the  system  or  external  to  it, 
in  a  state  of  regular  periodic  motion,  that  motion  will  be  pfropa<jated 
throughout  the  whole  systems,  and  will  give  rise,  in  every  member  of  it 
and  in  every  part  of  ea^h  member,  to  periodic  movements  executed  in 
equal  period,  vrith  that  to  which  they  owe  their  origin,  though  not  neces- 
sarily oynchronous  with  them  in  tlieir  maxima  and  minima.^ 

*  See  a  demonstration  of  thia  theorem  for  the  forced  vibrationa  of  systems  connected 
by  material  ties  of  imperfect  elasticity,  in  my  tr^tise  on  Sound,  Encyc.  Metrop.  art. 
323.    The  demonstration  is  easily  extended  and  generalized  to  take  in  other  systems. 


PRINCIPLE  OP  FORCED  VIJJRATIONS. 


858 


tion  of  tbe 

as  we  have 

ind  tbe  pole 

m  and  nuta- 

leradd  to  the 

Id  cause  the 

set  tbe  undu- 

,  will  produce 

e  earth's  axis 

JO  phenomena 

ither  both  of 

Dienon.     it  w 

It  problem,  by 

,n  of  their  dy- 

9  of  precession 

olar  and  lunar 

,  those  portions 

ibout  2  to  5. 

n  example  (the 

\  movement  in 

le  same  precise 

a  here,  %ve  see, 
the  same  exact 
id  impressed  on 
ortunity  pass  of 
ia  one  which  ve 
^sical  astronomy, 
(Stated  as  "the 
and  thus  gene- 

Val  tiesy  or  hy  th 
Vntaiiwd  hy  any 
1  or  external  to  it, 
Kl  he  p-opaifated 
\ry  memher  of  t< 
nenfcJ  executed  I'n 
\h,mgh  not  necosr 
jw'rna.' 

LfflyBtems  connected 
J  Encyc.  Metrop.  att. 
Ike  in  other  systems. 


The  system  may  be  favourably  or  unfavourably  constituted  for  such  a 
transfer  of  periodic  movomonta,  or  favourably  in  some  of  its  parts  and 
unfavourably  in  others ;  and  accordingly  as  it  is  the  one  or  the  other,  the 
derivative  oscillation  (as  it  may  be  termed)  will  be  imperceptible  in  one 
case,  of  appreciable  magnitude  in  another,  and  oven  more  perceptible  in 
its  visible  effects  than  tbe  original  cause  in  a  third ;  of  this  last  kind  wo  have 
an  instance  in  the  moon's  acceleration,  to  be  hereafter  noticed. 

(651.)  It  so  happens  that  our  situ.aion  on  the  earth,  and  the  delicacy 
which  our  observations  have  attained,  enable  us  to  make  it  as  it  were  an 
instrument  to  feel  these  forced  vibrations,  —  these  derivative  motions, 
communicated  from  various  quarters,  especially  from  our  near  neighbour, 
the  moon,  much  in  the  same  way  as  we  detect,  by  the  trembling  of  a 
board  beneath  us,  the  secret  transfer  of  motion  by  which  the  sound  of  an 
organ-pipe  is  dispersed  through  the  air,  and  carried  down  into  the  earth. 
Accordingly,  the  monthly  revolution  of  the  moon,  and  the  annual  motion 
of  the  sun,  produce,  each  of  them,  small  nutations  in  the  earth's  axis, 
whose  periods  are  respectively  half  a  month  and  half  a  year,  each  of 
which,  in  this  view  of  the  subject,  is  to  be  regardc^d  as  one  portion  of  a 
period  consisting  of  two  equal  and  similar  parts.    But  the  most  remark- 
able instance,  by  far,  of  this  propagation  of  periods,  and  one  of  high 
importance  to  mankind,  is  that  of  the  tides,  which  are  forced  oscillations, 
excited  by  the  rotation  of  the  earth  in  an  ocean  disturbed  from  its  figure 
by  the  varying  attractions  of  the  sun  and  moon,  each  revolving  in  its  own 
orbit,  and  propagating  its  own  period  into  the  joint  phenomenon.     The 
explanation  of  the  tides,  however,  belongs  more  properly  to  that  part  of 
the  general  subject  of  perturbations  wiiich  treats  of  the  action  of  the 
radial  component  of  the  disturbing  force,  and  is  therefore  postponed  to  a 
subsequent  chapter. 


'  V 


itt. 


.!««    I! 


•»v¥»L-«u«rj 


>1 


^••.4 


■3 


Wf' 


1   I 

I 


854 


OUTLINES  OF  ASTRONOMY. 


CHAPTER  XIII. 


THEORY  OF  THE   AXES,   PERIHELIA,   AND  EXCENTRICITIES. 


I 
-I 


I* 

14 
IX 
t» 

IP 

r? 

«c 


i: 


tir 

Si 


'««i» 


VARIATION  OF  ELEMENTS  IN  OENEUAL. — DISTINCTION  BETWEEN  PE- 
RIODIC AND  SECULAR  VARIATIONS. — GEOMETRICAL  EXPRESSION  OP 
TANGENTIAL  AND  NORMAL  FORCES.  —  VARIATION  OF  THE  MAJOR 
AXIS  PRODUCED  ONLY  BY  THE  TANGENTIAL  FORCE.  —  LAGRANGE's 
THEOREM  OF  THE  CONSERVATION  OF  THE  MEAN  DISTANCES  AND 
PERIODS. — THEORY  OP  THE  PERIHELIA  AND  EXCENTRICITIES.— 
GEOMETRICAL  REPRESENTATION  OF  THEIR  MOMENTARY  VARIA- 
TIONS.—  ESTIMATION  OP  THE  DISTURBING  FORCES  IN  NEARLY 
CIRCULAR  ORBITS.  —  APPLICATION  TO  THE  CASE  OP  THE  MOON. — 
THEORY  OF  THE  LUNAR  APSIDES  AND  EXCENTRICITY.  —  EXPERI- 
MENTAL ILLUSTRATION.  —  APPLICATION  OF  THE  FOREGOING  PRIN- 
CIPLES  TO  THE  PLANETARY  THEORY. — COMPENSATION  IN  ORBITS 
VERY   NEARLY  CIRCULAR.  —  EFFECTS    OP    ELLIPTICITY.  —  GENERAL 

RESULTS.  —  Lagrange's    theorem   of  the    stability  of  the 

EXCENTRICITIES. 

« 

(652.)  In  the  foregoing  chapter  we  have  sufficiently  explained  the  action 
of  the  orthogonal  component  of  tho  disturbing  force,  and  traced  it  to  its 
results  in  a  continual  displacement  of  tho  plane  of  the  disturbed  orbit,  Id 
virtue  of  which  the  nodes  of  that  plane  alternately  advance  and  recede 
upon  the  plane  of  the  disturbing  body's  orbit,  with  a  general  preponde- 
rance on  the  side  of  advance,  so  as  after  the  lapse  of  a  long  period  to 
cause  the  nodes  to  make  a  complete  revolution  and  come  round  to  their 
former  situation.  At  the  same  time  the  inclination  of  the  plane  of  the 
disturbed  motion  continually  changes,  alternately  increasing  and  diminish- 
ing; the  increase  and  diminution,  however,  compensating  each  o^;ber, 
nearly  in  single  revolutions  of  the  disturbed  and  disturbing  bodies,  more 
exactly  in  many,  and  with  perfect  accuracy  in  long  periods,  such  as  those 
of  a  complete  revolution  of  the  nodes  and  apsides.  In  the  present  anii 
following  chapters  we  shall  endeavour  to  trace  the  effects  of  the  other  | 
components  of  the  disturbing  force,  —  those  which  act  in  the  plane  (foi 


VARIATION   OP   ELEMENTS. 


855 


[TRICITIES. 

y 
BETWEEN  PE- 
XPRE88I0N  OP 
p  THE   MAJOR 
—LAQRANOE's 
1STANCE8   AND 
INTRICITIES.  — 
«TARY    VARIA- 
SS    IN    NEARLY 
THE  MOON.— 
IXY.  —  EXPERI- 
.REGOINO   PRIN- 
riON  IN   ORBITS 
TY.  ■ —  GENERAL 
ilLlTY    OP    THE 

plained  tho  action 
nd  traced  it  to  iU 
isturbcd  orbit,  in 
vance  and  recede  I 
reneral  preponde- 
'a  long  period  to 
10  round  to  theii 

tbo  plane  of  the 
ling  and  diminish- 
sating  each  otber, 
bing  bodies,  more 
iods,  such  as  those 
the  present  and 

fects  of  the  other 
in  the  plane  (for 


tbo  time  being)  of  tho  di.^  wibcd  orbit,  and  which  tend  to  derange  the 
elliptic  form  of  tho  orbit,  and  the  laws  of  elliptic  motion  in  that  plane. 
The  small  inclination,  generally  speaking,  of  the  orbits  of  the  planets  and 
satellites  to  each  other,  permits  us  to  separate  these  effects  in  theory  one 
from  the  other,  and  thereby  greatly  to  simplify  their  consideration.  Ac- 
cordingly, in  what  follows,  we  shall  throughout  neglect  the  mutual  ine' 
nation  of  the  orbits  of  the  d':turbed  and  disturbing  bodies,  and  regard  all 
the  forces  as  acting  and  all  the  motions  as  performed  in  one  plane. 

(653.)  In  considering  the  changes  induced  by  the  mutual  action  of  two 
bodies,  in  different  aspects  with  respect  to  each  other,  on  the  magnitude } 
and  forms  of  their  orbits,  and  in  their  positions  therein,  it  will  be  proper 
in  tho  first  instance  to  explain  the  conventions  under  which  geome'cers 
and  astronomers  have  alike  agreed  to  use  the  language  and  laws  of  tho 
elliptic  system,  and  to  continue  to  upply  them  to  disturbed  orbits,  altlough 
those  orbits  so  disturbed  are  no  longer,  in  mathematical  strictness,  ellipses, 
or  any  known  curves.  This  they  do,  partly  on  account  of  the  convenience 
of  conception  and  calculation  which  attaches  to  this  system,  but  much 
more  for  this  reason,  —  that  it  is  found,  and  may  bo  demonstrated  from 
the  dynamical  relations  of  the  case,  that  the  departure  of  each  planet  from 
its  ellipse,  as  determined  at  any  epoch,  is  capable  of  being  truly  repre- 
sented, by  supposing  the  ellipse  itself  to  be  slowly  variable,  to  change  its 
magnitude  and  excentricity,  and  to  shift  its  position  and  the  plane  in 
which  it  lies  according  to  certain  laws,  while  the  planet  all  the  time  con- 
tinues to  move  in  this  ellipse,  just  as  it  would  do  if  the  ellipse  remained 
invariable  and  the  disturbing  forces  had  no  existence.  By  this  way  of 
considering  the  subject,  the  whole  effect  of  the  disturbing  forces  is  regarded 
as  thrown  upon  the  orbit,  while  the  relations  of  the  planet  to  that  orbit 
remain  unchanged.  This  course  of  procedure,  indeed,  is  the  most  natural, 
and  is  in  some  sort  forced  upon  us  by  the  extreme  slowness  with  which 
the  variation  of  the  elements,  at  least  where  the  planets  only  are  con- 
cerned, develop  themselves.  For  instance,  the  fraction  expressing  the 
excentricity  of  the  earth's  orbit  changes  no  more  tbnr  0.00004  in  its 
amount  in  a  century;  and  the  place  of  its  periheKon^  os  referred  to  the 
sphere  of  the  heavens,  by  only  19'  39"  in  the  ^^im  time.  For  several 
years,  therefore,  it  would  be  next  to  impossible  to  distinguish  between  an 
ellipse  so  varied  and  one  that  had  not  varied  at  all ;  and  in  a  single  revo- 
lution, the  difference  between  the  original  ellipse  and  the  curve  really 
represented  by  the  varying  one,  is  so  excessively  minute,  that,  if  accu- 
rately drawn  on  a  table,  six  feet  in  diameter,  the  nicest  examination  with 
microscopes,  continued  along  the  whole  outlines  of  the  two  curves,  would 
hardly  detect  any  perceptible  interval  between  them.     Not  to  call  a  mo- 


! 


.'4„-..JiS*l 


■•f.-ifw 


W- 


if^« 


f 


■•1\.%l' 


* 


I*   . 


856 


OUTLINES   OP  ASTRONOMY. 


fP 


I 


t>V 

•a 

if 

•  «' 


t; 

It) 


««» 


tion  so  minutely  conforming  itself  to  an  elliptic  cu-/vj,  dUptlr,  would  be 
affectation,  even  granting  the  existence  of  trivial  dcparturea  nlternately  on 
one  side  or  on  the  other ;  though  on  the  other  hand,  to  neglect  a  varia- 
tion, which  continues  to  accumulate  from  ago  to  oge,  till  it  forces  itself  on 
our  notice,  would  bo  wilful  blindness. 

(654,)  Geometers,  then,  have  agreed,  in  each  single  revolution,  or  for 
any  moderate  interval  of  time,  to  regard  the  motion  of  each  planet  as 
elliptic,  and  performed  according  to  Kepler's  laws,  with  a  reserve  in 
favour  of  those  very  small  and  tranfiont  fluctuations  which  take  place 
within  that  time,  but  at  the  same  time  to  regard  all  the  elements  of  each 
ellipse  as  in  a  continual,  thcigh  extremely  slow,  state  of  change;  and,  in 
tracing  the  eflfects  of  perturbation  on  the  system,  they  take  account  prin- 
cipally, or  entirely,  of  this  change  of  the  elements,  as  that  upon  which  any 
material  change  in  the  great  features  of  the  system  will  ultimately  depend. 

(055.)  And  here  we  encounter  the  distinction  between  what  aro  termed 
secular  variations,  and  such  as  are  rapidly  periodic,  and  are  compensated 
in  short  intervals.  In  our  exposition  of  the  variation  of  the  inclination 
of  a  disturbed  orbit  (art.  636,)  for  instance,  we  showed  that,  in  each 
single  revolution  of  the  disturbed  body,  the  plane  of  its  motion  underwent 
fluctuations  to  and  fro  in  its  inclination  to  that  of  the  disturbing  body, 
which  nearly  compensated  each  other;  leaving,  however,  a  portion  out- 
standing, which  again  is  nearly  compensated  by  the  revolution  of  the  dis- 
turbing body,  yet  still  -leaving  outstanding  and  uncompensated  a  minute 
portion  of  the  change  which  requires  a  whole  revolution  of  the  node  to 
compensate  and  bring  it  back  to  an  average  or  mean  value.  Now,  the 
two  first  compensations  which  are  operated  by  the  planets  going  through 
the  succession  of  configurations  with  each  other,  and  therefore  in  compara- 
tively short  periods,  are  called  penodic  variations ;  and  the  deviations  thus 
compensated  are  oalled  inequalities  depending  on  eonjiyurations ;  while 
the  last,  which  is  operated  by  a  period  of  the  node  (one  of  the  elements,) 
has  nothing  to  do  with  the  configurations  of  the  individual  planets,  requires 
a  very  long  period  of  time  for  its  consummation,  and  is,  therefore,  distin- 
guished from  the  former  by  the  term  secxdar  variation. 

(056.)  It  is  true,  that,  to  afford  an  exact  representation  of  the  motions 
of  a  disturbed  body,  whether  planet  or  satellite,  both  periodical  and 
secular  variations,  with  their  corresponding  inequalities,  require  to  be 
*expressed ;  and,  indeed,  the  former  even  more  than  the  latter ;  seeing  that 
the  secular  inequalities  are,  in  fact,  nothing  but  what  remains  after  the 
mutual  destruction  of  a  much  larger  amount  (as  it  very  often  is)  of  peri- 
odical. Bnt  th  se  are  in  their  nature  transient  and  temporary:  they 
disappear  iu  shoi  i  periods,  and  leave  no  trace.    The  planet  is  temporarily 


GEOMETRICAL   EXPRESSION  OF  FORCE. 


857 


,  would  be 
ernately  on 
lect  a  viiria- 
ccB  itself  on 

ution,  or  for 
ih  planet  aa 
t  reserve  in 
1  take  place 
icnts  of  each 
Qgo ;  and, in 
iccount  prin- 
on  whicb  any 
lately  depend, 
at  are  termed 
compensated 
be  inclination 
that,  in  each 
ion  underwent 
iturbing  body, 
ft  portion  out- 
ion  of  the  dis- 
sated  a  niinnto 
of  the  node  to 
ae.     Now,  the 
going  through 
re  in  compara- 
deviationa  thus 
rations',  while 
tho  elements,) 
anets,  requires 
lereforc,  distin- 

of  the  motions 
periodical  and 
require  to  be 
ter ;  seeing  that 
mains  after  the 
ften  is)  of  peri- 
imporary:  they 
is  temporarily 


drawn  from  its  orbit  (its  slowly  varying  orbit,)  but  forthwith  returns  to 
it,  to  deviate  presently  aa  niiicli  tho  other  way,  while  tho  varied  orbit 
accommodates  and  adjusts  itself  to  tho  average  of  these  excursions  on 
either  side  of  it ;  and  thus  continues  to  present,  for  a  succession  of  indefi- 
nite ages,  a  kind  of  medium  picture  of  all  that  the  planet  has  been  doing 
in  their  lapse,  in  which  tho  expression  and  the  character  is  preserved;  but 
the  individual  features  arc  merged  and  lost.  These  periodic  inequalities, 
however,  are,  as  wo  have  observed,  by  no  means  neglected,  but  it  is  more 
convenient  to  take  account  of  them  by  a  separate  process,  independent 
of  tho  secular  variations  of  tho  clumcnts. 

(G57.)  In  order  to  avoid  complication,  while  endeavouring  to  give  tho 
reader  an  insight  into  both  kinds  of  variations,  we  shall  henceforward 
conceive  all  tho  orbits  to  lie  in  one  plane,  and  confine  our  attention  to  the 
case  of  two  only,  that  of  tho  disturbed  and  disturbing  body,  a  view  of  the 
subject  which  (as  wo  have  seen)  comprehends  the  case  of  tho  moon  dis- 
turbed by  tho  sun,  since  any  one  of  the  bodies  may  be  regarded  as  fixed 
at  pleasure,  provided  we  conccivo  all  its  motions  transferred  in  a  contrary 

Fig.  86.  ' 


direction  to  each  of  the  others.  Let  therefore  A  P  B  be  the  undisturbed 
elliptic  orbit  of  a  planet  P;  M  a  disturbing  body,  join  M  P,  and  supposing 
M  K=  M  S  take  M  N  :  M  K  : :  M  K^ :  M  P^.  Then  if  S  N  be  joined, 
N  S  will  represent  the  disturbing  force  of  M  or  P,  on  the  same  scale  that 
S  M  represents  M's  attraction  on  S.  Suppose  Z  P  Y  a  tangent  at  P,  S  Y ' 
perpendicular  to  it,  and  N  T,  N  L  perpendicular  respectively  to  S  Y  and 
P  S  produced.  Then  will  N  T  represent  the  tangential,.T  S  the  normal, 
N  L  the  transversal,  and  L  S  the  radial  components  of  the  disturbing 
force.    In  circular  orbits  or  orbits  only  slightly  elliptic,  the  directions 

t* 


i.«' » 


It 


-•I 

i 


77- 


858 


OUTLINES  OF  ikSTRONOMT. 


1 

II 

1' 

't 

1 

f 

1 

• 

1 

tt 

1 

t. 

f  ■ 

f,' 

f 

te 

*m 

riu 

i>& 

/■ 

•  Ri 

i 

»•*•" 

ir 

Uttt? 

>'t«k 

&r 

K 

«: 

PS  L  and  SY  are  nearly  coincident,  and  the  former  pair  of  forces  will 
differ  but  slightly  from  the  latter.  We  shall  here,  however,  take  the 
general  case,  and  proceed  to  investigate  in  an  elliptic  orbit  of  any  degree 
of  excentricity  the  momentary  changes  produced  by  the  action  of  the  dia. 
turbing  force  in  those  elements  on  which  the  magnitude,  situation,  and 
form  of  the  orbit  depend  (i.  e.  the  length  and  position  of  the  major  axis 
and  the  excentricity,)  in  the  same  way  as  in  the  last  chapter  we  deter- 
mined the  momentary  changes  of  the  inclination  and  node  similarly  pro- 
duced by  tho  orthogonal  force. 

(658.)  We  shall  begin  with  the  momentary  variation  in  the  lei  jh  of 
the  axis,  an  element  of  the  first  importance,  as  on  it  depends  (art.  487) 
the  periodic  time  and  mean  angular  motion  of  the  planet,  as  well  as  the 
average  suppiy  of  light  and  heat  it  receives  in  a  given  time  from  the  sun, 
any  permanent  or  constantly  progressive  change  in  which  would  alter 
most  materially  the  conditions  of  existence  of  living  beings  on  its  surface. 
Now  it  is  a  property  of  elliptic  motion  performed  under  the  influence  of 
gravity,  and  in  conformity  with  Kepler's  laws,  that  if  the  velocity  with 
which  a  planet  moves  at  any  point  of  its  orbit  be  given,  and  also  the 
distance  of  that  point  from  the  sun,  the  major  axis  of  the  orbit  is  thereby 
also  given.  It  is  no  matter  in  what  direction  the  planet  may  be  moving 
at  that  moment.  This  will  influence  the  excentricity  and  the  position  of 
its  ellipse,  but  not  its  length.  This  property  of  elliptic  motion  has  been 
demonstrated  by  Newton,  and  is  one  of  the  most  obvious  and  elementary 
conclusions  from  his  theory.  Let  us  now  consider  a  planet  describing  an 
indefinitely  small  arc  of  its  orbit  about  the  sun,  under  the  joint  influence 
of  its  attraction,  and  the  disturbing  power  of  another  planet.  This  arc 
ivill  have  some  certain  curvature  and  direction,  and,  therefore,  may  be 
considered  as  an  arc  of  a  certain  ellipse  described  about  the  i^un  as  a 
focus,  for  this  plain  reason, — that  whatever  be  the  curvature  and  direction 
of  the  arc  in  question,  an  ellipse  may  always  be  assigned,  whose  focus 
shall  be  in  the  sun,  and  which  shall  coincide  with  it  throughout  the  whole 
interval  (supposed  indefinitely  small)  between  its  extreme  points.  This 
is  a  matter  of  pure  geometry.  It  does  not  follow,  however,  that  the 
ellipse  thus  instantaneously  determined  will  have  the  same  elements  as 
that  similarly  determined  from  the  arc  described  in  either  the  previous  or 
the  subsequent  instant.  If  the  disturbing  force  did  not  exist,  this  would 
be  the  case :  but,  by  its  action,  a  variation  of  the  element  from  instant  to 
instant  is  produced,  and  the  ellipse  so  determined  is  in  a  continual  state 
of  change.  Now  when  the  planet  has  reached  tho  end  of  the  small  arc 
under  consideration,  the  question  whether  it  will  in  tho  next  instant 
describe  an  arc  of  &n  ellipse  having  the  Ban\e  or  a  varied  axis  will  depend, 


VARIATION   OF  THE  MAJOR  AXIS. 


359 


•  forces  will 
!r,  take  the 
any  degree 
a  of  the  dis. 
ituatioD,  and 
3  major  axis 
iter  we  deter- 
limilarly  pro- 

tlie  lerjh  of 
ids  (art.  487) 
as  well  as  the 
from  the  sun, 
b  would  alter 
on  its  surface, 
le  influence  of 
e  velocity  with 
,  and  also  the 
arbit  is  thereby 
may  be  moving 
the  position  of 
lotion  has  been 
and  elementary 
t  describing  an 
joint  influence 
anet.    This  arc 
srefore,  may  be 
it  the  sun  as  a 
ire  and  direction 
icd,  whose  focus 
ighout  the  whole 
le  points.    This 
iwever,  that  the 
ime  elements  as 
p  the  previous  or 
exist,  this  would 
it  from  instant  to 
a  continual  state 
of  the  small  arc 
[the  next  instant 
axis  will  depend, 


not  on  the  new  direction  impressed  upon  it  by  the  acting  forces, — for  the 
axis,  as  we  have  seen,  is  independent  of  that  direction, — not  on  its  change 
of  distance  from  the  sun,  while  describing  the  former  arc,  —  for  the  ele- 
ments of  that  arc  are  accommodated  to  it,  so  that  one  and  the  same  axis 
must  belong  to  its  beginning  and  its  end.  The  question,  in  short,  whether 
in  the  next  aio  it  shall  take  up  a  new  major  axis  or  go  on  with  the  old 
one  will  depend  solely  on  this — whether  its  velocity  has  or  has  not  under- 
gone a  change  by  the  action  of  the  disturbing  force.  For  the  central 
force  residing  in  the  focus  can  impress  on  it  no  such  change  of  velocity 
as  to  be  incompatible  with  the  permanence  of  its  ellipse,  seeing  that  it  is 
by  the  action  of  that  force  that  the  velocity  is  maintained  in  that  due 
proportion  to  the  distance  which  elliptic  motion,  as  such,  requires. 

(659.)  Thus  we  see  that  the  momentary  variation  of  the  major  axis 
depends  on  nothing  but  the  momentary  deviation  from  the  law  of  elliptic 
velocity  produced  by  the  disturbing  force,  without  the  least  regard  to  the 
direction  in  which  that  extraneous  velocity  is  impressed,  or  the  distance 
from  the  sun  at  which  the  planet  may  be  situated,  at  the  moment  of  its 
impression.  Nay,  we  may  even  go  farther,  for,  as  this  holds  good  at  every 
instant  of  its  motion,  it  will  follow  that  after  the  lapse  of  any  time,  how- 
ever great,  the  total  amount  of  change  which  the  axis  may  have  under- 
gone will  be  determined  only  by  the  total  deviation  produced  by  the  action 
of  the  disturbing  force  in  the  velocity  of  the  disturbed  body  from  that 
which  it  would  have  had  in  its  undisturbed  ellipse,  at  the  same  distance 
from  the  centre,  and  that  therefore  the  total  amount  of  change  produced 
in  the  axis  in  any  lapse  of  time  may  be  estimated,  if  we  know  at  every 
instant  the  efficacy  of  the  disturbing  force  to  alter  the  velocity  of  the 
body's  motion,  and  that  without  any  regard  to  the  alterations  which  the 
action  of  that  force  may  have  produced  in  the  other  elements  of  the 
motion  in  the  same  time. 

(660.)  Now  it  is  not  the  whole  disturbing  force  which  is  effective  in 
changing  P's  velocity,  but  only  its  tangential  component.  The  normal 
component  tends  merely  to  alter  the  curvature  of  the  orbit  or  to  deflect  it 
into  conformity  with  a  circle  of  curvature  of  greater  or  lesser  radius,  as 
the  case  may  be,  and  in  no  way  to  alter  the  velocity.  Hence  it  appears 
that  the  variation  of  the  length  of  the  axis  is  due  entirely  to  the  tangen- 
tial force,  and  is  quite  independent  on  the  normal.  Now  it  is  easily  shown 
that  as  the  velocity  increases,  the  axis  increases  (the  distance  remaining 
unaltered')  though  not  in  the  same  exact  proportion.  Hence  it  follows 
'  If  o  be  the  semiaxis,  r  the  radius  vector,  and  i>  the  velocity  of  P  in  any  point  of  an 
ellipse,  a  is  given  by  the  relation  «'=- — ,  the  units  of  velocity  and  force  being  pro- 
perly assumed. 


:';^^ 


t, 


'3 


"<■«»  «*.■:! 


i 


,*■''  v..  .1 


:^-' 


*v  *w* 


*'TT|>JBjJf'' 


f^mm 


i*f 


3 


860 


OUTLINES   OP  ASTRONOMY. 


I 
I 

f 
f 


15 


to. 

ir 


mm 


that  if  the  tangential  disturbing  force  conspires  with  the  motion  of  P,  its 
momentary  action  increases  the  axis  of  the  disturbed  orbit,  whatever  bo 
the  situation  of  P  in  its  orbit,  and  vice  versd. 

(661.)  Let  A  S  B  (fig.  art.  657)  be  the  major  axis  of  the  ellipse  A  P 
B,  and  on  the  opposite  side  of  A  B  take  two  points  P'  and  M',  similarly 
situated  with  respect  to  the  axis  with  P  and  M  on  their  side.  Then  if  at 
F  and  M'  bodies  equal  to  P  and  M  be  placed,  the  lorces  exerted  by  W 
on  P'  and  S  will  be  equal  to  those  exerted  by  M  on  P  and  S,  and  there- 
fore the  tangential  disturbing  force  of  M'  on  P'  exerted  in  the  direction 
V!  Z'  (suppose)  will  equal  that  exerted  by  M  on  P  in  the  direction  P  Z. 
P'  therefore  (supposing  it  to  revolve  in  the  same  direction  round  S  as  P) 
will  be  retarded  (or  accelerated,  as  the  case  may  be)  by  precisely/  the  same 
force  by  which  P  is  accelerated  (or  retarded),  so  that  the  variation  in  the 
axis  of  the  respective  orbits  of  P  and  P'  will  be  equal  in  amount,  but  con- 
trary in  character.  Suppose  now  M's  orbit  to  be  circular.  Then  (//'  the 
periodic  times\of  M  ami  P  he  not  commensurate,  so  that  a  moderate 
number  of  revolutions  may  bring  them  back  to  the  same  precise  relative 
positions)  it  will  necessarily  happen,  that  in  the  course  of  a  very  great 
number  of  revolutions  of  both  bodies,  P  will  have  been  presented  to  M 
on  one  side  of  the  axis,  at  some  one  moment,  in  the  same  manner  as  at 
some  other  moment  on  the  other.  Whatever  variation  may  have  been 
eflfected  in  its  axis  in  the  one  situation  will  have  oeen  reversed  in  that 
symmetrically  opposite,  and  the  ultimate  result,  on  a  general  average  of 
an  infinite  number  of  revolutions,  will  be  a  complete  and  exact  compen- 
sation of  the  variations  in  one  direction  by  those  in  the  direction  opposite. 

(662.)  Suppose,  next,  P's  orbit  to  be  circular.  If  now  M's  orbit  were 
60  also,  it  is  evident  that  in  one  complete  synodic  revolution,  an  exact 
restoration  of  the  axis  to  its  original  length  would  take  plaee,  because  the 
tangential  forces  would  be  symmetrically  equal  and  opposite  during  each 
alternate  quarter  revolution.  But  let  M,  during  a  synodic  revolution, 
have  receded  somewhat  from  S,  then  will  its  disturbing  power  have  become 
gradually  weaker,  so  that,  in  a  synodic  revolution,  the  tangeutial  force  jn 
each  quadrant,  though  reversed  in  direction  being  inferior  in  ymer,  jn 
exact  compensation  will  not  huve  been  effected,  but  tisKvre  will  bf-  le^t  u; 
outstanding  uncompensated  portion,  the  excess  of  the  ;^ODg4:r  over  tie 
feebler  effects.  But  now  suppose  M  to  approach  by  tlie  sam«  gr  *datioM 
as  it  before  receded.  It  is  clear  that  this  result  will  b*'  reyc-at'A;  wiuw 
the  uncmpensatcd  stronger  actions  will  all  lie  in  the  opposite  dire^jtion. 
Now  suppose  M's  orbit  to  be  elliptic.  Then  during  its  recess  from  1^,  or 
in  the  half  revolution  from  its  perihelion  to  its  aphelion,  a  continual  tm- 
compensated  variation  will  go  on  accumulating  in  one  direction.     .Bwt 


VARIATION  OF  THE   MAJOR   AXIS. 


361 


on  of  P,  its 
whatever  bo 

ellipse  A  V 
M',  similarly 
Then  if  at 
terted  by  jSI' 
S,  and  there- 
the  direction 
lirection  P  Z. 
•ound  S  as  P) 
iseJi/  the  same 
vriation  in  the 
ount,  but  con- 
Then  {if  the 
it  a  moderate 
precise  relative 
of  a  very  great 
presented  to  M 
manner  as  at 
may  have  been 
sversed  in  that 
■ral  average  of 
I  exact  conipen- 
•ectiou  opposite. 
M's  orbit  were 
ution,  an  exact 
ucc,  because  the 
site  during  each 
iodic  revolution, 
wer  have  become 
ngential  force  in 
or  in  p'-'wer,  >ti 
ill  t^  left  as. 
jfongcf  over  tie 
tiaai^  g'  ».datu-*» 
revfwja;  »iue^- 
,posite  direction. 
rcwss  from  t^,  ^ 
ft  coTi^^inual  uD' 
direction-     Kw^ 


from  what  has  been  said,  it  is  clear  that  this  will  be  destroyed,  during  M's 
approach  to  S  in  the  other  half  of  its  orbit,  so  that  here  again,  on  the 
average  of  a  multitude  of  revolutions  during  which  P  has  been  presented 
to  M  in  evcrij  situation  for  every  distance  of  M  from  S,  the  restoration 
will  be  effected.  '  ' 

(608.)  If  neither  P's  nor  M's  orbit  be  circular,  and  if  moreover  the 
directions  of  their  axes  be  different,  this  reasoning,  drawn  from  the  sym- 
metry of  their  relations  to  each  other,  does  not  apply,  and  it  becomes 
necessary  to  take  a  more  general  view  of  the  matter.     Among  the  funda- 
mental relations  of  dynamics,  relations  which  presuppose  no  particular 
law  of  force  like  that  of  gravitation,  but  which  express  in  general  terms 
the  results  of  the  action  of  force  on  matter  during  time,  to  produce  or 
change   velocity^  is  one  u.sually  cited  as  the  "  Principle  of  the  conserva- 
tion of  the   vis  viva,"  which  applies  directly  to  the  case  before  us.     This 
principle  (or  rather  this  theorem)  declares  that  if  a  body  subjected  at 
every  instant  of  its  motion  to  the  action  of  forces  directed  to  fixed  centres 
(no  matter  how  numerous),  and  having  their  intensity  dependent  only  on 
the  distances  from  their  respective  centres  of  action,  travel  from  one  point 
of  space  to  another,  the  velocity  which  it  has  on  its  arrival  at  the  latter 
point  will  differ  from  that  which  it  had  on  setting  out  from  the  former,  by 
a  quantity  depending  only  on  the  different  relative  situations  of  these  two 
points  in  space,  without  the  least  reference  to  the  form  of  the  curve  in 
which  it  may  have  moved  in  passing  from  one  point  to  the  other,  whether 
that  curve  have  been  described  freely  under  the  simple  influence  of  the 
central  forces,  or  the  body  have  been  compelled  to  glide  upon  it,  as  a  bead 
upoi!  a  smooth  wire.     Among  the  forces  thus  ?.c'>\r\g  may  be  included  any 
coi.stant  forces,  acting  in  parallel  directions,  wl->ich  may  be  regarded  as 
directed  to  fixed  centres  infinitely  distant.     It  follows  from  this  theorem, 
that,  if  the  body  return  to  the  point  P,  from  which  it  set  out,  its  velocity 
of  arrival  will  be  the  same  with  that  of  i^^  departure;  a  conclusion  which 
for  tilt'  purpose  we  have  in  view)  sets  us  free  from  the  necessity  of  onter- 
iDg  into  uny  consideration  of  the  laws  of  the  disturbing  force,  ihe  change 
which  its  aetion  may  have  induced  in  iho  form  of  the  orbit  of  P,  or  the 
,<«iece88ivo  steps  by  which  velocity  generated  at  one  point  of  its  interme- 
diat**  path  is  destroyed  at  another,  by  the  reversed  action  of  the  tangen- 
ial  forc<-.     Now  to  apply  this  theorem  to  the  ca.^o  in  question,  let  M  be 
suf^scd  to  r*»taiQ  a  fixed  position  during  one  whole  revolution  of  P. 
P  a^fl  i»  aet««l  «*,  during  that  revolution,  by  three  forces ;  1st.  by  the 
'it^Trtl  afamltmm  of  S  directed  always  to  S;  2nd.  by  that  to  M,  always 
-lircctwJ  to  M ;  ^rd.  by  a  force  equal  to  M's  attraction  on  S ;  but  in  the 
iif.;ctioii  M  ^,  which  therefore  is  a  constant  force,  actiog  always  in  parallel 


i^u 


^^-f 


't'*^, 
•^^. 


Iran 


>., 


:SNi 


362 


OUTLINES   OP  ASTRONOMY. 


^ 


altn 


I.'* 


directions.  On  completing  its  revolution,  then,  P'b  velocity,  and  therefore 
the  major  axis  of  its  orbit,  will  be  found  unaltered,  at  least  neglecting 
that  excessively  minute  diflFerence  which  will  result  from  the  non-arrival 
after  a  revolution  at  the  exact  point  of  its  departure  by  reason  of  the  per- 
turbations in  the  orbit  produced  in  the  interim  by  the  disturbing  force, 
which  for  the  present  we  may  neglect. 

(664.)  Now  suppose  M  to  revolve,  and  it  will  appear,  by  a  reasoning 
precisely  similar  to  that  of  art.  662,  that  whatever  uncompensated  varia- 
tion of  the  velocity  arises  in  successive  revolutions  of  P  during  M's  recess 
from  S  will  be  destroyed  by  contrary  uncompensated  variations  arising 
during  its  approach.  Or,  more  simply  and  generally  thus :  whatever  M's 
situation  may  be,  for  every  place  which  P  can  have,  there  must  exist  some 
other  place  of  P  (as  P'),  in  which  the  action  of  M  shall  be  precisely 
reversed.  Now  if  the  periods  be  incommensurable,  in  an  indefinite 
number  of  revolutions  of  both  bodies,  for  every  possible  combination  of 
situations  (M,  P)  there  will  occur,  at  some  time  or  other,  the  combination 
(M,  P')  which  neutralizes  the  effect  of  the  other,  when  carried  to  the 
general  account ;  bo  that  ultimately,  and  when  very  long  periods  of  time 
are  embraced,  a  complete  compensation  will  be  found  to  be  worked  out. 

(665.)  This  supposes,  however,  that  in  such  long  periods  the  orbit  of 
M  is  not  so  altered  as  to  render  the  occurrence  of  the  compensating  situ- 
ation (M,  P')  impossible.  This  would  be  the  case  if  M's  orbit  ware  to 
dilate  or  contract  indefinitely  by  a  variation  in  its  axis.  But  the  same 
reasoning  which  applies  to  P,  applies  also  to  M.  P  retaining  a  Jixed 
situation  M's  velocity,  and  therefore  the  axis  of  its  orbit,  would  be  ex- 
actly restored  at  the  end  of  a  revolution  of  M ;  so  that  for  every  position 
P  M  there  exists  a  compensating  position  P  M'.  Thus  M's  orbit  is  main- 
tained of  the  same  magnitude,  and  the  possibility  of  the  occurrence  of 
the  compensating  situation  (M,  P')  is  secured. 

(666)  To  demonstrate  as  a  rigorous  mathematical  truth  the  complete 
and  absolute  ultimate  compensation  of  the  variations  in  question,  it  would 
be  requisite  to  show  tbat  the  minute  outstanding  changes  due  to  the  non- 
arrivals  of  P  and  M  at  the  same  cxart  points  at  the  end  of  each  revolu- 
tion, cannot  accumulate  in  the  course  of  infinite  ages  in  one  direction. 
Now  it  will  appear  in  the  subsequent  part  of  this  chapter,  that  the  effect 
of  pertuHaation  on  the  excentricities  and  apsides  of  the  orbits  is  to  cause 
the  former  to  undergo  only  periodical  variations,  and  the  latter  to  revolve 
and  take  up  in  succession  every  possible  situation  Hence  in  ti*e  course 
of  infinite  age?';  tlwj  points  of  arrival  of  P  and  M  at  fixer!  lines  ^f  direc- 
tion, S  P,  S  M,  in  auccessivn  revolutions,  though  at  one  time  tVy  wi!' 
upproach  8,  at  aaother  will  recede  from  it^  fluctuating  to  and  fro  i«»out  I 


VARIATION  OF  THE  MAJOR  AXIS. 


863 


ind  therefore 
jt  neglectiog 
B  non-arrival 
n  of  the  per- 
nrbing  force, 

y  a  reasoning 

jensated  varia- 

ing  M's  recess 

iations  arising 
-whatever  M's 

lust  exist  some 

11  be  precisely 

1   an  indefinite 

combination  of 

the  combination 

I  carried  to  the 
periods  of  time 

)e  worked  out. 

iods  the  orbit  of 

mpensating  situ- 

L's  orbit  were  to 
But  the  same 

retaining  a  fixed 

)it,  would  be  ex- 
'or  every  position 
tl's  orbit  is  main- 
he  occurrence  of 

ruth  the  complete 
[question,  it  would 
es  due  to  the  non- 
^d  of  each  revolu- 
in  one  direction. 
Iter,  that  the  effect 
orbits  is  to  cause 
le  latter  to  revolve 
[nee  iu  tiw;  course 
ixed  lines  /f  direc- 
[ne  time  tl»*y  wil'. 
to  and  froa»»out| 


meon  points  from  wiiich  they  never  greatly  depart.  And  if  the  arrival 
of  either  of  them  at  P,  at  a  point  nearer  S,  at  the  end  of  a  complete 
revolution,  cause  an  excess  of  velocity,  its  arrival  at  a  more  distant  point 
will  cause  a  deficiency,  and  thus,  as  the  fluctuations  of  distance  to  and  fro 
ultimately  balance  each  other,  so  will  also  the  er:co8ses  and  defects  of 
velocity,  though  in  periods  of  enormous  length,  being  no  less  than  that 
of  a  complete  revolution  of  P's  apsides  for  the  one  cause  of  inequality, 
and  of  a  «omplete  restoration  of  its  excentricity  for  the  other. 

(667.)  The  dynamical  proposition  on  which  this  reasoning  is  based  is 
gene»  n\,  and  applies  equally  well  to  cases  wherein  the  forces  act  in  one 
plane,  or  are  directed  to  centres  anywhere  situated  in  space.  Hence,  if 
we  take  into  consideration  the  inclinativ.:*  of  P's  orbit  to  that  of  M,  the 
same  reasoning  will  apply.  Only  that  in  this  case,  upon  a  complete  revo- 
lition  of  P,  the  variation  of  inclination  and  the  motion  of  the  nodes  of 
Ft  orbit  will  prevent  its  returning  to  a  point  in  the  exact  plane  of  its 
original  orbit,  as  that  of  the  excentricity  and  perihelion  prevent  its  arrival 
at  the  same  exact  distance  from  S.  But  since  it  has  been  shown  that  the 
inclination  fluctuates  round  a  mean  state  from  which  it  never  departs 
much,  and  since  the  node  revolves  and  makes  a  complete  circuit,  it  is 
obvious  that  in  a  complete  period  of  the  latter  the  points  of  arrival  of  P 
at  the  same  longitude  will  deviate  as  often  and  by  the  same  quantities 
above  as  below  its  original  point  of  departure  from  exact  coincidence; 
and,  therefore,  that  on  the  average  of  un  infinite  number  of  revolutions, 
the  effect  of  this  cause  of  non-compensation  will  also  be  destroyed. 

(668.)  It  is  evident,  also,  that  the  dynamical  proposition  in  question 
being  general,  and  applying  equally  to  any  mimher  of  fixed  centres,  as 
well  as  to  any  distribution  of  them  in  spaoe,  the  conclusion  would  be  pre- 
cisely the  same  whatever  be  the  number  of  disturbing  bodies,  only  that 
the  periods  of  compensation  would  become  more  intricately  involved. 
We  are,  therefore,  conducted  to  this  most  remarkable  and  important  con- 
clusion, viz.  that  the  m»jor  axes  of  the  planetary  (and  lunar)  orbits,  and, 
consequently,  also  their  mean  motions  and  periodic  times,  are  subject  to 
none  but  periodical  changes;  that  the  length  of  the  year,  for  exanjple,  in 
the  lapse  of  infinite  ages,  has  no  preponderating  tendency  either  to  increase 
or  diminution, — that  the  planets  will  neither  recede  idefinitely  from  the 
sun,  nor  fall  into  it,  but  continue,  so  far  as  their  mutual  perturbations  at 
least  are  concerned,  to  revolve  for  ever  in  orbits  of  very  nearly  the  same 
dimensions  as  at  present. 

(669.)  This  theorem  (the  Mayna  Charta  of  our  system),  the  discovery 
of  which  is  due  to  Lagrange,  is  justly  regarded  as  the  most  important,  as 
a  siogle  result,  of  any  which  have  hitherto  rewarded  the  researches  of 


•It   ■'■*' 


:•  ->! 

Www*'. 
"■«Vit»P' 


''•"•IJ 


r;- 


864 


OUTLINES  OF  ASTRONOMY. 


*i 


I 


i; 

iKy 

I- 

\ 

tir. 

HW 

»•>■. 

•»; 

kii,> 

■r 

•  «7 

#>*• 

f;r 

«c 


I 


5*" 

Ml 


mathematicians  in  this  application  of  their  science ;  and  it  is  especially 
worthy  of  remark,  and  follows  evidently  from  the  view  here  taken  of  it, 
that  it  would  not  be  true  but  for  the  influence  of  the  perturbing  forces  on 
other  elements  of  the  orbit,  viz.  the  perihelion  and  excentricity,  and  the 
inclination  and  nodes ;  since  we  have  seen  that  the  revolution  of  the  ap- 
sides and  nodes,  and  the  periodical  increase  and  diminution  of  the  ec- 
centricities and  inclirations,  are  both  essential  towards  operating  that  final 
and  complete  compensation  which  gives  it  a  character  of  mathematical 
exactness.  We  have  here  an  instance  of  a  perturbation  of  one  kind 
operating  on  a  perturbation  of  another  to  annihilate  an  effect  which  would 
otherwise  accumulate  to  the  destruction  of  the  system.  It  must,  however, 
be  borne  in  mind,  that  it  is  the  smallness  of  the  excentricities  of  the  more 
influential  planets,  which  gives  this  tlieorem  its  practical  importance,  and 
distinguishes  it  from  a  mere  barren  (speculative  result.  Within  the  limits 
of  ultimate  restoration,  it  is  this  alone  which  keeps  the  periodical  fluctua- 
tions of  the  axis  to  and  fro  about  a  mean  value  within  moderate  and 
reasonable  limits.  Although  the  earth  might  not  fall  into  the  sun,  or  re- 
cede from  it  beyond  the  present  limits  of  our  system,  any  considerable 
increase  or  diminution  of  its  mean  distance,  to  the  extent,  for  instance,  of 
a  tenth  of  its  actual  amount,  would  not  fail  to  subvert  the  conditions  on 
which  the  existence  of  the  present  race  of  animated  beings  depends. 
Constituted  as  our  system  is,  howover,  changes  to  anything  like  this  ex- 
tent  are  utterly  precluded.  The  greatest  departure  from  the  mean  value 
of  the  axis  of  any  planetary  orbit  yet  recognized  by  theory  or  observation 
(that  of  the  orbit  of  Saturn  disturbed  by  Jupiter),  does  not  amount  to  a 
thousandth  part  of  its  length.'  The  effects  of  these  fl,uctuations,  how- 
ever, are  very  sensible,  and  manifest  themselves  in  alternate  accelerations 
and  retardations  in  the  angular  motions  of  the  disturbed  about  the  central 
body,  which  cause  it  alternately  to  outrun  and  to  lag  behind  its  elliptic 
place  in  its  orbit,  giving  rise  to  what  are  called  equations  in  its  motion, 
some  of  the  chief  instances  of  which  will  be  hereafter  specified  when  we 
come  +0  trace  more  particularly  in  detail  the  effects  of  the  tangential  force 
in  various  configurations  of  the  disturbed  and  disturbing  bodies,  and  to 
explain  the  consequences  of  a  near  approach  to  commensurability  in  their 
periodic  times.  An  exact  commensurability  in  this  respect,  such,  for  in- 
stance, as  would  bring  both  planets  round  to  the  same  configuration  in  two 
or  three  revolutions  of  one  of  them,  would  appear  at  first  sight  to  desiroy 
one  of  the  essential  elements  of  our  demonstration.     But  even  supposing 

'  Grcnter  deviations  will  probably  be  found  to  exist  ir»  the  orbits  of  the  small  extra- 
tropical  planets,  fiut  these  are  too  insignificant  members  of  our  system  to  need  special 
notice  .ti  a  work  of  this  nature. 


DISPLACEMENT  OF  THE   UPPER  FOCUS. 


365 


is  especially 
}  taken  of  it, 
oing  forces  on 
•icity,  and  the 
on  of  the  ap- 
on  of  the  ex- 
iting that  final 
mathematical 
1  of  one  kind 
et  which  would 
must,  however, 
iea  of  the  more 
raportanco,  and 
ithin  the  limits 
iriodical  fluctua- 
1  moderate  and 
3  the  sun,  or  re- 
any  considerable 
for  instance,  of 
le  conditions  on 
[beings  depends, 
ng  like  this  ex- 
the  mean  value 
ry  or  observation 
not  amount  to  a 
.uctuations,  how- 
aate  accelerations 
about  the  central  1 
ehind  its  elliptic 
as  in  its  motion, 
ipecified  when  wo 
■e  tangential  force 
ig  bodies,  and  to 
surability  in  their 
lect,  such,  for  in- 
mfiguration  in  two 
it  sight  to  dcsvroy 
|ut  even  supposing 

,  of  the  small  extra- 
irstem  to  need  special 


such  an  exact  adjustment  to  subsist  at  any  epoch,  it  could  not  remain  per- 
manent, since  by  a  remarkable  property  of  perturbations  of  this  class, 
which  geometers  have  demonstrated,  but  the  reasons  of  which  we  cannot 
stop  to  explain,  any  change  produced  on  the  axis  of  the  disturbed  planet's 
orbit  is  necessarily  accompanied  by  a  change  in  the  contrary/  direction  in 
that  of  the  disturbing,  so  that  the  periods  would  recede  from  commensu- 
lability  by  the  mere  effect  of  their  mutual  action.  Cases  are  not  wanting 
in  the  planetary  system  of  a  certain  approach  to  coinmcnsurability,  and  in 
one  very  remarkable  case  (that  of  Uranus  and  Neptune)  of  a  considerably 
near  one,  not  near  enough,  however,  in  the  smallest  degree  to  affect  the 
validity  of  the  argument,  but  only  to  give  rise  to  inequalities  of  very  long 
periods,  of  which  more  presently.' 

(G70.)  The  variation  of  the  length  of  the  axis  of  the  disturbed  orbit 
is  due  solely  to  the  action  of  the  tangential  disturbing  force.  It  is  other- 
wise with  that  of  its  excentricity  and  of  the  position  of  its  axis,  or,  which 
is  the  same  thing,  the  longitude  of  its  perihelion.  Both  the  normal  and 
tangential  components  of  the  disturbing  force  affect  these  elements.  Wo 
sball,  however,  consider  separately  the  influence  of  each,  and,  commencing, 

Fig.  87. 


-9 


las  ♦ne  simplest  case,  with  that  of  the  tangential  force; — let  P  be  the 

place  of  the  disturbed  planet  in  its  elliptic  orbit  A  P  B,  whose  axis  at  the 

niomeut  is  A  S  B  and  focus  S.     Suppose  Y  P  Z  to  be  a  tangent  to  this 

I  orbit  at  P.     Then,  if  wo  suppose  AB  =  'la,  the  other  focus  of  the 

pse,  II,  will  be  found  by  making  the  angle  Z  P  II  =  Y  P  S  or  Y  P  H 

1=  1S0°  —  Y  P  Z,  or  S  P  H  =  180°  —  2  V  P  S,  and  taking  P  H  =  2  a 

I—  S  }'.     This  is  evident  from  the  nature  of  the  ellipse,  in  which  lines 

Iflrawn  from  any  point  to  the  two  foci  make  equal  angles  with  the  tangent, 

'41  rei'olutions  of  Neptune  a«  nearly  equal  to  81  of  Uranus,  giving  rise  to  an  ine- 
quality, Having  6806  years  ifjt  its  period. 


JC-'* 


.'?!j<** 


"Miosis 


,!»> 


(■   ''•.el"*' 
;'■-«"  Mi' 


in 


I'V.'iaay 


(. 


866 


OUTLINES  OF  A6TB0N0MT. 


ir 


I 


£ 


Itv- 


I? 


fcart 

::2 


and  have  their  sum  equal  to  the  major  axis.  Suppose,  now,  the  tangen- 
tial force  to  act  on  P  aud  to  increase  its  velocity.  It  will  therefore  increase 
the  axis,  so  that  the  new  value  assumed  by  a  (viz.  a')  will  be  greater  than 
a.  But  the  tangential  force  does  not  alter  the  angle  of  tangency,  so  that 
to  find  the  new  position  (H')  of  the  upper  focus,  we  must  measure  off 
along  the  same  line  P  H,  a  distance  P  H'  (=  2  a,  —  S  P)  greater  than 
P  H.  Do  this  then,  and  join  S  H'  and  produce  it.  Then  will  A'  B'  be 
the  new  position  of  the  axis,  and  i  S  H'  the  new  excentrioity.  Hence  we 
conclude,  1st,  that  the  new  position  of  the  perihelion  A'  will  deviate  from 
the  old  one  A  towards  the  same  side  of  the  axis  A  B  on  which  P  is  when 
the  tangential  force  acts  to  increase  the  velocity,  whether  P  be  moving 
from  perihelion  to  aphelion,  or  the  contrary.  2dly,  That  on  the  same  sup- 
position as  to  the  action  cf  the  tangential  force,  the  excentrioity  increases 
when  P  is  between  the  pt^rihelion  and  the  perpendicular  to  the  axis  F  H  G 
drawn  through  the  upper  focus,  and  diminishes  when  between  the  aphelion 
and  the  same  perpendicular.  3dly,  That  for  a  given  change  of  velocity, 
t.  e.  for  a  given  value  of  the  tangential  force,  the  momentary  variation  in 
the  place  of  the  perihelion  is  a  maximum  when  P  is  at  F  or  G,  from 
which  situation  of  P  to  the  perihelion  or  aphelion,  it  decreases  to  nothing, 
the  perihelion  being  stationary  when  P  is  at  A  or  B.  4thly,  That  the 
variation  of  the  excentricity  due  to  this  cause  is  complementary  in  its  law 
of  increase  and  decrease  to  that  of  the  perihelion,  being  a  maximum  for  a 
given  tangential  force  when  P  is  at  A  or  B,  and  vanishing  when  at  G  or 
F.  And  lastly,  that  where  the  tangential  force  acts  to  diminish  the  velo- 
city, all  these  results  are  reversed.  If  the  orbit  be  very  nearly  circular' 
the  points  F^  G,  will  be  so  situated  that,  although  not  at  opposite  extremi- 
ties of  a  diameter,  the  timss  of  describing  A  F,  F  B,  B  G,  and  G  A  will 
be'^all  9qual,  and  each  of  course  one  quarter  of  the  whole  periodic  time 
of  P.       ' 

(671.)  Let  us  now  consider  the  effects  of  the  normal  component  of  the 
disturbing  force  upon  the  same  elements.  The  direct  effect  of  this  force 
is  to  increase  or  diminish  the  curvature  of  the  orbit  at  the  point  P  of  its 
action,  without  producing  any  change  on  the  velocity,  so  that  the  length 
of  the  axis  remains  unaltered  by  its  action.  Now,  an  increase  of  curva- 
ture at  P  is  synonymous  with  a  decrease  in  the  angle  of  tangency  SPY 
iW)^n  P  is  approaching  towards  S,  and  with  an  increase  in  that  angle 
/when  receding  from  S.  Suppose  the  former  case,  and  while  P  approaches 
'S  (or  is  moving  trom  aphelion  to  perihelion),  let  the  normal  force  act 
ii^gnrdi  or  towards  the  concavity  of  the  ellipse.  Then  will  the  tangent 
P  Y  by  the  action  of  that  force  have  taken  up  the  position  P  Y'.    To  find 


'  So  nearly  that  the  cube  of  the  excentricity  may  be  neglected. 


DISPLACEMENT  OF  THE  UPPER  FOCUS. 


867 


tbo  tangen- 
fore  increase 
greater  than 
ency,  so  tbat 
measure  off 
greater  than 
will  A'  B'  be 
.    Hence  we 
,  deviate  from 
ich  P  is  ^lien 
p  be  moving 
the  same  sup- 
ricity  increasea 
the  axis  FH a 
en  the  aphelion 
ige  of  velocity, 
ary  variation  in 
F  or  G,  from 
ases  to  nothing, 
4tbly,  That  the 
jntary  in  its  law 
maximum  for"  a 
ig  when  at  G  or 
minisb  the  velo- 
r  nearly  circular' 
)ppo8ite  extremi- 
G,  and  G  A  will 
)le  periodic  time 

Bomponent  of  the 
Feet  of  this  force 
he  point  P  of  its 
0  that  tbe  length 
ttcrease  of  curva- 
f  tangency  S  P  i 
aae  in  tbat  angle 
hile  P  approaches 
normal  force  act 
Q  will  tbe  tangent 
ionPY'.   To  find 


Fig.  88. 


Mi 


glected. 


the  corresponding  position  H'  taken  up  by  the  focus  of  tbe  orbit  so  dis* 
turbed,  we  must  make  the  angle  SPH'=180°— 2  SPY',  or,  which 
comes  to  tbe  3amo,  draw  P  H'  on  the  side  of  P  H  opposite  to  S,  making 
the  angle  H  P  H'=.twice  tbe  angle  of  deflection  Y  P  Y'  and  in  P  H'  take 
P  H'  =  P  H.  Joining,  then,  S  H'  and  producing  it,  A'  S  H'  M'  will  bo 
the  new  position  of  tbe  axis.  A'  tbe  new  perihelion,  and  ^  S  H'  tbe  new 
excentricity.  Hence  we  conclude,  1st,  tbat  tbe  normal  force  acting 
inwards f  and  P  moving  totcards  tbe  perihelion,  tbe  new  direction  S  A' 
of  tbe  perihelion  is  in  advance  (with  reference  to  tbe  direction  of  P's 
revolution)  of  tbe  old  —  or  the  apsides  advance  —  when  Pis  anywhere 
situated  between  F  and  A  ;  "uce  when  at  F  tbe  point  H'  falls  upon  H  M 
hetween  H  and  M.)  When  P  is  at  F  the  apsides  are  stationary,  but 
when  P  is  anywhere  betweon  M  and  F  the  apsides  retrograde,  H'  in  this 
case  lying  on  tbe  opposite  side  of  tbe  axis.  2dly,  Tbat  tbe  same  direc- 
tions of  the  normal  force  and  of  P's  motion  being  supposed,  tbe  excentri- 
city increases  while  P  moves  through  tbe  whole  semiellipse  from  aphelion 
to  perihelion — the  rate  of  its  increase  being  a  maximum  when  P  is  at  F, 
and  nothing  at  the  aphelion  and  perihelion.  3dly,  Tbat  these  effects  are 
reversed  in  tbe  opposite  half  of  the  orbit,  A  G  M,  in  which  P  passes  from 
perihelion  to  aphelion  or  recedes  from  S.  4thly,  Tbat  they  are  also 
reversed  by  a  reversal  of  the  direction  of  tbe  normal  force,  outwards,  in 
place  of  inwards.  5tbly,  Tbat  here  also  tbe  variations  of  tbe  excentricity 
and  perihelion  are  complementary  to  each  other;  tbe  one  variation  being 
most  rapid  when  the  other  vanishes,  and  vice  versd.  6thly,  And  lastly, 
that  the  changes  in  the  situation  of  the  focus  H  produced  by  tbe  actions 
of  the  tangential  and  normal  components  of  the  disturbing  force  are  at 
right  angles  to  each  other  in  every  situation  of  P,  and  therefore  where 
the  tangential  force  is  most  efficacious  (in  proportion  to  its  intensity)  in 
varying  cither  tbe  one  or  the  other  of  the  elements  in  question,  the 
I  normal  is  least  so,  and  vice  versd. 


<r«aff' '  -iV 


>w. ;-; 


".n^' 


m 


868 


OUTLINES   OF  ASTRONOMY. 


\ 

I' 

I 

t> 

« 
It 


5 


"lai.-. 


r.»». 


«*•• 


(672.")  To  determine  the  momentary  effect  of  the  whole  d'^urbing 
force,  t,  >n,  we  have  only  to  resolve  it  into  its  tangential  and  normal 
componiMits,  and  eatimating  by  these  principles  Bcparatoiy  the  effocts  of 
either  constituent  on  both  elements,  add  or  -il.  .'i  ict  the  results  according 
as  they  conspire  or  oppose  each  otlif  r.  Or  wo  may  at  once  make  the 
angle  H  P  H"  equal  to  twice  the  angle  of  deflection  produced  by  the 
normal  force,  and  lay  off  P  H"=P  11  + twice  the  variation  of  a  produced 
in  the  same  moment  of  time  by  the  tangential  force,  and  II"  will  be  the 
new  focus.  The  momentary  velocity  generated  by  the  tangential  force  is 
calculable  from  a  knowledge  of  that  force  by  the  ordinary  principles  of 
dynamics;  and  from  this,  the  variation  of  the  axis  is  easily  derived.' 
The  momentary  velocity  generated  by  the  normal  force  in  its  own  direc- 
tion is  ill  like  manner  caculable  from  a  knowledge  of  that  force,  and 
dividing  this  by  the  linear  velocity  of  P  at  that  instant,  wo  deduce  the 
angular  velocity  of  the  tangent  about  P,  or  the  momentary  variation  of 
the  angle  of  tangency  SPY,  corresponding. 

(673.)  The  following  rhum4  of  these  several  results  in  a  tabular  form 
includes  every  variety  of  case  according  as  P  is  approaching  to  or  receding 
from  S ;  as  it  is  situated  in  the  arc  FAG-  of  its  orbit  about  the  jperihc- 
lion,  or  in  the  remoter  arc  G  M  F  alwtit  (lie  aphelion,  as  the  tangential 
force  accelerates  or  retards  the  disturbed  body,  or  as  the  normal  acts  in- 
wart's  or  outwards  with  reference  to  the  concavity  of  the  orbit. 

EFFECTS   OF   THE   TANGENTIAL  DISTURBING   FORCE. 


Direction  of  P's  mo- 
tion. 

Situation  of  P  ia 
orbit. 

Action  of  Tangential 

Force. 

Effect  on  Elemente. 

Approaching  S. 

Ditto. 
Receding  from  S. 

Ditto. 
Indifferent. 

Ditto. 

Ditto. 

Ditto. 

Anywhere. 

Ditto. 

Ditto. 

Ditto. 
About  Aphelion. 

Ditto. 
About  Perihelion. 

Ditto. 

Accelerating  P. 
Retarding  P. 
Accelerating  P. 
Retarding  P. 
Accelerating  P. 
Retarding  P. 
Accelerating  P. 
Retard' ng  P. 

Apsides    recede. 

advance. 

advance. 

recede. 
Excentr.  decreases. 

increases. 

increases, 

decreases. 

2  12  11 

= D%and  — = «"  ;. -r =d*— »'*=(»+t>')  (»—«')  '^r  when  infi- 

r  a!       r  a!       a 


mtesimal  variations  only  are  considered  — r-=2w  (t»' 

a* 


»)  or  a! — a=%aH  («'—«) 
from  which  it  appears  thut  the  variation  of  the  axis  arising  from  a  given  variation  ol 
velocity  is  independent  of  r,  or  is  the  same  at  whatever  distance  from  S  the  change 
takes  place,  and  that  eateris  paribus  it  is  greater  for  a  given  change  of  velocity  (or  for 
a  given  tangential  force)  in  the  direct  ratio  of  the  velocity  itself. 


EFFECTS  ON  THE  APSIDES  AND   EXCENTRICITIES. 


869 


duiurVing 
,nd  normal 
3  effocts  of 
;a  uccording 
J  make  llic 
iced  by  the 
a  produced 
will  be  the 
ntial  force  is 
principles  of 
iily  dcrivc'l.' 
ts  own  direc- 
it  force,  and 

0  deduce  the 
f  variatiou  of 

1  tabular  form 
to  or  receding 
>iU  the  perihc- 
the  tangential 
ormal  acta  m- 
irbit. 

)RCE. 


[ect  on  Elements. 


EFFECTS  OF   THE   NORMAL   DI8TURBINU   FORCE. 


eides    recede. 

advance. 

advance. 

recede, 
centr.  decreases. 

increases. 

increases. 

decreases. 


— t)')  '^r  when  infi- 

'— a=2a««  (t)'— «) 
a  given  variation  ot 
from  S  the  change 
e  of  velocity  (or  for 


DIrBCtlon  of  P's  mo- 
tion. 

Situation  of  V  in 
orUt. 

Action  of  Normal 
Force. 

Effort  on  Elements. 

Indifferent. 

Ditto. 

Ditto. 

Ditto. 
Approaching  S. 

Ditto. 
Receding  from  S. 

Ditto. 

About  Apholion. 

Ditto. 
About  Perihelion. 

Ditto. 
Anywhere. 

Ditto. 

Ditto. 

Ditto. 

Inwards. 
Outwards. 
Inwards. 
Outwards. 
Inwards. 
Outwords. 
inwards, 
twards. 

Apsidca    recede. 

advnnco. 

advance. 

rooede. 
Excontr.  increases. 

decreases. 

decreases. 

Increases. 

(074.)  From  the  momentary  cha  elements  of  the  disturbed 

orbit  corresponding  to  successive  situcuioud  oi  P  and  M,  to  conclude  the 
total  amount  of  changio  produced  in  any  given  time  is  the  business  of  the 
integral  calculus,  and  lies  far  beyond  the  scope  of  the  present  work. 
Without  its  aid,  however,  and  by  general  consideration  of  the  periodical 
recurrence  of  configurations  of  the  same  character,  we  have  been  able  to 
demonstrate  many  of  the  most  interesting  conclusions  to  which  geometers 
have  been  conducted,  e^  iinples  of  which  have  already  been  given  in  the 
reasoning  by  which  the  permanence  of  the  axes,  the  periodicity  of  the 
inclinations,  and  the  revolutions  of  the  nodes  of  the  planetary  orbits  have 
been  demonstrated.  We  shall  now  proceed  to  apply  similar  considerations 
to  the  motion  of  the  apsides,  and  the  variations  of  the  exccntricities.  To 
this  end  we  must  first  trace  the  changes  induced  on  the  disturbing  forces 
themselves  with  the  varying  positions  of  the  '  lodies,  and  here  as  in  treat* 
ing  of  the  inclinations  we  shall  suppose,  unless  the  contrary  is  expressly 
indicated,  both  orbits  to  be  very  nearly  circular,  without  which  limitation 
the  complication  of  the  subject  would  become  too  embarrassing  for  the 
render  to  follow,  and  defeat  the  end  of  explanation. 

(675.)  On  this  supposition  the  directions  of  S  P  and  S  Y,  the  perpen- 
dicular on  the  tangent  at  1',  may  be  regarded  as  coincident,  and  the 
normal  and  radial  disturbing  forces  become  nearly  identical  in  quantity, 
also  the  tangential  and  transversal,  by  the  near  coincidence  of  the  points 
T  and  L  (fig.  art.  687).  So  far  then  as  the  intensity  of  the  forces  is  con- 
cerned, it  will  make  very  little  difference  in  which  way  the  forces  are  re- 
solved, nor  will  it  at  all  materially  affect  our  conclusions  as  to  the  effects 
of  the  normal  and  tangential  forces,  if  in  estimating  their  quantitative 
values,  we  take  advantage  of  the  simplification  introduced  into  their  nu- 
merical expression  by  the  neglect  of  the  angle  P  S  Y,  ^.  e.  by  the  substi- 
|tution  for  them  of  the  radial  and  transversal  components.  The  character 
24 


•^■■""•■'..Jllli* 


'*«!►, 


14 


.y 


%  ■:-  -y- 


•r 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


V. 


r.^ 


^A 


4ia 


4^6 


% 


1.0    ^1^  1^ 


I.I 


^  Ufi    |2£ 


I 

■l 


V 


FholDgraphic 

Sciences 

CbrpoiBtian 


•S! 


;\ 


23  WBT  MAM  STRUT 

WilSTRR,N.Y.  I4SM 
(71«)I73^S09 


4^ 


v\ 


870 


OUTLINES  OF  ASTRONOMY. 
Fig.  89. 


E 

i 

m 

\-         •' 

tt 

'■       •• 

H 

-         •' 

F  ' 

H       W* 

f 

-rl' 

i 
1 

>• 

. 

• 

1:    ' 

f 

of  these  eflFects  depends  (art.  670,  671,)  on  the  direction  in  which  the 
forces  act,  which  we  shall  suppose  normal  and  tangential  as  before,  and  it 
is  only  on  the  estimation  of  their  quantitative  effects  that  the  error  in- 
duced by  the  neglect  of  this  angle  can  fall.  In  the  lunar  orbit  this  angle 
never  exceeds  3°  10',  and  its  influence  on  the  quantitative  estimation  of 
the  acting  forces  may  therefore  be  safely  neglected  in  a  first  approxima- 
tion. Now  M  N  being  found  by  the  proportion  M  P" :  M  S* : :  M  S  : 
M  N,  N  P  (=  M  N  —  M  P)  is  also  known,  and  therefore  N  L  =  N  P. 
sin  NPS  =  NP.  sin  (ASP+SMP)  and  LS  =  PL— PS  =  NP. 
cos  N  P  S  — P  S  =  N  P.  cos  (A  S  P+  S  M  P)  —  S  P  become  known, 
which  express  respectively  the  tangential  and  normal  forces  on  the  same 
scale  that  S  M  represents  M's  attraction  on  S.'  Suppose  P  to  revolve  in 
the  direction  E  A  I)  B.  Then,  by  drawing  the  figure  in  various  situations 
of  P  throughout  the  whole  circle,  the  reader  will  easily  satisfy  himself— 
Ist.  That  the  tangential  force  accelerates  P,  as  it  moves  from  E  towards 
A,  and  from  D  towards  6,  but  retards  it  as  it  passes  from  A  to  D,  and 
from  B  to  E.  2d.  That  the  tangential  force  vanishes  rt  the  four  points 
A,  D,  E,  B,  and  attains  a  maximum  at  some  intermediate  points. 
3dly.  That  the  normal  force  is  directed  outwards  at  the  syzygies  A,  6, 
and  inwards  at  the  points  D,  E,  at  which  points  respectively  its  outward 
and  inward  intensities  attain  their  maxima.    Lastly,  that  this  force  n- 

'MS  =  R;SP  =  r;MP=/;  ASP  =  tf;  AMP  =  M;  MN=^;  NP  = 

5-^=^=(R-/)(l  +  jH- J-]);  whence  we  have  NL  =  (R-/).  8in(fl  +  M). 

(l  +  ^  +  ^);  LS  =  (R-/).  co8(0  +  M).(l+-^  +  j|\-r.    When  R  and/, 

p 
owing  to  the  great  distance  of  M,  are  nearly  equal,  we  have  R— /=P  V, ••7-  =  l| 

nearly,  and  the  angle  M  may  be  neglected ;  so  that  we  have  N  P  =  3  P  V. 


DISTURBING  FORCES  IN  CIRCULAR  ORBITS. 


871 


on  in  which  the 
as  before,  and  it 
hat  the  error  in- 
r  orbit  this  angle 
ive  estimation  of 
1  first  approxima- 
«  :  M  S' : :  M  S : 
fore  NL=NP. 
L_PS  =  NP. 
become  known., 
forces  on  the  same 
ise  P  to  revolve  in 
various  situations 
satisfy  himself - 
les  from  E  towards 
from  A  to  D,  and 
rt  the  four  points 
[tcrmediate  points. 
ihe  syzygies  A,  B, 
[ctively  its  outward 
that  this  force  va- 

|(R_/).  Bin(e  +  M). 
|__r.    When  Rand/, 

P=»3PV. 


nishes  at  points  intermediate  between  A  D,  D  B,  B  E,  and  E  A,  which 
points,  when  M  is  considerably  remote,  are  situated  nearer  to  the  quadra- 
ture than  the  syzygies. 

(676.)  In  the  lunar  theory,  to  which  we  shall  now  proceed  to  apply 
these  principles,  both  the  geometrical  representation  and  the  algebraic 
expression  of  the  disturbing  forces  admit  of  great  simplification.  Owing 
to  the  great  distance  of  the  sun  M,  at  whose  centre  the  radius  of  the 
moon's  orbit  never  subtends  an  angle  of  more  than  about  8',  N  P  may  be 
regarded  as  parallel  to  A  B.  And  D  S  E  becomes  a  straight  line,  coinci- 
dent with  the  line  of  quadratures,  so  that  V  P  becomes  the  cosine  of 
A  S  P  to  radius  S  P,  and  N  L  =  N  P .  sin  A  S  P;  L  P  =  N  P.  cos 
ASP.  Moreover,  in  this  case  (see  the  note  on  the  last  article)  N  P  = 
3  P  V=  3  S  P .  cos  A  S  P;  and  consequently  N  L  =  3  S  P .  cos  A  S  P. 
sin  A  S P  =  I  S  P.  sin  2  A  S  P,  and  L  S  =  S  P  (3 .  cos  AS  P''— 1) 
=  jSP(l  +  3.co8  2ASP)  which  vanishes  when  cos  A  S  P*  =  i,  or  at 
64°  14'  from  the  syzygy.  Suppose  through  every  point  of  P's  orbit 
there  be  drawn  S  Q  =  3  S  P .  cos  A  S  P^  then  will  Q  trace  out  a  certain 
looped  oval,  as  in  the  figure,  cutting  the  orbit  in  four  points  64°  14'  from 
A  and  B  respectively,  and  P  Q  will  always  represent  in  quantity  and  di- 
rection the  normal  force  acting  at  P. 


(677.)  It  is  important  to  remark  here,  because  upon  this  the  whole 
lunar  theory  and  especially  that  of  the  motion  of  the  apsides  hinges,  that 
all  the  acting  disturbing  forces,  at  equal  angles  of  elongation  A  S  P  of  the 
moon  from  the  sun,  are  cseteris  paribus  proportional  to  S  P,  the  moon's 
distance  from  the  earth,  and  are  therefore  greater  when  the  moon  is  near 
its  apogee  than  when  near  it«  perigee;  the  extreme  proportion  being  that 
of  about  28  :  25.  This  premised,  let  us  first  consider  the  effect  of  the 
normal  force  in  displacing  the  lunar  apsides.  This  we  shall  best  be  ena- 
bled to  do  by  examining  separately  those  cases  in  which  the  effects  are 


X' 


tm<M»9 


872 


OUTLINES  OF  ASTRONOMY. 


« 


s 


•DIM  ' 


most  strongly  contrasted ;  viz.  when  the  major  axis  of  the  moon's  orbit  is 
directed  towards  the  sun,  and  when  at  right  angles  to  that  direction. 
First,  then,  let  the  line  of  apsides  be  directed  to  the  sun  as  in  the  an- 
nexed figure,  where  A  is  the  perigee,  and  take  the  arcs  A  a,  A  6,  B  c,  B  c^ 


+  + 


M 


eaohss64**  14'.  Then  while  P  b  between  a  and  6  the  normal  force  act- 
ing outwards,  and  the  moon  being  near  itd  perigee,  by  art.  671,  the 
apsides  will  recede,  but  when  between  c  and  d,  the  force  there  actiug  out- 
wards, but.  the  moon  being  near  its  apogee,  they  will  advance.  The  ra- 
pidity of  these  movements  will  bo  respectively  at  its  maxima  at  A  and  B, 
not  only  because  the  disturbing  forces  are  then  most  intense,  but  also 
because  (see  art.  671)  they  act  most  advantageously  at  those  points  to 
displace  the  axis.  Proceeding  from  A  and  B  towards  the  neutral  points 
abed,  the  rapidity  of  their  recess  and  advance  diminishes,  and  is  nothing 
(or  the  apsides  are  stationary)  when  P  is  at  either  of  e  points.  From 
b  to  D,  or  rather  to  a  point  some  little  beyond  D  (ar  1)  the  force  acts 
inwards,  and  the  moon  is  still  near  perigee,  so  that  in  this  arc  of  the  orbit 
the  apsides  advance.  But  the  rate  of  advance  is  fe«ble,  because  in  the 
early  part  of  that  arc  the  normal  force  h  small,  and  as  P  approaches  D 
and  the  force  gains  power,  it  acts  disadvantageously  to  move  the  axis,  its 
effect  vanishing  altogether  when  it  arrives  beyond  D  at  the  extremity  of 
the  perpendicular  to  the  upper  focus  of  the  lunar  ellipse.  Thence  up  to 
c  this  feeble  advance  is  reversed  and  converted  into  a  recess,  the  force  still 
acting  inwards,  but  the  moon  now  being  near  its  apogee.  And  so  also 
for  the  arcs  (2E,  E  a.     In  the  figure  these  changes  are  indicated  by  +  + 

for  rapid  advance, for  rapid  recess,  -f  and  —  for  feeble  advance  and 

recess,  and  0  for  the  stationary  points.  Now  if  the  forces  were  equal  on 
the  sides  of  +  and  —  it  is  evident  that  there  would  be  an  exact  counter- 
balance of  advance  and  recess  on  the  average  of  a  whole  revolution.  But 
this  is  not  the  case.    The  force  in  apogee  is  greater  than  that  in  perigee 


MOTION   OF  THE   LUNAR  APSIDES. 


878 


icon's  orbit  is 

lat  direction. 

18  in  tbe  an- 

A6,Bc,Bd 


normal  force  act- 
by  art.  671,  tbe 
tbere  actiug  out- 
Ivance.    Tbe  ra- 
:ima  at  A  and  B, 
intense,  but  also 
t  tbose  points  to 
he  neutral  points 
SB,  and  is  notbing 
e  points.    S'rom 
1)  tbe  force  acts 
lia  arc  of  tbe  orbit 
)le,  because  in  tbe 
18  P  approacbes  D 
[move  tbe  axis,  its 
tbe  extremity  of 
■e.    Tbence  up  to 
fcesfl,  tbe  force  still 
ree.    And  bo  also 
[indicated  by  +  + 
2eble  advance  and 
rces  were  equal  on 
5  an  exact  counter- 
le  revolution.    But 
lan  that  in  perigee 


in  tbe  proportion  of  28  :  25,  wbile  in  tbe  quar^atures  about  D  and  E 
they  are  equal.  Therefore^  while  the  feeble  movements  +  and  —  in  tbe 
neighbourhood  of  these  points  destroy  each  otler  almost  exactly,  there 
will  necessarily  remain  a  considerable  balance  in  favour  of  advance,  in 
this  situation  of  the  line  of  apsides. 

(678.)  Next,  suppose  the  apogee  to  lie  at  A,  and  the  perigee  at  B.  In 
this  case  it  is  evident  that,  so  far  as  the  direction  of  the  motions  of  the 
apsides  is  concerned,  all  tbe  conclusions  of  the  foregoing  reasoning  will 
be  reversed  by  the  substitution  of  the  word  perigee  for  apogee,  and  vice 
versd ;  and  all  the  signs  in  the  figure  referred  to  will  be  changed.  But 
now  the  most  powerful  forces  act  on  the  side  of  A,  that  is  to  say,  still  on 
the  side  of  advance,  this  condition  also  being  reversed.  In  either  situa- 
tion of  the  orbit,  then,  the  apsides  advance. 

(679.)  (Case  3.)  Suppose,  now,  the  major  axis  to  have  the  situation 
D  E,  and  the  perigee  to  be  on  the  side  of  D.     Here,  in  the  arc  6  c  of  P's 
motion  the  normal  force  acts  inwards,  and  the  moon  is  near  perigee,  con- 
sequently the  apsides  advance,  but  with  a  moderate  rapidity,  the  maxi- 
mum of  the  inward  normal  force  being  only  half  that  of  tbe  outward. 
In  the  arcs  A  b  and  c  B  tbe  moon  is  still  near  perigee,  and  the  force  acts 
outwards,  but  though  powerfully  towards  A  and  B,  yet  at  a  constantly 
increasing  disadvantage  (art.  671.)     Therefore  in  these  arcs  the  apsides 
recede,  but  moderately.     In  a  A  and  B  d  (being  towards  apogee)  they 
again  advance,  still  with  a  model  .>te  velocity.     Lastly,  throughout  the  arc 
da,  being  about  apogee  with  an  inward  force,  they  recede.     Here  as 
before,  if  the  perigee  and  apogee  forces  were  equal,  the  advance  and  recess 
would  counterbalance ;  but  as  in  fact  the  apogee  forces  preponderate,  there 
will  be  a  balance  on  the  entire  revolution  in  favour  of  recess.     The  same 
reasoning  of  course  holds  good  if  the  perigee  be  towards  E.     But  now, 
between  these  casea  and  those  in  the  foregoing  articles,  there  is  this  dif- 
ference, viz.  that  in  this  the  dominant  effect  results  from  the  inward  action 
of  the  normal  force  in  quadratures,  while  in  the  others  it  results  from  its 
outward,  and  doubly  powerful  action  in  syzygies.     The  recess  of  the  ap- 
sides in  their  quadratures  arising  from  the  action  of  the  normal  force  will 
therefore  be  less  than  their  advance  in  their  syzygies ;  and  not  only  on 
this  account,  but  also  because  of  the  much  less  extent  of  the  arcs  5  c  and 
da  on  which  the  balance  is  mainly  struck  in  this  case,  than  of  ah  and 
cd,  the  corresponding  most  influential  arcs  in  the  other. 

(680.)  In  intermediate  situations  of  the  line  of  apsides,  the  effect  will 
be  intermediate,  and  there  will  of  course  be  a  situation  of  them  in  which 
on  an  average  of  a  whole  revolution,  they  are  stationary.  This  situation 
it  is  easy  to  see  will  be  nearer  to  the  line  of  quadratures  than  of  syzygies, 


! 


'OIK' 


■^ 


-^      rf:. 


•>«*• 


7^ 


374 


OUTLINES  OF  ASTRONOMY. 


K 

;    lit 

V 

Kl 

B 

>    m 

F 

•  i» 

'•      Vli 

■'II' 

>•" 

•;* 

i 

«;. 

1 

•R:' 

1 

.» 

Ik! 

«» 


r* 


I 


1*^ 


and  the  preponderance  of  advance  will  be  maintained  over  a  much  more 
considerable  arc  than  that  of  recess,  among  the  possible  situations  which 
they  can  hold.  On  every  account,  therefore,  the  action  of  the  normal 
force  causes  the  lunar  apsides  to  progress  in  a  complete  revolution  of  M 
or  in  a  synodical  year,  during  which  the  motion  of  the  sun  round  the 
earth  (as  we  consider  the  earth  at  rest)  brings  the  line  of  syzygies  into  all 
situations  with  respect  to  that  of  apsides. 

(681.)  Let  us  next  consider  the  action  of  the  tangential  force.  And 
as  before  (Case  1.),  supposing  the  perigree  of  the  moon  at  A,  and  the 
direction  of  her  revolution  to  be  A  D  B  E,  the  tangential  force  retards 
her  motion  through  the  quadrant  A  D,  in  which  she  recedes  from  S,  there* 
fore  by  art.  670  the  apsides  recede.  Through  D  B  the  force  accelerates^ 
while  the  moon  still  recedes,  therefore  they  advance.  Through  B  E  the 
force  retards,  and  the  moon  approaches,  therefore  they  continue  to  advance, 
and  finally  throughout  the  quadrant  E  A  the  force  accelerates,  and  the 
moon  approaches,  therefore  they  recede.  In  virtue  therefore  of  this  force, 
the  apsides  recede,  during  the  description  of  the  arc  E  A  D,  and  advance 
during  D  B  E,  but  the  force  being  in  this  case  as  in  that  of  the  normal 
force  more  powerful  at  apogee,  the  latter  will  preponderate,  and  the  apsides 
will  advance  on  an  average  of  a  whole  revolution. 
.  (682.)  (Case  2.)  The  perigee  being  towards  B,  we  have  to  substitute 
in  the  foregoing  reasoning  approach  to  S,  for  recess  from  it,  and  vice  versd, 
the  accelerations  and  retardations  remaining  as  before.  Therefore  the  re- 
sults, as  far  as  direction  is  concerned,  will  be  reversed  in  each  quadrant, 
the  apsides  advance  during  E  A  D  and  recede  during  D  B  E.  But  the 
situation  of  the  apogee  being  also  reversed,  the  predominance  remains  on 
the  side  of  E  A  D,  that  is,  of  advance.  .^ 

(683.)  (Case  3.)  Apsides  in  quadratures,  perigee  near  D. — Over  qua- 
drant A  D,  approach  and  retardation,  therefore  advance  of  apsides.  Over 
D  B  recess  and  acceleration,  therefore  again  advance;  over  B  E  recess 
and  retardation  with  recess  of  apsides,  and  lastly  over  E  A  approach  and 
acceleration,  producing  their  continued  recess.  Total  result:  advance 
during  the  half  revolution  A  D  B,  and  recess  during  B  E  A,  the  acting 
forces  being  more  powerful  in  the  latter,  whence  of  course  a  preponderant 
recess.     The  same  result  when  the  perigee  is  at  E. 

(684.)  So  far  the  analogy  of  reasoning  between  the  action  of  the  tan- 
gential and  normal  forces  is  perfect.  But  from  this  point  they  diverge. 
It  is  not  here  as  before.  The  recess  of  the  apsides  in  quadratures  docs 
not  now  arise  from  the  predominance  of  feeble  over  feebler  forces,  while 
that  in  syzygies  results  from  that  of  powerful  over  powerful  ones.  The 
maximum  accelerating  action  of  the  tangential  force  is  equal  to  its  max!- 


MOTION  OF  THE  LUNAR  APSIDES. 


376 


El  much  more 
nations  which 
if  the  normal 
volution  of  M 
un  round  the 
zygies  into  all 

1  force.    And 
at  A,  and  the 
I  force  retards 
s  from  S,  there- 
,rce  accelerates^ 
trough  B  E  the 
inue  to  advance, 
slerates,  and  the 
"ore  of  this  force, 
,  D,  and  advance 
it  of  the  normal 
B,  and  the  apsides 


I' 

action  of  the  tan- 
point  they  diverge. 
1  quadratures  docs 
leebler  forces,  while 
fwerful  ones.    The 

I  equal  to  its  maxi- 


mum retarding,  while  the  inward  action  of  the  normal  at  its  maximum  is 
only  half  the  maximum  of  its  outward.  Neither  is  there  that  difference 
in  the  extent  of  the  arcs  over  which  the  balance  is  struck  in  this,  as  in 
the  other  case,  the  action  of  the  tangential  fcce  being  inward  and  outward 
alternately  over  equal  arcs,  each  a  complete  quadrant.  Whereas,  there- 
fore, in  tracing  the  action  of  the  normal  force,  we  found  reason  to  con- 
clude it  much  more  effective  to  produce  progress  of  the  apsides  in  their 
syzygy,  than  in  their  quadrature  situations,  we  can  draw  no  such  conclu- 
sion in  that  of  the  tangential  forces :  there  being,  as  regards  that  force,  a 
complete  symmetry,  in  the  four  quadrants,  while  in  regard  of  the  normal 
force  the  symmetry  is  only  a  half-symmetry  having  relation  to  two  aemi- 
ctrcks. 

(685.)  Taking  the  average  of  many  revolutions  of  the  sun  about  the 
earth,  in  which  it  shall  present  itself  in  every  possible  variety  of  situations 
to  the  line  of  apsides,  we  see  that  the  effect  of  the  normal  force  is  to  pro- 
duce a  rapid  advance  in  the  syzygy  of  the  apsides,  and  a  less  rapid  recess 
in  their  quadrature,  and  on  the  whole,  therefore,  a  moderately  rapid  gene- 
ral advance,  while  that  of  the  tangential  is  to  produce  an  equally  rapid 
advance  in  syzygy,  and  recess  in  quadrature.  Directly,  therefore,  the 
tangential  force  would  appear  to  have  no  ultimate  influence  in  causing 
either  increase  or  diminution  in  the  mean  motion  of  the  apsides  resulting 
from  the  action  of  the  normal  force.  It  does  so,  however,  indirectly, 
conspiring  in  that  respect  with,  and  greatly  increasing,  an  indirect 
action  of  the  normal  force  in  a  manner  which  we  shall  now  proceed  to 
explain. 

(686.)  The  sun  moving  uniformly,  or  nearly  so,  in  the  same  direction 
as  P,  the  line  of  apsides  when  in  or  near  the  syzygy,  in  advancing  follows 
the  sun,  and  therefore  remains  materially  longer  in  the  neighbourhood  of 
syzygy  than  if  it  rested.  On  the  other  hand,  whefl  the  apsides  are  in 
quadrature  they  recede,  and,  moving  therefore  contrary  to  the  sun's 
motion,  remain  a  shorter  time  in  that  n(>\</l'hourhood,  than  if  they  rested. 
Thus  the  advance,  already  preponderant,  Is  made  to  preponderate  more 
by  its  longer  continuance,  and  the  recess,  already  deficient,  is  rendered 
still  more  so  by  the  shortening  of  its  duration.'  Whatever  cause,  then, 
increases  directly  the  rapidity  of  both  advance  and  recess,  though  it  may 
do  both  equally,  aids  in  this  indirect  process,  and  it  is  thus  that  the  tan- 
gential force  becomes  effective  through  the  medium  of  the  progress  already 
produced,  in  doing  and  aiding  the  normal  force  to  do  that  which  alone  it 
would  be  unable  to  effect.  Thus  we  have  perturbation  exaggerating 
perturbation,  and  thus  we  see  what  is  meant  by  geometei's,  when  they 

'Newton,  Princ.  i.  66.  Cor.  8.  '  '   "  ; 


'♦mo. 


tr3 


.■c^jT"- 


•*'■  •:/-« 


•■« 


<*<«MI» 


rSSSMr 


Si 


<'  '\ 


870 


OUTLINES  OF  ASTRONOMT. 


m 


lit 

t« 

9* 

■r 

mi' 


•  km. 


i**' 

**»* 

^«::j 

*,;»»' 

(: 


declare  that  a  considerable  part  of  the  motion  of  the  lunar  apsides  is  due 
to  the  square  of  the  disturbing  force,  or,  in  other  words,  arises  out  of  a 
second  approximation  in  which  the  influence  of  the  first  in  altering  the 
data  of  the  problem  is  taken  into  account. 

(687.)  The- curious  and  complicated  effect  of  perturbation,  described  in 
the  last  article,  has  given  more  trouble  to  geometers  than  any  other  part 
of  the  lunar  theory.  Newton  himself  had  succeeded  in  tracing  that  part 
of  the  motion  of  the  apogee  which  is  due  to  the  direct  action  of  the  radial 
force;  but  finding  the  amount  only  half  what  observation  assigns,  he 
appears  to  have  abandoned  the  subject  in  despair.  Nor,  when  resumed 
by  his  successors,  did  the  inquiry,  for  a  very  long  period,  assume  a  more 
promising  aspect.  On  the  contrary,  Newton's  result  appeared  to  be  even 
minutely  verified,  and  the  elaborate  investigations  which  were  lavished 
upon  the  subject  without  success,  began  to  excite  strong  doubts  whether 
this  feature  of  the  lunar  motions  could  be  explained  at  all  by  the  New- 
tonian law  of  gravitation.  The  doubt  was  removed,  however,  almost  in 
the  instant  of  it43  origin,  by  the  same  geometer,  Clairaut,  who  first  gave  it 
currency,  and  who  gloriously  repaired  the  error  of  his  momentary  hesita* 
tion,  by  demonstrating  the  exact  coincidence  between  theory  ai^d  o'bderva* 
tion,  when  the  effect  of  the  tangential  force  is  properly  taken  into  the 
account.  The  lunar  apogee  circulates,  in  3232''-575343,  or  about  9} 
years. 

(688.)  Let  us  now  proceed  to  investigate  the  influence  of  the  disturbing 
forces  so  resolved  on  the  excentricity  of  the  lunar  orbit,  and  the  foregoing 
articles  having  sufficiently  familiarized  the  reader  with  our  mode  of  fol- 

Fig.  92. 


lowing  out  the  changes  in  different  situations  of  the  orbit,  we  shall  take 
at  once  a  more  general  situation,  and  suppose  the  line  of  apsides  in  any 
position  with  respect  to  the  sun,  such  as  Z  Y,  the  perigee  being  at  Z,  a 
point  between  the  lower  syzygy  and  the  quadrature  next  following  it,  the 
direction  of  Fs  motion  as  all  along  supposed  being  A  D  B  E.    Then 


VARIATION   OF  THE  MOON'S  EXOBNTRICITT. 


377 


upsides  is  due 
rises  out  of  a 
\  altering  the 

a,  described  in 
any  other  part 
Being  that  part 
,n  of  the  radial 
on  assigns-  he 
vhen  resumed 
assume  a  more 
ared  to  be  even 
i  were  lavished 
doubts  whether 
ai  by  the  New- 
vever,  almost  in 
who  first  gave  it 
omentary  hesita- 
iory  acd  obaerw 
y  taken  into  the 
43,  or  about  9  J 


(commencing  with  the  normal  force)  the  momentary  change  of  excentri« 
city  will  vanish  at  a,  b,  c,  d,  by  the  vanishing  of  that  force,  and  at  Z  and 
Y  by  the  effect  of  situation  in  the  orbit  annulling  its  action  (art.  671). 
In  the  arcs  Z  h  and  Y  d  therefore  the  change  of  oxcentricity  will  be  small, 
the  acting  force  nowhere  attaining  either  a  great  magnitude  or  an  advan- 
tageous situation  within  their  limits.  And  the  force  within  these  two 
arcs  having  the  same  character  as  to  inward  and  outward,  but  being  oppo- 
sitely influential  by  reason  of  the  approach  of  P  to  S  in  one  of  them  and 
its  recess  in  the  other,  it  is  evident  that,  so  far  as  these  arcs  are  concerned, 
a  very  near  compensation  of  effects  will  take  place,  and  though  the  apo- 
geal  arc  Y  d  will  be  somewhat  more  influential,  this  will  tell  for  little 
upon  the  average  of  a  revolution. 

(689.)  The  arcs  &  D  c  and  c2  £  a  are  each  much  less  than  a  quadrant 
in  extent,  and  the  force  acting  inwards  throughout  them  (which  at  ita 
maximum  in  D  and  £  is  only  half  the  outward  force  at  A,  B)  degrades 
very  rapidly  in  intensity  towards  either  syzygy  (see  art.  676).  Henoe 
whether  Z  be  between  &  c  or  6  A,  the  effects  of  the  force  in  these  arcs 
will  not  produce  very  extensive  changes  on  the  excentricity,  and  the 
changes  which  it  does  produce  will  (for  the  reason  already  given)  be  op- 
posed to  each  other.  Although,  then,  the  arc  a  f2  be  farther  from  perigee 
than  h  c,  and  therefore  the  force  in  it  is  greater,  yet  the  predominance  of 
effect  here  will  not  be  very  marked,  and  will  moreover  be  partially  neu- 
tralized by  the  small  predominance  of  an  opposite  character  inY  d  over 
Z  b.  On  the  other  hand,  the  arcs  a  Z,  c  Y  are  both  larger  in  extent  than 
either  of  the  others,  and  the  seats  of  action  of  forces  doubly  powerful. 
Their  influence,  therefore,  will  be  of  most  importance,  and  their  prepon- 
derance one  over  the  other  (being  opposite  in  their  tendencies),  will  d(  <>'io 
the  question  whether,  on  an  average  of  the  revolution,  the  excentricit' 
shall  increase  or  diminish.  It  is  olear  that  the  decision  must  be  in  favour 
of  c  Y,  the  apogeal  arc,  and,  since  in  this  the  force  is  outwards  and  the 
moon  receding  from  the  earth,  an  increase  of  the  excentricity  will  arise 
from  its  influence.  A  similar  reasoning. will,  evidently,  lead  to  the  same 
conclusion  were  the  apogee  and  perigee  to  change  places,  for  the  directions 
of  Fs  motion  as  to  approach  and  recess  to  S  will  be  indeed  reversed,  but 
at  the  same  time  the  dominant  forces  will  have  changed  sides,  and  the 
arc  a  A  Z  will  now  give  the  character  to  the  result.  But  when  Z  lies 
between  A  and  £,  as  the  reader  may  easily  satisfy  himself,  the  case  will 
be  altogether  different,  and  the  reverse  conclusion  will  obtain.  Hence  the 
changes  of  excentricity  emergent  on  the  average  of  single  revolutions 
I  from  the  action  of  the  normal  force  will  be  as  represented  by  the  signs 
+  and  —  in  the  figure  above  annexed. 


'■•  ■■<»*.i 


M 


« 


»■■»« 


*^4WM» 


878 


OUTLINES  OF  ASTRONOMT. 


(600.)  Let  US  next  coDsidcr  the  effect  of  the  tangential  force.     This 
retards  P  in  the  quadrants  A  D,  B  £,  and  accelerates  it  in  the  alternate 


•  « 
tr 

t« 


;l 


•  •M  * 

•m  s 


ones.  In  the  whole  quadrant  A  D,  therefore,  the  effect  is  of  one  charac- 
ter, the  perigee  being  less  than  00°  from  every  point  in  it,  and  in  the 
whole  quadrant  B  E  it  is  of  the  opposite,  the  apogee  being  so  situated 
(art.  670).  Moreover,  in  the  middle  of  each  quadrant,  the  tangential 
force  is  at  its  maximum.  Now,  in  the  other  quadrants,  E  A  and  D  B, 
the  change  from  perigeal  to  apogeal  vicinity  takes  place,  and  the  tangen- 
tial force,  however  powerful,  has  its  effect  annulled  by  situation  (art.  670), 
and  this  happens  more  or  less  nearly  about  the  points  where  the  force  is  a 
maximum.  These  quadrants,  then,  are  far  less  influential  on  the  total 
result,  so  that  the  character  of  that  result  will  be  decided  by  the  predo- 
minance of  one  or  other  of  the  former  quadrants,  and  will  lean  to  thnt 
which  has  the  apogee  in  it.  Now  in  the  quadrant  B  E  the  force  retardt 
the  moon,  and  the  moon  is  in  apogee.  Therefore  the  excentrioity  in- 
creases. In  this  situation  therefore  of  the  apogee,  mch  is  the  average 
result  of  a  complete  revolution  of  the  moon.  Here  again  also,  if  the 
perigee  and  apogee  change  places,  so  will  also  the  character  of  all  the  par- 
tial influences,  arc  for  arc.  But  the  quadrant  A  D  will  now  preponderate 
instead  of  D  E,  so  that  under  this  double  reversal  of  conditions  the  result 
will  bo  identical.  Lastly,  if  the  line  of  apsides  be  in  A  E,  B  D,  it  may 
be  shown  in  like  manner  that  the  excentricity  will  diminish  on  the  average 
of  a  revolution. 

(691.)  Thus  it  appears,  that  in  varying  the  excentricity,  precisely  as  in 
moving  the  line  of  apsides,  the  direct  effect  of  the  tangential  force  con- 
spires with  that  of  the  normal,  and  tends  to  increase  the  extent  of  the 
deviations  to  and  fro  on  either  side  of  a  mean  value  which  the  varying 
situation  of  the  sun  with  respect  to  the  line  of  apsides  gives  rise  to,  having 
for  their  period  of  restoration  a  synodical  revolution  of  the  sun  and  apse. 
Supposing  the  sun  and  apsis  to  start  together,  the  sun  of  course  will 
outrun  the  apsis  (whose  period  is  nine  years,)  and  in  the  lapso  of  about 


^it 


EXPERIMENTAL  ILLUSTRATION. 


879 


force.    This 
tho  alterDate 


V, 


is  of  one  charac- 

D  it,  and  in  the 

leing  80  situated 

t,  the  tangential 

^  B  A  and  D  B, 

,  and  the  tangen- 

uation  (art.  670), 

lere  the  force  is  a 

itial  on  the  total 

ded  by  the  predo- 

vill  lean  to  that 

the  force  retardi 

te  excentrioity  in- 

ch  is  tho  average 

again  also,  if  the 

cter  of  all  the  par- 

now  preponderate 

mditions  the  result 

AE,BD,it  may 

lish  on  the  average 

jity,  precisely  as  in 
ugential  force  con- 

the  extent  of  the 
which  the  varying 
jives  rise  to,  having 
.  the  sun  and  apse. 
JBun  of  course  will 

the  lapse  of  ahout 


(\  +  -s\)  P&rt  of  a  year  will  have  gained  on  it  90**,  during  all  which  inter- 
val the  apse  will  have  been  in  the  quadrant  A  E  of  our  figure,  and  the 
excentricity  continually  decreasing.  The  decrease  will  then  cease,  but 
the  excentricity  itself  will  be  a  minimum,  the  sun  being  now  at  right 
angles  to  the  line  of  apsides.  Thence  it  will  increase  to  a  maximum 
when  the  sun  has  gained  another  90°,  and  again  attained  the  line  of 
apsides,  and  so  on  alternately.  The  actual  effect  on  the  numerical  value 
of  the  lunar  excentricity  is  very  considerable,  the  greatest  and  least  excen- 
tricities  being  in  the  ratio  of  8  to  2.' 

(692.)  The  motion  of  the  apsides  of  the  lunar  orbit  may  bo  illustrated 
by  a  very  pretty  mechanical  experiment,  which  is  otherwise  instructive  iu 
giving  an  idea  of  the  mode  in  which  orbitual  motion  is  carried  on  under 
the  action  of  central  forces  variable  according  to  the  situation  of  the 
revolving  body.     Let  a  leaden  weight  be  suspended  by  a  brass  or  iron 
wire  to  a  hook  in  the  under  side  of  a  firm  beam,  so  as  to  allow  of  its  free 
motion  on  all  sides  of  the  vertical,  and  so  that  when  in  a  state  of  rest  it 
shall  just  clear  the  floor  of  the  room,  or  a  table  placed  ten  or  twelve  feet 
beneath  the  hook.     The  point  of  support  should  be  well  secured  from 
wagging  to  and  fro  by  the  oscillation  of  the  weight,  which  should  be 
sufficient  to  keep  the  wire  as  tightly  stretched  as  it  will  bear,  with  the 
certainty  of  not  breaking.     Now,  let  a  very  small  motion  be  communi- 
cated to  tho  weight,  not  by  merely  withdrawing  it  from  the  vertical  and 
letting  it  fall,  but  by  giving  it  a  slight  impulse  sideways.     It  will  be  seen 
to  describe  a  regular  ellipse  about  the  poiut  of  rest  as  its  centre.     If  the 
weight  be  heavy,  and  carry  attached  to  it  a  pencil,  whose  point  lies 
exactly  in  the  direction  of  the  string,  the  ellipse  may  be  transferred  to 
paper  lightly  stretched  and  gently  pressed  against  it.     In  these  circum- 
stances, the  situation  of  the  major  and  minor  axes  of  the  ellipse  will 
remain  for  a  long  time  very  nearly  the  seme,  though  the  resistance  of  the 
air  and  the  stiffness  of  the  wire  will  gradually  diminish  its  dimensions  and 
excentricity.     But  if  the  impulse  communicated  to  the  weight  be  con- 
siderable, so  as  to  carry  it  out  to  a  great  angle  (15°  or  20°  from  the 
vertical,)  this  permanence  of  situation  of  the  ellipse  will  no  longer  subsist. 
Its  axis  will  be  seen  to  shift  its  position  at  every  revolution  of  the  weight, 
advancing  in  the  same  direction  with  the  weight's  motion,  by  an  uniform 
and  regular  progression,  which  at  length  will  entirely  reverse  its  situation, 
bringing  the  direction  of  the  longest  excursions  to  coincide  with  that  in 
which  the  shortest  were  previously  made ',  and  so  on,  round  the  whole 
circle ;  and,  in  a  word,  imitating  to  the  eye,  very  completely,  the  motion 
of  the  apsides  of  the  moon's  orbit. 

*  Airy,  Gravitation,  p.  106. 


^:;> 
'i 


■'•t«Jr 


'*»3 


880 


OUTLINES  OF  ASTRONOMY. 


■i 


IP 

'•J 


(698.)  Now,  if  we  inquire  into  the  caiue  of  this  progression  of  the 
apsidoH,  it  will  not  bo  difficult  of  detection.  When  a  weight  is  sunponded 
by  a  wire,  und  drawn  aside  from  the  vertical,  it  is  urged  to  the  lowest 
point  (or  rather  in  a  direction  at  every  instant  perpendicular  to  the  wire) 
by  a  force  which  varies  as  the  sine  of  the  deviation  of  the  wire  from  the 
perpoudiculor.  Now,  the  sines  of  very  small  arcs  arc  nean,  'n  the  pro* 
portion  of  the  arcs  themselves;  and  the  more  nearly,  as  tbe  urcs  are 
smaller.  If,  therefore,  the  deviations  from  the  vertical  be  so  small  that 
we  may  neglect  the  curvature  of  the  spherical  surface  in  which  the  weight 
moves,  and  regard  the  curve  described  as  coincident  with  its  projection  on 
a  horizontal  plane,  it  will  be  then  moving  under  the  same  circumstances 
as  if  it  were  a  revolving  body  attracted  to  a  centre  by  a  force  varying 
directly  as  the  distance;  and,  in  this  case,  the  curve  described  would  be 
an  ellipse,  having  its  centre  of  attraction  not  in  the  focus,  but  in  the 
centre',  and  the  apsides  of  this  ellipse  would  remain  fixed.  But  if  the 
excursions  of  the  weight  from  the  vertical  be  considerable,  the  force  urging 
it  towards  the  centre  will  deviate  in  its  law  from  the  simple  ratio  of  the 
distances ;  being  as  the  sine,  while  the  distances  are  as  the  arc.  Now  the 
sine,  though  it  continues  to  increase  as  the  are  increases,  yet  does  not  in* 
crease  so  fast.  So  soon  as  the  arc  has  any  sensible  extent,  the  sine  begins 
to  fall  somewhat  short  of  the  magnitude  which  an  exact  numerical  propor- 
tionality would  require ;  and  therefore  the  force  urging  the  weight  towards 


'f 


I"  '    '* 


its  centre  or  point  of  rest  at  great  distances  falls,  in  like  proportion,  some' 
what  short  of  that  which  would  keep  the  body  in  its  precise  elliptic  orbit. 
It  will  no  longer,  therefore,  have,  at  those  greater  distances,  the  same 
command  over  the  weight,  in  proportion  to  its  speed,  which  would  enable 
it  to  deflect  it  from  its  rectilinear  tangential  course  into  an  ellipse.  The 
true  path  which  it  describes  will  be  less  curved  in  the  remoter  parts  than 
is  consistent  with  the  elliptic  figure,  as  in  the  annexed  cut;  and,  therefore, 
it  will  not  so  soon  have  its  motion  brought  to  be  again  at  right  angles  to 

'  Newton,  Princip.  i.  47. 


APPLICATION   OP  THE  PLANETARY  TnEORY. 


881 


■Oftsion  of  tho 
b  18  BURpondod 

to  tho  lowest 
ar  to  tho  wire) 
wiro  from  the 
iri,  •1  tho  pro- 
ts  tliO  uros  are 
I  8o  small  that 
bich  tho  weight 
ts  projection  ou 
0  circumstances 
a  force  varying 
Ksribcd  would  be 
icus,  but  in  the 
^ed.     But  if  the 
,  the  force  urging 
nple  ratio  of  the 
e  arc.     Now  the 

yet  docfl  not  in- 
it,  the  sine  begins 

lumerical  propor- 

le  weight  towards 


proportion,  some- 
[ecise  elliptic  orbit, 
listances,  the  same 
jhich  would  enable 
loan  ellipse.  The 
remoter  parts  than 
Ltj  and,  therefore, 
at  right  angles  to 


the  radius.  It  will  require  a  longor  continued  action  of  the  central  foreo 
to  do  this ;  and  before  it  is  accomplished,  more  than  a  qi:adrant  of  its 
revolution  must  bo  passed  over  in  angular  motion  round  the  centre.  But 
this  in  only  stating  at  length,  and  in  a  more  circuitous  manner,  that  fact 
which  is  more  briefly  and  summarily  expressed  by  saying  that  the  apsidet 
of  its  orbit  are progremve.  Nothing  beyond  a  familiar  illustration  is  of 
course  intended  in  what  is  above  said.  The  case  is  not  an  exact  parallel 
with  that  of  the  lunar  orbit,  tho  disturbing  force  being  simply  radial, 
whereas  in  tho  lunar  orbit  a  transvorsal  force  is  also  ooncorned,  and  even 
wero  it  otherwise,  only  a  confused  and  indistinct  view  of  aspidal  motion 
can  be  obtained  from  this  kind  of  consideration  of  the  curvature  of  the 
disturbed  path.  If  we  would  obtain  a  dear  one,  the  two  foci  of  the  in- 
stantaneous ellipse  must  be  found  from  tho  laws  of  elliptic  motion  per- 
formed under  the  influence  of  a  force  directly  as  the  distance,  and  the 
radial  disturbing  force  being  decomposed  into  its  tangential  and  normal 
components,  the  momentary  influence  of  either  in  altering  their  positions 
and  consequently  tho  directions  and  lengths  of  the  axis  of  the  ellipse 
must  be  ascertained.  The  student  will  find  it  neither  a  difficult  nor  an 
uninstructivo  exercise  to  work  out  tho  case  from  these  principles,  which 
we  cannot  afford  the  space  to  do.  < 

(G04.)  The  theory  of  the  motion  of  the  planetary  apsides  and  the 
variation  of  their  excontricities  is  in  one  point  of  view  much  more  simple, 
but  in  another  much  more  complicated  than  that  of  the  lunar.  It  is 
simpler,  because  owing  to  the  exceeding  minuteness  of  the  changes  ope- 
rated in  the  course  of  a  single  revolution,  the  angular  position  of  the 
bodies  with  respect  to  the  line  of  apsides  is  very  little  altered  by  the 
motion  of  the  apsides  themselves.  The  line  of  apsides  neither  follows 
up  tho  motion  of  the  disturbing  body  in  its  state  of  advance,  nor  vice 
versd,  in  any  degree  capable  of  prolonging  materially  their  advancing  or 
shortening  materially  their  receding  phase.  Hence  no  second  approxima- 
tion of  the  kind  explained  (in  art.  686),  by  which  the  motion  of  the  lunar 
iidcs  is  so  powerfully  modified  aa  to  be  actually  doubled  in  amount,  is 
at  all  required  in  the  planetary  theory.  On  the  other  hand,  the  latter 
theory  is  rendered  more  complicated  than  the  former,  at  least  in  the  cases 
of  planets  whose  periodic  times  are  to  each  other  in  a  ratio  much  less  than 
13  to  1,  by  the  consideration  that  the  disturbing  body  shifts  its  position 
with  respect  to  the  line  of  apsides  by  a  much  greater  angular  quantity  in 
a  revolution  of  the  disturbed  body  than  in  the  case  of  the  moon.  In  that 
case  we  were  at  liberty  to  suppose  (for  the  sake  of  explanation),  without 
■any  very  egregious  error,  that  the  sun  held  nearly  a  fixed  position  during 
la  single  lunation.    But  in  the  case  of  planets  whose  times  of  revolution 


••■•Ik' 
.-V  .^W 


'3 


382 


OUTLINES  OF  ASTRONOMY. 


"Mr 

if 


w  .* 


lit, » 


r* 


I 

Vim  ' 


are  in  a  much  lower  ratio  this  cannot  be  permitted.  In  the  case  of  Jupiter 
disturbed  by  Saturn  for  example,  in  one  sidereal  revolution  of  Jupiter, 
Saturn  has  advanced  in  its  orbit  with  respect  to  the  line  of  apsides  of 
Jupiter  by  more  than  140°,  a  change  of  direction  which  entirely  alters 
the  conditions  under  which  the  disturbing  forces  act.  And  in  the  case 
of  an  exterior  disturbed  by  an  interior  planet,  the  situation  of  the  latter 
with  respect  to  the  line  of  the  apsides  varies  even  more  rapidly  than  the 
situation  of  the  exterior  or  disturbed  planet  with  respect  to  the  central 
body.  To  such  cases  then  the  reasoning  which  we  have  applied  to  the 
lunar  perturbatisns  becomes  totally  inapplicable ;  and  when  we  take  into 
consideration  also  the  excentricity  of  the  orbit  of  the  disturbing  body, 
which  in  the  most  important  cases  is  exceedingly  influential,  the  subject 
beci^mes  far  too  complicated  for  verbal  explanation,  and  can  only  be  suc- 
cessfully followed  out  with  the  help  of  algebraic  expression  and  the  appli- 
cation of  the  integral  calculus.  To  Mercury,  Venus,  and  the  earth  indeed, 
as  disturbed  by  Jupiter,  and  planets  superior  to  Jupiter,  this  objection  to 
the  reasoning  in  question  does  not  apply;  and  in  each  of  these  cases 
therefore  we  are  entitled  to  conclude  that  the  apsides  are  kept  in  a  state 
of  progression  by  the  action  of  all  the  larger  planets  of  our  system. 
Under  certain  conditions  of  distance,  excentricity,  and  relative  situation 
of  the  axes  of  the  orbits  of  the  disturbed  and  disturbing  planets,  it  is 
perfectly  possible  that  the  reverse  may  happen,  an  instance  of  which  is 
afforded  by  Venus,  whose  apsides  recede  under  the  combined  action  of  the 
earth  and  Mercury  more  rapidly  than  they  advance  under  the  joint  actions 
of  all  the  other  planets.  Nay,  it  is  even  possible  under  certain  conditions 
that  the  line  of  apsides  of  the  disturbed  planet,  instead  of  revolving  always 
in  one  direction,  may  librate  to  and  fro  within  assignable  limits,  and  in  a 
definite  and  regularly  recurring  period  of  time.  •  '      ' 

(695.)  Under  any  conditions,  however,  as  to  these  particulars,  the 
view  we  have  above  taken  of  the  subject  enables  us  to  assign  at  everv 
instant,  and  in  every  configuration  of  the  two  planets,  the  momentary 
effect  of  each  upon  the  perihelion  and  excentricity  of  the  other.    In  the 
simplest  case,  that  in  which  the  two  orbits  are  so  nearly  circular,  that  | 
the  relative  situation  of  their  perihelia  shall  produce  no  appreciable  differ- 
ence in  the  intensities  of  the  disturbing  forces,  it  is  very  easy  to  show  I 
that  whatever  temporary  oscillations  to  and  fro  in  the  positions  of  the  line  | 
of  apsides,  and  whatever  temporary  increase  or  diminution  in  the  excen- 
tricity of  either  planet  may  take  place,  the  final  effect  on  the  average  of  I 
a  great  multitude  of  revolutions,  presenting  them  to  each  other  in  all  I 
possible  configurations,  must  be  nil,  for  both  elements. 

(696.)  To  show  this,  all  that  is  necessary  ia  to  cast  our  eyes  on  tbel 


EFFECTS  OF  ELLIPTICITY. 


383 


jase  of  Jupiter 
on  of  Jupiter, 
B  of  apsides  of 

entirely  alters 
ad  in  the  case 
m  of  the  latter 
•apidly  than  the 
1  to  the  central 
e  applied  to  the 
en  we  take  into 
iisturbing  body, 
itial,  the  subject 
can  only  be  sue- 
on  and  the  appli- 
the  earth  indeed, 
,  this  objection  to 
ch  of  these  cases 
are  kept  in  a  state 
3  of  our  system. 

relative  situation 
jing  planets,  it  is 
stance  of  which  is 
bined  action  of  the 
er  the  joint  actions 
certain  conditions 
jf  revolving  always 
[le  limits,  and  in  a 

Ise  particulars,  the 
Ito  assign  at  every 
[ts,  the  momentary 

the  other.  In  the 
nearly  circular,  that 
|o  appreciable  differ- 
I  very  easy  to  show 
[positions  of  the  line 
lution  in  the  excen- 

[t  on  the  average  of 
each  other  in  all 


kst  our  eyes  on 


the 


Bynoptic  table  in  art.  673.    If  M,  the  disturbing  body,  be  supposed  to  be 
successively  placed  in  two  diametrically  opposite  situations  in  its  orbit,  the 
aphelion  of  P  will  stand  relate'?,  to  M  in  one  of  these  situations  precisely 
as  its  perihelion  in  the  other.     Now  the  orbits  being  so  nearly  circles  as 
supposed,  the  distribution  of  the  disturbing  forces,  whether  normal   or 
tangential,  is  symmetrical  relative  to   their  common   diameter  passing 
through  M,  or  to  the  line  of  syzygies.     Hence  it  follows  that  the  half  of 
P's  orbit  "  about  perihelion"  (art.  673)  will  stand  related  to  all  the  acting 
forces  in  the  one  situation  of  M,  precisely  as  the  half  "about  aphelion'' 
does  in  the  other :  and  also,  that  the  half  of  the  orbit  in  which  P  "  ap- 
proaches S/'  stands  related  to  them  in  the  one  situation  precisely  as  the 
half  in  which  it  "  recedes  from  S "  in  the  other.     Whether  as  regards, 
therefore,  the  normal  or  tangential  force,  the  conditions  of  advance  or 
recess  of  apsides,  and  of  increase  or  diminution  of  ezcentricities,  are 
reversed  in  the  two  supposed  cases.     Hence  it  appears  that  whatever 
situation  be  assigned  to  M,  and  whatever  influence  it  may  exert  on  P  in 
that  situation,  that  influence  will  be  annihilated  in  situations  of  M  and 
P,  diametrically  opposite  to  those  supposed,  and  thus,  on  a  general 
average,  the  effect  on  both   apsides  and  eccentricities  is  reduced  to 
nothing. 

(697.)  If  the  orbits,  however,  be  excentric,  the  symmetry  above  in- 
sisted on  in  the  distribution  of  the  forces  does  not  exist.  But,  in  the  first 
place,  il  is  evident  that  if  the  excentricitics  be  moderate,  (as  in  the  planet- 
ary orbits,)  by  far  the  larger  part  of  the  effects  of  the  disturbing  forces 
destroys  itself  in  the  manner  described  in  the  last  article,  and  that  it  is 
only  a  residual  portion,  viz.  that  which  arises  from  the  greater  proximity 
of  the  orbits  at  one  place  than  at  another,  which  can  tend  to  produce  per- 
manent or  secular  effects.  The  precise  estimation  of  these  effects  is  too 
complicated  an  affair  for  us  to  enter  upon ;  but  we  may  at  least  give  some 
idea  of  the  process  by  which  they  are  produced,  and  the  order  in  which 
they  arise.  In  so  doing,  it  is  necessary  to  distinguish  between  the  effects 
of  the  normal  and  tangential  forces.  The  effects  of  the  former  arc  greatest 
at  the  point  of  conjunction  of  the  planets,  because  the  normal  force  itself 
is  there  always  at  its  maximum ;  and  although,  where  the  conjunction 
takes  place  at  90°  from  the  line  of  apsides,  its  effect  to  move  the  apsides 
is  nullified  by  situation,  and  when  in  that  line  its  effect  on  the  excentri- 
cities  is  similarly  nullified,  yet,  in  the  situations  rectangular  to  these,  it 
acts  to  its  greatest  advantage.  On  the  other  hand,  the  tangential  force 
vanishes  at  conjunction,  whatever  be  the  place  of  conjunction  with  respect 
to  the  line  of  apsides,  and  where  it  is  at  its  maximum  its  effect  is  still 
liable  to  be  annulled  by  situation.     Thus  it  appears  that  the  normal 


384 


OUTLINES  OF  ASTRONOMT. 


i\ 


m 

'••"I 


5'^ 


•it.  <. 

♦teS*i 

•fen . 

I  KM  •' 


j; 


force  is  most  influential,  and  mainly  determines  the  character  of  the  ge- 
neral effect.  It  is,  therefore,  at  conjunction  that  the  most  influential 
effect  is  produced,  and  therefore,  on  the  long  average,  those  conjunctions 
which  happen  about  the  place  where  the  orbits  are  nearest  will  determine 
the  general  character  of  the  effect.  Now,  the  nearest  points  of  approach 
of  two  ellipses,  which  have  a  common  focus,  may  be  variously  situated 
with  respect  to  the  perihelion  of  either.  It  may  be  at  the  perihelion  or 
the  aphelion  of  the  disturbed  orbit,  or  in  any  intermediate  position.  Sup- 
pose it  to  be  at  the  perihelion.  Then,  if  the  disturbed  orbit  be  interior 
to  the  disturbing,  the  force  acts  outwards,  and  therefore  the  apsides  re- 
cede :  if  exterior,  the  force  acts  inwards,  and  they  advance.  In  neither 
case  does  the  excentricity  change.  If  the  conjunction  take  place  at  the 
aphelion  of  the  disturbed  orbit,  the  effects  will  be  reversed :  if  interme- 
diate, the  apsides  will  be  less,  and  the  excentricity  more  affected. 

(698.)  Supposing  only  two  planets,  this  process  would  go  on  till  the 
apsides  and  excentricities  had  so  far  changed  as  to  alter  the  point  of 
nearest  approach  of  the  orbits,  so  as  either  to  accelerate  or  retard  and 
perhaps  reverse  the  motion  of  the  apsides,  and  give  to  the  variation  of  the 
excentricity  a  corresponding  periodical  character.  But  there  are  many 
planets^  all  disturbing  one  another.  And  this  gives  rise  to  variations  in 
the  points  of  nearest  approach  of  all  the  orbits,  taken  ^wo  and  two  toge- 
ther, of  a  very  complex  nature. 

(699.)  It  cannot  fail  to  have  been  remarked,  by  any  one  who  has  fol- 
lowed attentively  the  above  reasonings,  that  a  close  analogy  subsists  between 
two  sets  of  relations ;  viz.  that  between  the  inclinations  and  nodes  on  the 
one  hand,  and  between  the  excentricity  and  apsides  on  the  other.  In  fact, 
the  strict  geometrical  theories  of  the  two  cases  present  a  close  analogy, 
and  lead  to  final  results  of  the  very  same  nature.  What  the  variation  of 
excentricity  is  to  the  motion  of  the  perihelion,  the  change  of  inclination 
is  to  the  motion  of  the  node.  In  either  case  the  period  of  the  one  is  also 
the  period  of  the  other;  and  while  the  perihelia  describe  considerable 
angles  by  an  oscillatory  motion  to  and  fro,  or  circulate  in  immense  periods 
of  time  round  the  entire  circle,  the  excentricities  increase  and  decrease  by 
comparatively  small  changes,  and  are  at  length  restored  to  their  original 
magnitudes.  In  the  lunar  orbit,  as  the  rapid  rotation  of  the  nodes  pre- 
vents the  change  of  inclination  from  accumulating  to  any  material 
amount,  so  the  still  more  rapid  revolution  of  its  apogee  effects  a  speedy 
compensation  in  the  fluctuations  of  its  excentricity,  and  never  suffers  tbem 
to  go  to  any  material  extent ;  while  the  same  causes,  by  presenting  in 
quick  svccession  the  lunar  orbit  in  every  possible  situation  to  all  the  dis- 
turbing forces,  whether  of  the  sun,  the  planets,  or  the  protuberant  matter 


COMPOUND   CYC- 


OP  EXCENTRICITIES,  ETC. 


385 


jr  of  tbe  ge- 
(St  influential 
conjunctions 
»ill  determine 
,B  of  approach 
Lously  situated 
I  perihelion  or 
position.   Sup- 
rbit  be  inUrior 
the  apsides  re- 
le.    In  neither 
te  place  at  the 
,ed:  if  interme- 
jafected. 

L  go  on  till  the 
er  the  point  of 
a  or  retard  and 
3  variation  of  the 
there  are  many 
;e  to  variations  in 
wo  and  two  toge- 

one  who  has  fol- 
,  subsists  between 
land  nodes  on  the 
L  other.  In  fact, 
It  a  close  analogy, 
U  the  variation  of 
fnge  of  inclination 
I  of  the  one  is  also 
[cribe  considerahle 
1  immense  periods 
^e  and  decrease  hy 
Bd  to  their  original 
I  of  the  nodes  pre- 
to  any  material 
lee  effects  a  speedy 
never  suffers  them 

B,  by  presenting  "i 
Ltiontoallthedis- 
I  protuberant  matter 


at  the  earth's  equator,  prevoui  any  secular  accumulation  of  small  changes, 
by  which,  in  the  lapse  of  ages,  its  ellipticity  might  be  materially  increased 
or  diminished.     Accordingly,  observation  shows  the  mean  excentricity  of 
the  moon's  orbit  to  be  the  same  now  as  in  the  earliest  ages  of  astronomy. 
(700.)  The  movements  of  the  perihelia,  and  variations  of  excentricity 
of  the  planetary  orbits,  are  interlaced  and  complicated  together  in  the 
same  manner  and  nearly  by  the  same  laws  as  the  variations  of  their  nodes 
and  inclinations.     Each  acts  upon  every  other,  and  every  such  mutual 
action  generates  its  own  peculiar  period  of  circulation  or  compensation ; 
and  every  such  period,  in  pursuance  of  the  principles  of  art.  650,  is 
thence  propagated  throughout  the  system.    Thus  arise  cycles  upon  cycles, 
of  whose  compound  duration  some  notion  may  be  formed,  when  we  con- 
sider what  is  the  length  of  one  such  period  in  the  case  of  the  two  prin- 
cipal planets  —  Jupiter  and  Saturn.    Neglecting  the  action  of  the  rest, 
the  effect  of  their  mutual  attraction  would  be  to  produce  a  secular  varia- 
tion in  the  excentricity  of  Saturn's  orbit,  from  0-08409,  its  maxiniunif 
to 001345,  its  minimum  value :  while  that  of  Jupiter  would  vary  be- 
tween the  narrow  limits,  006036  and  0-02606  :  the  greatest  excentricity 
of  Jupiter  corresponding  to  the  least  of  Saturn,  and  vice  versd.     The 
period  in  which  these  changes  are  gone  through,  would  be  70414  years. 
After  this  example,  it  will  be  easily  conceived  that  many  millions  of  years 
will  require  to  elapse  before  a  complete  fulfilment  of  the  joint  cycle  which 
shall  restore  the  whole  system  to  its  original  state  as  far  as  the  excentri- 
cities  of  its  orbits  are  concerned. 

(701.)  The  place  of  the  perihelion  of  a  planet's  orbit  is  of  little  con- 
sequence to  its  well-being ;  but  its  excentricity  is  most  important,  as  upon 
this  (the  axes  of  the  orbits  being  permanent)  depends  the  mean  tempera- 
ture of  its  surface,  and  the  extreme  variations  to  which  its  seasons  may 
bo  liable.  For  it  may  be  easily  shown  that  the  mean  anmtal  amount 
of  light  and  heat  received  by  a  planet  from  the  sun  is,  cseteris  parihiis, 
as  tlic  minor  axis  of  the  ellipse  described  by  it.  Any  variation,  there- 
fore, in  the  excentricity,  by  changing  the  minor  axis,  will  alter  the  mean 
temperature  of  the  surface.  How  such  a  change  will  also  influence  the 
extremes  of  temperature  appears  from  art.  368.  Now  it  may  naturally 
be  inquired  whether  (in  the  vast  cycle  above  spoken  of,  in  which,  at  some 
period  or  other,  conspiring  changes  may  accumulate  on  the  orbit  of  one 
planet  from  several  quarters,)  it  may  not  happen  that  the  excentricity  of 
any  one  planet  —  as  the  earth  —  may  become  exorbitantly  great,  so  as  to 
[subvert  those  relations  which  render  it  habitable  to  man,  or  to  give  rise  to 
eat  changes,  at  least,  in  the  physical  comfort  of  his  state.  To  this  the 
fesearches  of  geometers  have  enabled  us  to  answer  in  the  negative.  A 
25 


# 


'  ■.rm.m 


«<Mtft 


^JSM 


*«3P 

'•UK!. 


1:1 


886 


OUTLINES  OF  ASTRONOMT. 


II* 

X  Hi 

■>■■«• 


relation  has  been  demonstrated  by  Lagrange  between  the  masses,  axes  of 
the  orbits,  and  excentricities  of  each  planet,  similar  to  what  we  have  al- 
ready stated  with  respect  to  their  inclinations,  viz.  tJiat  if  the  mass  of 
each  planet  be  multiplied  hy  the  square  root  of  the  axis  of  its  orbit,  and 
the  product  by  the  square  of  its  excentricitt/,  the  sum  of  all  such  products 
throughout  the  system  is  invariable  ;  and  as,  in  point  of  fact,  this  sum  is 
extremely  small,  so  it  will  always  remain.  Now,  since  the  axes  of  the 
orbits  are  liable  to  no  secular  changes,  this  is  equivalent  to  saying  that  no 
one  orbit  shall  increase  its  excentricity,  unless  at  the  expense  of  a  common 
fund,  the  whole  amount  of  which  is,  and  must  for  ever  remain,  extremely 
minute.' 

'  There  is  nothing  in  this  relation,  however,  taken  per  te,  to  secure  the  smaller  pla- 
nets — Mercury,  Mars,  Juno,  Ceres,  &c. — from  a  catastrophe,  could  they  accumulate 
on  themselves,  or  any  one  of  them,  the  whole  amount  of  this  excentricity  fund.  But 
that  can  never  be :  Jupiter  and  Saturn  will  always  retain  the  lion's  share  of  it.  A 
similar  remark  applies  to  the  inclination  fund  of  art.  639.  These  fundi,  be  it  observed, 
can  never  get  into  debt.    Every  term  of  them  is  essentially  positive. 


fe&t'Nt 


•>w.»ii: 

in 

•M  ■ 


Vv 


COMPOUND  MOTION   OF  THE  UPPER   FOCUS. 


387 


masses,  axes  of 
kat  we  have  al- 
ifthe  mass  of 
if  its  orbit,  and 
II  such  products 
;act,  this  sum  is 
the  axes  of  the 
bo  saying  that  no 
jnse  of  a  common 
emwn,  extremely 


sure  the  smaller  pla- 
mid  they  accumulate 
'.entricityfund.  But 
ion's  share  of  it.  A 
fund$,  be  it  observed, 
ive. 


CHAPTER  XIV. 

OP  THE  INEQUALITIES  INDEPENDENT  OP  THE  EXOENTRICITIES. — THE 
moon's  VARIATION  AND  PARALLACTIC  INEQUALITY.  —  ANALOGOUS 
PLANETARY  INEQUALITIES. — THREE  CASES  OP  PLANETARY  PERTUR- 
BATION DISTINGUISHED. — OP  INEQUALITIES  DEPENDENT  ON  THE 
EXOENTRICITIES. — LONG  INEQUALITY  OP  JUPITER  AND  SATURN. — 
LAW  OP  RECIPROCITY  BETWEEN  THE  PERIODICAL  VARIATIONS  OP 
THE  ELEMENTS  OP  BOTH  PLANETS. — LONG  INEQUALITY  OP  THE  EARTH 
AND  VENUS. — ^VARIATION  OP  THE  EPOCH. — INEQUALITIES  INCIDENT 
ON  THE  EPOCH  AFPECTING  THE  MEAN  MOTION. — INTERPRETATION  OP 
THE  CONSTANT  PART  OP  THESE  INEQUALITIES. — ANNUAL  EQUATION 
OP  THE  MOON. — HER  SECULAR  ACCELERATION. — LUNAR  INEQUALI- 
TIES DUE  TO  THE  ACTION  OP  VENUS.  —  EFFECT  OF  THE  SPHEROIDAL 
FIGURE  OP  THE  EARTH  AND  OTHER  PLANETS  ON  THE  MOTIONS  OF 
THEIR  SATELLITES. — OP  THE  TIDES. — MASSES  OF  DISTURBING  BODIES 
DEDUCIBLE  FROM  THE  PERTURBATIONS  THEY  PRODUCE.  —  MASS  OP 
THE  MOON,  AND  OF  JUPITER's  SATELLITES,  HOW  ASCERTAINED.  — 
PERTURBATIONS  OP  URANUS  RESULTIPG  IN  THE  DISCOVERY  OF 
NEPTUNE. 

(702.)  To  calculate  the  actual  place  of  a  planet  or  the  moon,  in  longi- 
tude and  latitude  at  any  assigned  time,  it  is  not  enough  to  know  the 
changes  produced  by  perturbation  in  the  elements  of  its  orbit,  still  less  to 
know  the  secular  changes  so  produced,  which  are  only  the  outstanding  or 
uncompensated  portions  of  much  greater  changes  induced  in  short  periods 
of  configuration.  We  must  be  enabled  to  estimate  the  actual  effect  on  its 
longitude  of  those  periodical  accelerations  and  retardations  in  the  rate  of 
its  mean  angular  motion,  and  on  its  latitude  of  those  deviatioQS  above  and 
below  the  mean  plane  of  its  orbit,  which  result  from  the  continued  action 
of  the  perturbative  forces,  not  as  compensated  in  long  periods,  but  as  in 
the  act  of  their  generation  and  destruction  in  short  ones.  In  this  chapter 
we  purpose  to  give  an  account  of  some  of  the  most  prominent  of  the 
equations  or  inequalities  thence  arising,  several  of  which  are  of  high  his- 
torical interest,  as  having  become  known  by  observation  previous  to  the 


Oh..-.  . 


'f 


:t>' 


'^"^M 


888 


OUTLINES   OF   ASTRONOMY. 


I  A 

■  A 
■    »* 

"Mr 
•  ? 

•r  »> 


«  ." 


•v.  *. 


h** 


discovery  of  their  theoretical  causes,  and  as  having,  by  their  successive 
explanations  from  the  tlieory  of  gravitation,  removed  what  were  in  some 
instances  regarded  as  formidable  objections  against  that  theory,  and  afforded 
in  all  most  satisfactory  and  triumphant  verifications  of  it. 

(703.)  We  shall  begin  with  those  which  compensate  themselves  in  a 
synodic  revolution  of  the  disturbed  and  disturbing  body,  and  which  are 
independent  of  any  permanent  excentricity  of  either  orbit,  going  through 
their  changes  and  effecting  their  compensation  in  orbits  slightly  elliptic, 
almost  precisely  as  if  they  were  circular.  These  inequalities  result,  in 
fact,  from  a  circulation  of  the  true  upper  focus  of  the  disturbed  ellipse 
about  its  mean  place  in  a  curve  whose  form  and  magnitude  the  principles 
laid  down  in  the  last  chapter  enable  us  to  assign  in  any  proposed  case. 
If  the  disturbed  orbit  be  circular,  this  mean  place  coincides  with  its  cen- 
tre :  if  elliptic,  with  the  situation  of  its  upper  focus,  as  determined  from 
the  principles  laid  down  in  the  last  chapter. 

(704.)  To  understand  the  nature  of  this  circulation,  we  must  consider 
the  joint  action  of  the  two  elements  of  the  disturbing  force.  Suppose  H 
to  be  the  place  of  the  upper  focus,  corresponding  to  any  situation  P  of  the 

Fig.  95. 


disturbed  body,  and  let  P  P'  be  an  infinitesimal  element  of  its  orbit,  de- 
scribed in  an  instant  of  time.  Then  supposing  no  disturbing  force  to  act, 
P  F  will  he  a  portion  of  an  ellipse,  having  H  for  its  focus,  equally 
whether  the  point  P  or  F  be  regarded.  But  now  let  the  disturbing 
forces  act  during  the  instant  of  describing  P  P'.  Then  the  focus  H  will 
shift  its  position  to  H'  to  find  which  point  wo  must  recollect,  1st.  What  is 
demonstrated  (in  art.  671),  viz.  that  the  effect  of  the  normal  force  is  to 
var^  the  position  of  the  line  F  H  so  as  to  make  the  angle  H  P  H'  equal 
to  double  the  variation  of  the  angle  of  tangency  due  to  the  action  of  that 


"variation"  op  the  moon  explained. 


889 


eir  successive 

were  in  some 

^,  and  afforded 

icmselves  in  a 
and  wbicb  are 
going  through 
lightly  elliptic, 
lities  result,  in 
isturbed  ellipse 
le  the  principles 
J  proposed  case, 
ies  with  its  cen- 
ietermined  from 

jye  must  consider 
rce.  Suppose  H 
iituation  P  of  the 


force,  without  altering  the  distance  P  H :  so  that  in  virtue  of  the  normal 
force  alone,  H  would  move  to  a  point  h,  along  the  lino  H  Q,  drawn  from 
H  to  a  point  Q,  90"  in  advance  of  P,  (because  S  H  being  exceedingly 
small,  the  angle  P  H  Q  may  be  taken  as  a  right  argle  when  P  S  Q  is  so,) 
H  approaching  Q  if  the  normal  force  act  outwards,  but  receding  from  Q 
if  inwards.  And  siniihxrly  the  effect  of  tlie  tangential  force  (art.  670)  is 
to  vary  the  position  of  H  in  the  direction  H  P  or  P  H,  according  as  the 
force  retards  or  accelerates  P's  motion.  To  find  H'  then  from  H  draw 
H  P,  H  Q,  to  P  and  to  a  point  of  P's  orbit  90°  in  advance  of  P.  On 
H  Q  take  H  Ji,  the  motion  of  the  focus  due  to  the  normal  force,  and  on 
H  P  take  H  k  the  motion  due  to  the  tangential  force ;  complete  the 
parallelogram  H  H',  and  its  diagonal  H  H'  will  be  the  element  of  the 
true  path  of  H  in  virtue  of  the  joint  action  of  both  forces. 

(705.)  The  most  conspicuous  case  in  the  planetary  system  to  which  the 
above  reasoning  is  applicable,  is  that  of  the  moon  disturbed  by  the  sun. 
The  inequality  thus  arising  is  known  by  the  name  of  the  moon's  varia- 
tion, and  was  discovered  so  early  as  about  the  year  975  by  the  Arabian 
astronomer  Aboul  Wefa.'     Its  magnitude  (or  the  extent  of  fluctuation  to 
and  fro  in  the  moon's  longitude  which  it  produces)  is  considerable,  being 
no  less  than  1°  4',  and  it  is  otherwise  interesting  as  being  the  first  ine- 
quality produced  by  perturbation,  which  Newton  succeeded  in  explaining 
by  the  theory  of  gravity.     A  good  general  idea  of  its  nature  may  be 
formed  by  considering  the  direct  action  of  the  disturbing  forces  on  the  moon, 
supposed  to  move  in  a  circular  orbit.     In  such  an  orbit  undisturbed,  the 
velocity  would  be  uniform ;  but  the  tangential  force  acting  to  accelerate 
her  motion  through  the  quadrants  jireccding  her  conjunction  and  oppo- 
sition, and  to  retard  it  through  the  alternate  quadrants,  it  is  evident  that 
the  velocity  will  have  two  maxima  and  two  minima,  the  former  at  the 
syzygies,  the  latter  at  the  quadratures.    Hence  at  the  syzygies  the  velocity 
will  exceed  that  which  corresponds  to  a  circular  orbit,  and  at  quadratures 
will  fall  short  of  it.     The  true  orbit  will  therefore  be  less  curved  or  more 
flattened  than  a  circle  in  syzygies,  and  more  curved  (t.  e.  protuberant  be- 
yond a  circle)  in  quadratures.     This  would  be  the  case  even  were  the 
normal  force  not  to  act.     But  the  action  of  that  force  increases  the  effect 
in  question,  for  at  the  syzygies,  and  as  far  as  64°  14'  on  either  side  of 
them,  it  acts  outwards,  or  in  counteraction  of  the  earth's  attraction,  and 
thereby  prevents  the  orbit  from  being  so  much  curved  as  it  otherwise 
would  be ;  while  at  quadratures,  and  for  25°  46'  on  either  side  of  them, 
it  acts  inwards,  aiding  the  earth's  attraction,  and  rendering  that  portion 

'Sedillot,  Nouvelles  Recherches  pour  scrvir  a  I'Histoire  de  rAstronomie  chez  .es 
Arabes. 


•''■:'  v  kit 


.:«r  *'t^« 


ft  I. 


^S» 


■■■■%mm 

1 

» 

' 

'':m 

•t  ■. 

':3aw» 

;;:3^ 

f**" 

890 


OUTLINES  OF  ASTRONOMT. 


I 


'lit; 
•I* 

•2 

•  « 


f: 


Ir  '<■ 


%0K 


8^" 


of  the  orbit  more  curved  than  it  otherwise  would  be.  Thus  the  joint 
action  of  both  forces  distorts  the  orbit  from  a  circle  into  a  flattened  or 
elliptic  form,  having  the  longer  axis  in  quadratures,  and  the  shorter  in 
syzygies ',  and  in  this  orbit  the  moon  moves  faster  than  with  her  mean 
velocity  at  syzygy  (/.  e.  where  she  ia  nearest  the  earth)  and  slower  at 
quadratures  where  farthest.  Her  angular  motion  about  the  earth  is  there- 
fore for  both  reasons  greater  in  the  former  than  in  the  latter  situation. 
Hence  at  syzygy  her  true  longitude  seen  from  the  earth  will  be  in  the  act 
of  gaining  on  her  mean, — in  quadratures  of  losing,  and  at  some  interme- 
diate points  (not  very  remote  from  the  octants)  will  neither  be  gaining 
nor  losing.  But  at  these  points,  having  been  gaining  or  losing  through 
the  whole  previous  90°  the  amount  of  gain  or  loss  will  have  attained  its 
maximum.  Consequently  at  the  octants  the  true  longitude  will  deviate 
most  from  the  mean  in  excess  and  defect,  and  the  inequality  in  question 
ia  therefore  nil  at  syzygies  and  quadratures,  and  attains  its  maxima  in 
advance  or  retardation  at  the  octants,  which  is  agreeable  to  observation. 

(706.)  Let  us,  however,  now  see  what  account  can  be  rendered  of  this 
inequality  by  the  simultaneous  variations  of  the  axis  and  excentricity  as 
above  explained.     The  tangential  force,  as  will  be  recollected,  is  nil  at 
syzygies  and  quadratures,  and  a  maximum  at  the  octants,  accelerative  in 
the  quadrants  E  A  and  D  B,  and  retarding  in  A  D  and  B  E.     In  the  two 
former  then  the  axis  is  in  process  of  lengthening ;  in  the  two  latter,  short- 
ening.    On  the  other  hand  the  normal  force  vanishes  at  (a,  6,  d,  e)  64' 
14'  from  the  syzygies.     It  acts  outwards  over  c  A  a,  6  B  e?,  and  inwards 
over  aJ)h  and  d^e.     In  virtue  of  the  tangential  force,  then,  the  point 
H  moves  towards  P  when  P  is  in  A  D,  B  E,  and  from  it  when  in  D  B, 
E  A,  the  motion  being  nil  when  at  A,  B,  D,  E,  and  most  rapid  when  at 
the  octant  D,  at  which  points,  therefore,  (so  far  as  this  force  is  concerned,) 
the  focus  H  would  have  its  mean  situation.     And  in  virtue  of  the  normal 
focus,  the  motion  of  H  in  the  direction  H  Q  will  be  at  its  maximum  of 
rapidity  towards  Q  at  A,  or  B,  from  Q  at  D  or  E,  and  nil,  at  a,  h,  d,  e.  It 
will  assist  us  in  following  out  these  indications  to  obtain  a  notion  of  the 
form  of  the  curve  really  described  by  H,  if  we  trace  separately  the  paths 
which  H  would  pursue  in  virtue  of  either  motion  separately,  since  its  true 
motion  will  necessarily  result  from  the  superposition  of  these  partial  mo- 
tions, because  at  every  instant  they  are  at  right  angles  to  each  other,  and 
therefore  cannot  interfere.     First,  then,  it  is  evident,  from  what  we  have 
said  of  the  tangential  force,  that  when  P  is  at  A,  H  is  for  an  instant  at 
rest,  but  that  as  P  removes  from  A  towards  D,  H  continually  approachej 
P  along  their  line  of  junction  H  P,  which  is,  therefore,  at  each  instant  a 
tangent  to  the  path  of  H.     When  P  is  in  the  octant,  H  is  at  its  mean  | 


"variation"  of  the  moon  explained. 


891 


rhus  the  joint 
0  a  flattened  or 
the  sborter  in 
mth  her  mean 

and  slower  at 
e  earth  is  there- 
latter  situation, 
nil  be  in  the  act 
at  some  interme- 
ither  be  gaining 
)r  hsing  through 
have  attained  its 
itudo  will  deviate 
uality  in  question 
QS  its  maxima  in 

to  observation. 
le  rendered  of  this 
ind  excentricity  as 
BoUected,  is  nil  at 
its,  accelerative  in 

BE.    Itt  *'^®  *''"' 
e  two  latter,  short- 
i  at  (a,  &,  d,  e)  64» 
b3d,  and  inwards 
ce,  then,  the  point 
a  it  when  in  DB, 
lost  rapid  when  at 
force  is  concerned,) 
irtue  of  the  normal 
t  its  maximum  of 
nil,a~ta,hyd,e.  It 
lin  a  notion  of  the 
separately  the  paths 
rately,  since  its  true 
of  these  partial  mo- 
s  to  each  other,  and 
from  what  we  have 
is  for  an  instant  at 
itinually  approachcj 
,re,  at  each  instant  a 
it,  H  is  at  its  mean 


1! 


distance  from  P  (eqnal  to  F  S),  and  is  then  in  the  act  of  approaching  P 
most  rapidly.  From  thence  to  the  quadrature  D  the  movement  of  H  to- 
wards F  decreases  in  rapidity  till  the  quadrature  is  attained,  when  H  rests 
for  an  instant,  and  then  begins  to  reverse  its  motion,  and  travel  from  P 
at  the  same  rate  of  progress  as  before  towards  it.  Thus  it  is  clear  that, 
in  virtue  of  the  tangential  force  alone,  H  would  describe  a  four-cusped 
curve  a,d,  b,  e,  its  direction  of  motion  round  S  in  this  curve  being  oppo- 
site to  that  of  F,  so  that  A  and  a,  D  and  d,  B  and  5,  E  and<;,  shall  be 
corresponding  points. 

(707.)  Next  as  regards  the  normal  force.  When  the  moon  is  at  A  the 
motion  of  H  is  towards  D,  and  is  at  its  maximum  of  rapidity,  but  slackens 
as  P  proceeds  towards  D  and  as  Q  proceeds  towards  B.  To  the  curve 
described,  H  Q  will  be  always  a  tangent,  and  since  at  the  neutral  point  of 
the  normal  force  (or  when  P  is  64°  14'  from  A,  and  Q  64°  14'  from  D), 
the  motion  of  H  is  for  an  instant  nil  and  is  then  reversed,  the  curve  will 
have  a  cusp  at  I  corresponding,  and  H  will  then  begin  to  travel  along  the 
arc  7  m,  while  P  describes  the  corresponding  arc  from  neutral  point  to 
neutral  point  through  D.  Arrived  at  the  neutral  point  between  D  and  B, 
the  motion  of  H  along  Q  H  will  be  again  arrested  and  reversed,  giving 
rise  to  another  cusp  at  m,  and  so  on.  Thus,  in  virtue  of  the  normal  force 
acting  alone,  the  path  of  H  would  be  the  four-cusped,  elongated  curve 
Imno,  described  with  a  motion  round  S  the  reverse  of  P's,  and  having 
a,  d,  h,  e  for  points  corresponding  to  A,  B,  D,  E,  places  of  P. 

(708.)  Nothing  is  now  easier  than  to  superpose  these  motions.     Sup- 


£'*: 

*"•••  ■«^^ 

«:X 

VTB 

•cac 

»^> 

'■'""■•  fc^ 

«"^t> 

-^t 


'"mi 


-•1. 


892 


OUTLINES  OF  ASTRONOMT. 


V.UI 


CI 

«Bi|»r. 


ir 


*s; 


posing  H„  H,  to  be  the  points  in  either  curve  corresponding  to  P,  we 
have  nothing  to  do  but  to  set  from  off  S,  SA  equal  and  parallel  to  S  H, 
in  the  one  curve  and  from  h,hB.  equal  and  parallel  to  S  H,  in  the  other. 
Let  this  be  done  for  every  corresponding  point  in  the  two  curves,  and 
there  results  an  oval  curve  abde,  having  for  its  semiazis  8 a=sS a,  +  Suj ; 
and  8d=sSdi+Sda.  And  this  will  be  the  true  path  of  the  upper  focus, 
the  points  a,  d,  b,  e,  corresponding  to  A,  D,  B,  E,  places  of  P.  And  from 
this  it  follows,  1st,  that  at  A,  B,  the  sjzygies,  the  moon  is  in  perigee  in 
her  momentary  ellipse,  the  lower  focus  being  nearer  than  the  upper. 
2dly,  That  in  quadratures  D,  E,  the  moon  is  in  apogee  in  her  then  mo- 
mentary ellipsOi  the  upper  focus  being  then  nearer  than  the  lower.    3dly, 

Fig.  98. 


That  H  revolves  in  the  oval  adbe  the  contrary  way  to  P  in  its  orbit, 
making  a  complete  revolution  from  syzygy  to  syzygy  in  one  synodic  revo- 
lution of  the  moon. 
(709.)  Taking  1  for  the  moon's  mean  dbtance  firom  the  earth,  suppose 


"variation"  of  the  moon  explained. 


898 


nding  to  P,  we 
larallelto  SH, 
I,  in  the  other, 
wo  curves,  and 

he  upper  focus, 

P.   And  from 

is  in  perigee  ia 

lan  the  upper. 

In  her  then  mo- 

Le  lower.    3dly, 


p  in  its  orhit, 
bne  synodic  revo- 

le  earth,  suppose 


we  represent  Sa,  or  Srf,  (for  they  iiro  equal)  by  2a,  Sa,  by  2/>,  and  Sd^  by 
2c,  then  will  the  scmiaxes  of  the  ovnl  a  d  h  f,  Sa  and  St/  be  rcHpectivcly 
'Za-\-'ib  and  2a  +  2c,  so  that  the  cxccntricitics  of  the  momentary  ellipses 
at  A  and  D  will  bo  respectively  a  +  b  and  a-\-c.  The  total  amount  of  the 
effect  of  the  tangential  force  on  the  oxfM,  in  passing  from  syzygy  to  qua- 
rature,  will  evidently  bo  equal  to  the  length  of  the  curvilinear  arc  a,  </, 
{Ji(/.  art.  708),  which  is  necessarily  less  than  Sa,  +  S<?i  or  4a.  There- 
fore the  total  effect  on  the  semiaxtit  or  distance  of  the  moon  is  less  than 
2a,  and  the  excess  and  defect  of  the  greatest  and  least  values  of  this  dis- 
tance thus  varied  above  and  below  the  mean  value  S  A  =  1  (which  call  a) 
will  bo  less  than  a.  The  moon  then  is  moving  ut  A  in  the  perij/ee  of  an 
ellipse  whose  semiaxis  is  1+a  and  exccntricity  a-\-h,  so  that  its  actual 
distance  from  the  earth  there  is  1-f  a  —  u  —  h,  which  (because  o  is  less 
than  a)  is  less  than  1  —  b.  Again,  at  D  it  is  moving  in  apogee  of  an 
ellipse  whose  semiaxis  is  1 — a  and  excentricity  a+c,  so  that  its  distance 
then  from  the  earth  is  1 — a-f  a-fc,  which  (a  being  greater  than  a)  is 
greater  than  1+c,  the  latter  distance  exceeding  the  former  by  2a  —  2a + 
h-\-c. 

(710.)  Let  us  next  consider  the  corresponding  changes  induced  upon 
the  angular  velocity.  Now  it  is  a  law  of  elliptic  motion  that  at  different 
points  of  different  ellipses,  each  differing  very  little  from  a  circle,  the  an- 
gular velocities  are  to  each  other  as  the  square  roots  of  the  semiaxes 
directly,  and  as  the  squares  of  the  distances  inversely.  In  this  case  the 
semiaxes  at  A  and  D  are  to  each  other  as  1  +a  to  1  — a,  or  as  1  :  1  — 2a, 
so  that  their  square  roots  arc  to  each  other  as  1  :  1  —  a.  Again,  the  dis- 
tances being  to  each  other  as  l+o — a  —  6:1 — a-f-a+c,  the  inverse 
ratio  of  their  squares  (since  a,  a,  6,  c,  are  all  very  small  quantities)  is  that 
of  1  — 2a+2a+2c:l+2o  — 2a~26,  orasl:!— 4a— 4a— 26— 2c. 
The  angular  velocities  then  arc  to  each  other  in  a  ratio  compounded  of  these 
two  proportions,  that  is  in  the  ratio  of 

1  :  l+3o  — 4a  — 26  — 2c, 
which  is  evidently  that  of  a  greater  to  a  less  quantity.    It  is  obvious  also^ 
from  the  constitution  of  the  second  term  of  this  ratio,  that  the  normal 
force  is  far  more  influential  in  producing  this  result  than  the  tangential. 

(711.)  In  the  foregoing  reasoning  the  sun  has  been  regarded  as  fixed. 
Let  us  now  suppose  it  in  motion  (in  a  circular  orbit),  then  it  is  evident  that 
at  equal  angles  of  elongation  (of  P  from  M  seen  from  S),  equal  disturb- 
ing forces,  both  tangential  and  normal,  will  act :  only  the  syzygies  and 
quadratures,  as  well  as  the  neutral  points  of  the  normal  force,  instead  of 
being  points  fixed  in  longitude  on  the  orbit  of  the  moon,  will  advance  on 
that  orbit  with  a  uniform  angular  motion  equal  to  the  angular  motion  of 


*m,(\ 


:»^ 


■tr*.-W 


■3 


t-A. 


'3 


894 


OUTLINES  OF  ASTRONOMY. 


tflt 


* 

■i» 

■  t« 

5- 

lb, 

**. 

•WI 

US' 

•<u. 

•i' 

«^ 

A 

•«.!( 

-t- 

•fe> 

»A 

i^ 

-« 

••ir 

«•>. 

I? 

•4 

tc 

<:: 

•> 

'«« 

the  sun.  The  cuspidated  curves  «,  f^i  Ai  f  i  and  Oj  r?,  b,  e„  fig.  art.  708,  will, 
therefore,  no  longer  be  re-entering  curves ;  but  each  vrill  have  its  cusps 
Bcreioed  round  as  it  were  in  the  direction  of  the  sun's  motion,  so  as  ir  in< 
crease  the  angles  between  them  in  the  ratio  of  the  synodioal  to  the  side- 
real revolution  of  the  moon  (art.  418).  And  if,  in  like  manner,  the  mo- 
tions in  these  two  curves,  thus  separately  described  by  H,  be  compounded, 
the  resulting  curve,  though  still  (loosely  speaking)  a  species  of  oval,  will 
not  return  into  itself,  but  will  make  successive  spiroidal  convolutions  about 
S,  its  farthest  and  nearest  points  being  in  the  same  ratio  more  than  00° 
asunder.  And  to  this  movement  that  of  the  moon  herself  will  conform, 
describing  a  species  of  elliptic  spiroid,  having  its  least  distances  always  in 
the  lino  of  syzygies  and  its  greatest  in  that  of  quadratures.  It  iSfCviden^, 
also,  that,  owing  to  the  longer  continued  action  of  both  forces,  i.  e.  owing 
to  the  greater  arc  over  which  their  intensities  increase  and  dccrcnsn  by 
equal  steps,  the  branches  of  each  curve  between  the  cusps  will  be  longer, 
and  the  cusps  themselves  will  be  more  remote  from  S,  and  in  the  same 
degree  will  the  dimensions  of  the  resulting  oval  bo  enlarged,  and  with 
them  the  amount  of  the  inequality  in  the  moon's  motion  which  they 
represent. 

(712.)  In  the  above  reasoning  the  sun's  distance  is  supposed  so  great, 
that  the  disturbing  forces  in  the  scini  orbit  nearer  to  it  shall  not  sensibly 
differ  from  those  in  the  more  rnmote.  The  sun,  however,  is  actually 
nearer  to  the  moon  in  conjunclion  than  in  opposition  by  about  one  tw(^ 
hundredth  part  of  its  whole  distance,  and  this  suffices  to  give  rise  to  a 
very  sensible  inequality  (called  the  paralhxctie  inequaliti/)  in  the  lunar 
motions,  amounting  to  about  2'  in  its  effect  on  the  moon's  longitude,  and 
having  for  its  period  one  synodical  revolution  or  one  lunation.  As  this 
'lequality,  though  subordinate  in  the  case  of  the  moon  to  the  great  ine- 
quality of  the  variation  with  which  it  stands  in  connexion,  becomes  a 
prominent  feature  in  the  system  of  inequalities  corresponding  to  it  in  the 
planetary  perturbations  (by  reason  of  the  very  great  •.  ilrticnp  of  their 
distances  from  conjunction  to  opposition,)  it  will  be  r".<b;..  :  indicate 
what  modifications  this  consideration  will  introduce  icro  iliu  foiuts  of  our 
focu^t  curves,  and  of  their  superposed  oval.  Eecurring  then  to  our  figures 
in  art.  706,  707,  and  supposing  the  moon  to  set  out  from  E,  and  the 
upper  focus,  in  each  curve  from  e,  it  is  evident  that  the  interouspidal  arcs 
ettftt  cr,  .i  the  OP?,  and  ep,  pal,  Id,  in  the  other,  being  described  under 
the  intliieu.  <:  si  ii-ore  p>>werful  forces,  will  be  greater  than  the  arcs  db, 
b  e^  at'd  a  nt^  mbn^nt  corresponding  in  the  other  half  revolution.  The 
two  extremities  of  these  curves  then,  the  initial  and  terminal  places  of  e 
in  each,  will  not  meet,  and  the  same  conclusion  will  hold  respecting  those 


»rt.  708,  will, 
ave  its  cusps 
n,  BO  08  tr  in- 
al  to  the  Bvio- 
mner,  tUo  mo- 
j  compounded, 
>g  of  oval,  will 
solutions  about 
more  than  90 
f  will  conform, 
ances  always  in 
It  i8*cviden*, 
rces,  i-  «•  owing 
ind  dccrcnsfi  by 
ig  will  be  longer, 
ind  in  the  same 
arged,  and  with 
(tion  which  they 

apposed  so  great, 
ihall  not  sensibly 
rever,  is  actually 
y  about  one  two- 
to  give  rise  to  a 
Ity)  in  the  lunar 
•g  longitude,  and 
ination.    As  this 
to  the  great  ine- 
lexion,  becomes  a 
mding  to  it  in  the 
aiiationp  of  their 
.'6s?v'/  to  indicate 
)  ,Uo  foiias  of  our 
then  to  our  figures 
from  E,  and  the 
intercuspidal  arcs 
ig  described  under 
than  the  arcs  d  h, 
revolution.    The 
>rminal  places  of  e 
fid  respecting  those 


"variation"   op  THt:   MOON  EXPLAINED.  895 

rig. "' 


V 


of  the  compound  oval  in  which  the  focus  really  revolves,  which  will, 
therefore,  bo  as  in  the  annexed  figure.  Thus,  at  the  end  of  a  comj  ote 
lunation,  the  focus  will  have  shifted  its  place  from  e  to /in  a  line  parallel 
to  the  line  of  quadratures.  The  next  revolution,  and  the  next,  tbo  same 
thing  would  happen.  Meanwhile,  however,  the  sun  has  advanced  in  irs 
orbit,  and  the  line  of  quadratures  has  changed  its  situation  by  an  equal 
angular  motion.  In  consequence,  the  next  terminal  situation  (//)  of  the 
forces  will  not  lie  in  the  line  ef  prolonged,  but  in  a  line  parallel  to  the 
new  situation  of  the  lino  of  quadratures,  and  this  process  continuing,  will 
evidently  give  rise  to  a  movement  of  circulation  of  the  point  e,  round  a 
mean  situation  in  an  annual  period ;  and  this,  it  is  evident,  is  equivalent 
to  an  annual  circulation  of  the  central  point  of  the  compound  oval  itself, 
in  a  small  orbit  about  its  mean  position  S.  Thus  we  see  that  no  perma- 
nent and  indefinite  increase  of  excentricity  can  arise  from  this  cause; 
which  would  be  the  case,  however,  but  for  the  annual  motion  of  the  sun. 
(713.)  Inequalities  precisely  similar  in  principle  to  the  variation  and 
parallactic  inequality  af  the  moon,  though  greatly  modified  by  the  different 
relations  of  the  dimensions  of  the  orbits,  prevail  in  all  cases  where  planet 
disturbs  planet.  To  what  extent  this  modification  is  carried  will  be  evi- 
dent, if  we  cast  our  eyes  on  the  examples  given  in  art.  612,  where  it  will 
be  seen  that  the  disturbing  force  in  conjunction  often  exceeds  that  in 
opposition  in  a  vury  high  ratio,  (being  in  the  case  of  Neptune  disturbing 
Uranus  more  than  ten  times  as  great.)  The  effect  will  be,  that  the  orbit 
described  by  the  centre  of  the  compound  oval  about  S,  will  be  much 
greater  relatively  to  the  dimensions  of  that  oval  itself,  than  in  the  case  of 
the  moon.  Bearing  in  mind  the  naturo  and  import  of  this  modification, 
we  may  proceed  to  inquire,  apart  from  it,  into  the  number  and  distribution 
of  the  undulations  in  the  contour  of  the  oval  itself,  arising  from  the  alter- 


:u4 


,f 


^ 


ar 


I 


896 


OUTLINES   OF  ASTRONOMY. 


.'ir' 


c 


»1> 


*"rfl* 


Hi". 

tT"* 


I 


^»* 


nations  of  direction  pins  and  minus  of  the  disturbing  forces  in  the  course 
of  a  synodic  revolution.  But  first  it  should  be  mentioned  that,  in  the 
case  of  an  exterior  disturbed  by  an  interior  planet,  the  disturbing  body's 
angular  motion  exceeds  that  of  the  disturbed.  Hence  P,  though  advan- 
cing in  its  orbit,  recedes  relatively  to  the  line  of  syzygies,  or,  which  comes 
to  the  same  thing,  the  neutral  points  of  either  force  overtake  it  in  succes- 
sion, and  each,  as  it  comes  up  to  it,  gives  rise  to  a  cusp  in  the  corresponding 
focus  curve.  The  angles  between  the  successive  cusps  will  therefore  be 
to  the  angles  between  the  corresponding  neutral  points  for  a  fixed  position 
of  M,  in  the  same  constant  ratio  of  the  synodic  to  the  sidereal  period  of  P, 
which  however  is  now  a  ratio  of  less  inequality.  These  angles  then  will 
be  contracted  in  amplitude,  and,  for  the  same  reason  as  before,  the  excur- 
sions of  the  focus  will  be  diminished,  and  the  more  so  the  shorter  the 
synodic  revolution. 

(714.)  Since  the  cusps  of  either  curve  recur,  in  successive  synodic 
revolutions  in  the  same  order,  and  at  the  same  angular  distances  from 
each  other,  and  from  the  line  of  conjunction,  the  same  will  be  true  of  all 
the  corresponding  points  in  the  curve  resulting  from  their  superposition. 
In  that  curve,  every  cusp,  of  either  constituent,  will  give  rise  to  a  con- 
vexity, and  every  intercuspidal  arc  to  a  relative  concavity.  It  is  evident 
then  that  the  compound  curve  or  true  path  of  the  focus  so  resulting,  but 
for  the  cause  above  mentioned,  would  return  into  itself,  whenever  the 
periodic  times  of  the  disturbing  and  disturbed  bodies  are  commensurate, 
because  in  that  case  the  synodic  period  will  also  be  commensurate 
with  either,  and  the  arc  of  longitude  intercepted  between  the  sidereal 


Fig.  100. 


1^ 


place  of  any  one  conjunction,  and  that  next  following  it,  will  be  an  ali- 
quot part  of  360°.  In  all  other  cases  it  would  be  a  non-reentering,  more  or 
less  undulating  and  more  or  less  regular,  spiroid,  according  to  the  number 
of  cusps  in  each  of  the  constituent  curves  (that  is  to  say,  according  to 
the  number  of  neutral  points  or  changes  of  direction  from  inwards  to 


ANALOGOUS   PLANETARY  DISTURBANCES. 


897 


in  the  course 

I  that,  in  the 
Dirbing  body's 
though  advan- 
:  which  comes 
je  it  in  succes- 
j  corresponding 

II  therefore  be 
a  fixed  position 
eal  period  of  P, 
ngles  then  -will 
jfore,  the  escur- 
the  shorter  the 

ccessivo  synodic 
f  distances  from 
ill  be  true  of  all 
eir  superposition, 
ive  rise  to  a  con- 
ty.     It  is  evident 
1  so  resulting,  but 
slf,  whenever  the 
re  commensurate, 
)e  commensurate 
rccn  the  sidereal 


\< 


[  it,  will  be  an  ali- 

Ireentering,  more  or 

Eing  to  the  number 

say,  according  to 

from  inwards  to 


outwards,  or  from  acceleratirjg  to  retarding,  and  vire  versa,  of  the  normal 
and  tangential  forces,)  in  a  complete  synodic  revolution,  and  their  distri- 
bution over  the  circumference. 

(715.)  With  regard  to  these  changes,  it  is  necessary  to  distinguish 
three  cases,  in  which  the  perturbations  of  planet  by  planet  are  very  dis- 
tinct in  character.     1st.  When  the  disturbing  planet  is  exterior.     In  this 
case  there  are  four  neutral  points  of  either  force.     Those  of  the  tangen- 
tial force  occur  at  the  syzygies,  and  at  the  points  of  the  disturbed  orbit 
(which  we  shall  call  points  of  equidistance),  equidistant  from  the  sun 
and  the  disturbing  planet  (at  which  points,  as  we  have  shown  (art.  614), 
the  total  disturbing  force  is  always  directed  inwards  towards  the  sun.) 
Those  of  the  normal  force  occur  at  points  intermediate  between  these  last 
mentioned  points,  and  the  syzygies,  which,  if  the  disturbing  planet  be 
very  distant,  hold  nearly  the  situation  they  do  in  the  lunar  theory,  i.  e. 
considerably  nearer  the  quadratures  than  the  syzygies.    In  proportion  as  the 
distance  of  the  disturbing  planet  diminishes,  two  of  these  points,  viz.  those 
nearest  the  syzygy,  approach  to  each  other,  and  to  the  syzygy,  and  in  the 
extreme  case,  when  the  dimensions  of  the  orbits  are  equal,  coincide  with  it. 
(710.)  The  second  case  is  that  in  which  the  disturbing  planet  is  inte- 
rior to  the  disturbed,  but  at  a  distance  from  the  sun  greater  than  half  that 
of  the  latter.     In  this  case  there  are  four  neutral  points  of  the  tangential 
force,  and  only  two  of  the  normal.     Those  of  the  tangential  force  occur 
at  the  syzygies,  and  at  the  points  of  equidistance.     The  force  retards  the 
disturbed  body  from  conjunction  to  the  first  such  points  after  conjunction, 
accelerates  it  thence  to  the  opposition,  thence  again  retards  it  to  the  next 
point  of  equidistance,  and  finally  again  accelerates  it  up  to  the  conjunc- 
tion.    As  the  disturbing  orbit  contracts  in  dimension,  the  points  of  equi- 
distance approach;  their  distance  from  syzygy  from  00°  (the  extreme 
case)  diminishing  to  nothing,  when  they  coincide  with  each  other,  and 
with  the  conjunction.     In  the  case  of  Saturn  disturbed  by  Jupiter,  that 
distance  is  only  23°  38'.     The  neutral  points  of  the  normal  force  lie 
somewhat  beyond  the  quadratures,  on  the  side  of  the  opposition,  and  do 
not  undergo  any  very  material  change  of  situation  with  the  contraction 
of  the  disturbing  orbit. 

(717.)  The  third  case  is  that  in  which  the  diameter  of  the  disturbing 
iuterior  orbit  is  less  than  half  that  of  the  disturbed.  In  this  ca;<o  there 
are  only  two  points  of  evanescence  for  either  force.  Those  of  the  tan- 
gential force  are  the  syzygies.  The  disturbed  planet  is  accelerated  through- 
out the  whole  semi-revolution  from  conjunction  to  opposition,  ami  retarded 
I  from  opposition  to  conjunction,  the  maxima  of  acceleration  and  retardation 
1  occurring  not  far  from  quadrature.     The  neutral  points  of  the  nnnml 


1;5: 


Z;2  "'^^ 


3 


te 


>'»' 
l$»".i 

h 


It 


898 


OUTLINES   OF  ASTRONOMY. 


force  are  situated  nearly  as  in  the  last  case ;  that  is  to  say,  beyond  the 
quadratures  towards  the  opposition.  All  these  varieties  the  student  will 
easily  trace  out  by  simply  drawing  the  figures,  and  resolving  the  forces  in 
a  series  of  cases,  beginning  with  a  very  large  and  ending  with  a  very 
small  diameter  of  the  disturbing  orbit.  It  will  greatly  aid  him  in  im- 
pressing on  his  imagination  the  general  relations  of  the  subject,  if  be 
construct,  as  he  proceeds,  for  each  case,  the  elegant  and  symmetrical  ovals 


tt:»ia: 


Fig.  101. 


in  which  the  points  N  and  L  (/</.  art.  675,)  always  lie,  for  a  fixed  posi- 
tion of  M,  and  of  which  the  annexed  figure  expresses  the  forms  they 
respectively  assume  in  the  third  case  now  under  consideration.  The 
second  only  differs  from  this,  in  having  the  common  vertex  m,  of  both 
ovals,  outside  of  the  disturbed  orbit  A  P,  while  in  the  case  of  an  exterior 
disturbing  planet,  the  oval  m  L  assumes  a  four-lobed  form ;  its  lobes 
respectively  touching  the  oval  m  N  in  its  vertices,  and  cutting  the  orbit 
A  P  in  the  points  of  equidistance  and  of  tangency,  (i.  e.  where  M  P  S  is 
a  right  angle)  as  in  this  figure. 

Fig.  102. 


THREE  CASES  DISTINGUISHED. 


899 


y,  beyond  tbe 
e  student  will 
y  the  forces  in 
^  with  a  very 
id  him  in  im- 
subject,  if  he 
mmetrical  ovals 


;,  for  a  fixed  posi- 
;s  the  forms  they 
^nsideration.    The 
/ertex  wi,  of  both 
pase  of  an  exterior 
[d  form;  its  lobes 
.  cutting  the  orbit 
e.  where  M  P  S  is 


(718.)  It  would  be  easy  now,  bearing  these  features  in  mind,  to  trace 
in  any  proposed  case  the  form  of  the  spiroid  curve,  described,  as  above 
explained,  by  the  upper  focus.  It  will  suffice,  however,  for  our  present 
purpose,  to  remark,  1st,  That  between  every  two  successive  conjunctions 
of  P  and  M,  the  same  general  form,  the  same  subordinate  undulations, 
and  the  same  terminal  displacement  of  the  upper  focus,  are  continually 
repeated.  2dly,  That  the  motion  of  the  focus  in  this  curve  is  retrograde 
whenever  the  disturbing  planet  is  exterior,  and  that  in  consequence  the 
apsides  of  the  momentary  ellipse  also  recede,  with  a  mean  velocity  such 
as,  but  for  that  displacement,  would  bring  them  round  at  the  each  con- 
junction to  the  same  relative  situation  with  respect  to  the  line  of  syzygies. 
8dly,  That  in  consequence  of  this  retrograde  movement  of  the  apse,  the 
disturbed  planet,  apart  from  that  consideration,  would  be  twice  in  peri- 
helio  and  twice  in  aphelio  in  its  momentary  ellipse  in  each  synodic  revo- 
lution, just  as  in  the  case  of  the  moon  disturbed  by  the  sun — and  that  in 
consequence  of  this  and  of  the  undulating  movement  of  the  focus  H  it- 
self, an  inequality  will  arise,  analogous,  mutatis  mutandis  in  each  case,  to 
the  moon's  variation ;  under  which  term  we  comprehend  (not  exactly  in 
conformity  to  its  strict  technical  meaning  in  the  lunar  theory)  not  only 
the  principal  inequality  thus  arising,  but  all  its  subordinate  fluctuations. 
And  on  this  the  parallactic  inequality  thus  violently  exaggerated  is 
superposed. 

(719.)  We  come  now  to  the  class  of  inequalities  which  depend  for 
their  existence  on  an  appreciable  amount  of  permanent  excentricity  in 
the  orbit  of  one  or  of  both  the  disturbing  and  disturbed  planets,  in  con- 
sequence of  which  all  their  conjunctions  do  not  take  place  at  equal 
distances  either  from  the  central  body  or  from  each  other,  and  therefore 
that  symmetry  in  every  synodic  revolution  on  which  depends  the  exact 
restoration  of  both  the  axis  and  excentricity  to  their  original  values  at  the 
completion  of  each  such  revolution  no  longer  subsists.  In  passing  from 
conjunction  to  conjunction,  then,  there  will  no  longer  be  effected  a  com- 
plete restoration  of  the  upper  focus  to  the  same  relative  situation,  or  of 
the  axis  to  the  same  length,  which  they  respectively  had  at  the  outset. 
At  the  same  time  it  is  not  less  evident  that  the  differences  in  both  re- 
spects are  only  what  remain  outstanding,  after  the  compensation  of  by  far 
the  greater  part  of  the  deviations  to  and  fro  from  a  mean  state,  which 
occur  in  the  course  of  the  revolution ;  and  that  they  amount  to  but  small 
fractions  of  the  total  excursions  of  the  focus  from  its  first  position,  or  of 
the  increase  and  decrease  in  the  length  of  the  axis  effected  by  the  direct 
action  of  the  tangential  force,  —  so  small,  indeed,  that,  unless  owing  to 
peculiar  adjustments  they  be  enabled  to  accumulate  again  and  again  at 


u4. 


a>miia 


400 


OUTLINES   OF  ASTRONOMY. 


11%. 


*»•*, 
f^*^.- 


Buccessive  conjunctions  in  the  same  direction,  they  would  be  altogether 
undeserving  of  any  especial  notice  in  a  work  of  this  nature.  Such  ad- 
justments, however,  would  evidently  exist  if  the  periodic  times  of  the 
planets  were  exactly  commensurable ;  since  in  that  case  all  the  possible 
conjunctions  which  could  ever  happen  (the  elements  not  being  materially 
changed)  would  take  place  at  fixed  points  in  longitude,  the  intermediate 
points  being  never  visited  by  a  conjunction.  Now,  of  the  conjunctions 
thus  distributed,  their  relations  to  the  lines  of  symmetry  in  the  orbits 
being  all  dissimilar,  some  one  must  be  more  influential  than  the  rest  on 
each  of  the  elements  (not  necessarily  the  sa7ne  upon  all).  Consequently, 
in  a  complete  cycle  of  conjunctions,  wherein  each  has  been  visited  in  its 
turn,  the  influence  of  that  one  on  the  element  to  which  it  stands  so  espe- 
cially related,  will  preponderate  over  the  counteracting  and  compensating 
influence  of  the  rest,  and  thus,  although  in  such  a  cycle  as  above  specified 
a  further  and  much  more  exact  compensation  will  have  been  effected  in 
its  value  than  in  a  single  revolution,  still  that  compensation  will  not  be 
complete,  but  a  portion  of  the  effect  (be  it  to  increase  or  to  diminish  the 
excentricity  or  the  axis,  or  to  cause  the  apse  to  advance  or  to  recede,) 
will  remain  outstanding.  In  the  next  cycle  of  the  same  kind  this  will  be 
repeated,  and  the  result  will  be  of  the  same  character,  and  so  on,  till  at 
length  a  sensible  and  ultimately  a  large  amount  of  change  shall  have 
taken  place,  and  in  fact  until  the  axis  (and  with  it  the  mean  motion)  shall 
have  so  altered  as  to  destroy  the  commensurability  of  periods,  and  the  ap- 
sides have  so  shifted  as  to  alter  the  place  of  the  most  influential  conjunction. 
(720.)  Now,  although  it  is  true  that  the  mean  motions  of  no  two 
planets  are  exactly  commensurate,  yet  cases  are  not  wanting  in  which 
there  exists  an  approach  to  this  adjustment.  For  instance,  in  the  case  of 
Jupiter  and  Saturn,  a  cycle  composed  of  five  periods  of  Jupiter  and  two 
of  Saturn,  although  it  does  not  exactly/  bring  about  the  same  configura- 
tion, does  so  pretty  nearly.  Five  periods  of  Jupiter  arc  21663  days,  and 
two  periods  of  Saturn,  21519  days.  The  dift'erence  i3  only  146  days,  in 
which  Jupiter  describes,  on  an  average,  12",  and  Saturn  about  5°;  so 
that  after  the  lapse  of  the  former  interval  they  will  only  be  7°  from  a 
conjunction  in  the  same  parts  of  their  orbits  as  before.  If  we  calculate 
the  time  which  will  exactly  bring  about,  on  the  average,  three  conjunc- 
tions of  the  two  planets  we  shall  find  it  to  be  21760  days,  their  synodical 
period  being  7253-4  days.  In  this  interval  Saturn  will  have  described 
8°  6'  in  excess  of  two  sidereal  revolutions,  and  Jupiter  the  same  angle  in 
excess  of  five.  Every  third  conjunction,  then,  will  take  place  8°  G'  in 
advance  of  the  preceding,  which  is  near  enough  to  establinh,  not,  it  is 
true,  an  identity  with,  but  still  a  great  approach  to  the  case  in  question. 


LONG  EQUATION   OF  JUPITER  AND   SATURN. 


401 


)e  altogether 
5.     Such  ad- 
times  of  the 
I  the  possible 
iog  materially 
5  intermediate 
5  conjunctions 
r  in  the  orbits 
lan  the  rest  on 
Consequently, 
en  visited  in  its 
t  stands  so  espe- 
id  compensating 
9  above  specified 
been  effected  in 
ition  wUl  not  be 
,r  to  diminish  the 
ce  or  to  recede,) 
3  kind  this  will  be 
and  so  on,  till  at 
l,ange  shall  have 
Ijican  motion)  shall 
eriods,  and  the  ap- 
lential  conjunction. 

notions  of  no  two 
wanting  in  which 
nee,  in  the  case  of 
Jupiter  and  two 
same  configura- 
0  21063  days,  and 
s  only  146  days,  in 
turn  about  5° ;  so 
ro  from  a 


f 
■le 


only  be  7 

If  we  calculate 

[age,  three  conjunc- 
kys,  their  synodical 
nil  have  described 
br  the  same  angle  in 
ttake  place  8°  G'  in 
establisii,  not,  it  is 
Ihe  case  in  question. 


The  excess  of  action,  for  several  such  triple  conjunctions  (7  or  8)  in  suc- 
cession, will  lie  the  same  way,  and  at  each  of  them  the  elements  of  P's 
orbit  and  its  angular  motion  will  be  similarly  influenced,  so  as  to  accu- 
mulate the  effect  upon  its  longitude ;  thus  giving  rise  to  an  irregularity 
of  considerable  magnitude  and  very  long  period,  which  is  well  known  to 
astronomers  by  the  name  of  the  great  inequality  of  Jupiter  and  Saturn. 

(721.)  The  ar    S°  6'  is  contained  44^  times  in  the  whole  circumference 

of  360° ;  and  accordingly,  if  we  trace  round  this  particular  conjunction, 

we  shall  find  it  will  return  to  the  same  point  of  the  orbit  in  so  many 

times  21760  days,  or  in  2648  years.     But  the  conjunction  we  are  now 

considering  is  only  one  out  of  three.     The  other  two  will  happen  at 

points  of  the  orbit  about  128°  and  246°  distant,  and  these  points  also  will 

advance  by  the  same  arc  of  8®  6'  in  21760  days.     Consequently  the 

period  of  2648  years  will  bring  them  all  round,  and  in  that  interval  each 

of  them  will  pass  through  that  point  of  the  two  orbits  from  which  we 

commenced :  hence  a  conjunction  (one  or  other  of  the  three)  will  happen 

at  that  point  once  in  one  third  of  this  period,  or  in  883  years ;  and  this 

is,  therefore,  the  cycle  in  which  the  "great  inequality"  would  undergo 

its  full  compensation,  did  the  elements  of  the  orbits  continue  all  that 

time  invariable.     Their  variation,  however,  is  considerable  in  so  long  an 

interval ;  and,  owing  to  this  cause,  the  period  itself  is  prolonged  to  about 

918  years. 

(722.)  We  have  selected  this  inequality  as  the  most  remarkable  in- 
stance of  this  kind  of  action  on  account  of  its  magnitude,  the  .length  of 
its  period,  and  its  high  historical  interest.  It  had  long  been  remarked 
by  astronomers,  that  on  comparing  together  modern  with  ancient  observa- 
tions of  Jupiter  and  Saturn,  the  mean  motions  of  these  planets  did  not 
appear  to  be  uniform.  The  period  of  Saturn,  for  instance,  appeared  to 
kve  been  lengthening  throughout  the  whole  of  the  seventeenth  century, 
and  that  of  Jupiter  shortening — that  is  to  say,  the  one  planet  was  con- 
stantly lagging  behind,  and  the  other  getting  in  advance  of  its  calculated 
place.  On  the  other  hand,  in  the  .eighteenth  century,  a  process  precisely 
tlie  reverse  seemed  to  be  going  on.  It  is  true  the  whole  retardations  and 
accelerations  observed  were  not  very  great ;  but,  as  their  influence  went  on 
pccumulating,  they  produced,  at  length,  material  differences  between  the 
observed  and  calculated  places  of  both  these  planets,  which  as  they  could 
|not  then  be  accounted  for  by  any  theory,  excited  a  high  degree  of  atten- 
lon,  and  were  even,  at  one  time,  too  hastily  regarded  as  almost  subversive 
f  the  Newtonian  doctrine  of  gravity.  For  a  long  while  this  difference 
led  every  endeavour  to  account  for  it ;  till  at  length  Laplace  pointed 
26 


net 


'"£:  ■'*■■" 

**,i-_^ 


■<■-.«  "J 


!&i-4- 


W. 


3 


iV 


402 


OUTLINES  OF  ASTRONOMY. 


IS' 


out  its  cause  in  the  near  coinmensurabUity  of  the  mean  motions,  as  above 
shown,  and  succeeded  in  culcuhiting  its  period  and  amount. 

(7"23.)  The  inequality  in  question  amounts,  at  its  maximum,  to  an  al- 
ternate gain  and  loss  of  about  0°  49'  in  the  longitude  of  Saturn,  and  a 
corresponding  loss  and  gain  of  about  0°  21'  in  that  of  Jupiter.     That  an 
acceleration  in  the  one  planet  must  necessarily  be  accompanied  by  a  re- 
tardation in  the  other,  might  appear  at  first  sight  self-evident,  if  we  con- 
sider, that  action  and  reaction  being  equal,  and  in  contrary  directionsi, 
•whatever  momentum  Jupiter  communicates  to  Saturn  in  the  direction 
P  M,  the  same  momentum  must  Saturn  communicate  to  Jupiter  in  the 
direction  M  P.     The  one,  therefore,  it  might  seem  to  be  plausibly  argued, 
will  be  dragged  tbrward,  whenever  the  other  is  pulled  back  in  its  orbit. 
The  inference  is  correct,  so  fur  as  the  general  and  final  result  goes  ;  but 
the  reasoning  by  which  it  would,  on  the  first  glance,  appear  to  be  thus 
summarily  established  is  fallacious,  or  at  least  incomplete.     It  is  perfectly 
true  that  whatever  momentum  Jupiter  communicates  directly  to  Saturn, 
Saturn  communicates  an  equal  momentum  to  Jupiter  in  an  opposite  linear 
direction.    But  it  is  not  with  the  absolute  motions  of  the  two  planets  in 
space  that  we  are  now  concerned,  but  with  the  relative  motion  of  each 
separately,  with  respect  to  the  sun  regarded  as  at  rest.     The  perturhaticc 
forces  (the  forces  which  disturb  these  relative  motions)  do  not  act  along 
the  line  of  junction  of  the  planets  (art.  614.)     In  the  reasoning  thus 
objected  to,  the  attraction  of  each  on  the  sun  has  been  left  out  of  the 
account',  and  it  remains  to  be  shown  that  these  attractions  neutralize  and 
destroy  each  other's  effects  in  considerable  periods  of  time,  as  bearing 
upon  the  result  in  question.    Suppose  then  that  we  for  a  moment  abandon 
the  point  of  view,  in  which  we  have  hitherto  all  along  considered  the 
subject,  and  regard  the  sun  as  free  to  move,  and  liable  to  be  displaced  by 
the  attractions  of  the  two  planets.     Then  will  the  movements  of  all  be 
performed  about  the  common  centre  of  gravity,  just  as  they  would  have 
been  about  the  sun's  centre  regarded  as  immoveable,  the  sun  all  the  while 
circulating  in  a  small  orbit  (with  a  motion  compounded  of  the  two  elliptic 
motions  it  would  have  in  virtue  of  their  separate  attractions)  about  the 
same  centre.     Now  in  this  case  M  still  disturbs  P,  and  P,  M,  but  the  | 
whole  disturbing  force  now  acts  aloug  their  line  of  junction,  and  since  it  i 
remains  true  that  whatever  momentum  M  generates  in  P,  P  will  generate  j 
the  same  in  M  in  a  contrary  direction ;  it  will  also  be  strictly  true  that,  so 

•  We  are  here  reading  a  sort  of  recantation.  In  the  edition  of  1833  the  remarkable  I 
result  in  question  is  sought  to  be  established  by  this  vicious  reasoning.  The  mistake  I 
is  a  very  natural  one,  and  is  so  apt  to  haunt  the  ideas  of  beginners  in  this  department | 
of  physics,  that  it  is  worth  while  expressly  to  warn  them  against  it. 


LAW  OF  RECIPROCITY. 


403 


ions,  as  above 

mura,  to  an  al- 
Saturn,  and  a 
,Uer.     That  an 
ipanied  by  a  rc- 
dont,  if  ^ve  con- 
trary directions, 
in  the  direction 
)  Jupiter  in  the 
plausibly  argued, 
,ack  in  its  orbit. 
I  result  goes ;  but 
,ppear  to  be  thus 
e.    It  is  perfectly 
directly  to  Saturn, 
,  an  opposite  bnear 
the  two  planets  in 
,ve  motion  of  each 
The  perturhativc 
Lg)  do  not  act  along 
tlie  reasoning  thus 
,een  left  out  of  the 
•tions  neutralize  and 
[of  time,  as  bearing 
.  a  moment  abandou 
[long  considered  the 
ie  to  be  displaced  hy 
lovements  of  all  he 
.  as  they  would  have 
[the  sun  all  the  whik 
^d  of  the  two  elliptic 
fttractions)  about  the 
.  and  P,  M,  but  tbe 
junction,  and  since  It 

in  P,  P  will  generate 
strictly  true  that,  80 

lnofl833thereniarkablel 

linnets  in  this  departmeBi| 
astit. 


far  as  a  disturbance  of  their  elliptic  motions  about  the  common  centre  of 
gmvity  of  the  system  is  alone  regarded,  whatever  disturbance  of  velocity 
is  generated  in  the  one,  a  contrary  disturbance  of  velocity  (only  in  the 
inverse  ratio  of  the  masses  and  modified,  though  never  contradicted,  by 
the  directions  in  which  they  are  respectively  moving),  will  bo  generated 
in  the  other.     Now  when  we  are  considering  only  inequalities  of  long 
period  comprehending  many  complete  revolutions  of  both  planets,  and 
which  arise  from  changes  in  the  axes  of  the  orbits,  aflfecting  their  mean 
motions,  it  matters  not  whether  we  suppose  these  motions  performed 
about  the    ommon  centre  of  gravity,  or  about  the  sun,  which  never  de- 
parts from  that  centre  to  any  material  extent  (the  mass  of  the  sun  being 
such  in  comparison  with  that  of  the  planets,  that  that  centre  always  lies 
within  his  surface.)    The  mean  motion  therefore,  regarded  as  the  average 
angular  velocity  during  a  revolution,  is  the  same  whether  estimated  by 
reference  to  the  sun's  centre,  or  to  the  centre  of  gravity,  or,  in  other 
words,  the  relative  mean  motion  referred  to  the  sun  is  identical  with  the 
absolute  mean  motion  referred  to  the  centre  of  gravity. 

(724.)  This  reasaning  applies  equally  to  every  case  of  mutual  disturb- 
ance resulting  in  a  long  inequality  such  as  may  arise  from  a  slow  and 
long-continued  periodical  increase  and  diminution  of  the  axes,  and  geom- 
eters have  accordingly  demonstrated  as  a  consequence  from  it,  that  the 
proportion  in  which  such  inequalities  affect  the  longitudes  of  the  two 
planets  concerned,  or  the  maxima  of  the  excesses  and  defects  of  their 
longitudes  above  and  below  their  elliptic  values,  thence  arising,  in  each, 
are  to  each  other  in  the  inverse  ratio  of  their  masses  multiplied  by  the 
square  roots  of  the  major  axes  of  their  orbits,  and  this  result  is  confirmed 
by  observation,  and  will  be  found  verified  in  the  instance  immediately  in 
question  as  nearly  as  the  uncertainty  still  subsisting  as  to  the  masses  of 
the  two  planets  will  permit. 

(725.)  The  inequality  in  question,  as  has  been  observed  in  general, 
(art.  718,)  would  be  much  greater,  were  it  not  for  the  partial  compensa- 
tion which  is  operated  in  it  in  every  triple  conjunction  of  the  planets. 
Suppose  PQR  to  be  Saturn's  orbit,  and  pqr  Jupiter's;  and  suppose  a 
conjunction  to  take  place  at  P^),  on  the  line  SA;  a  second  at  123°  dis- 
tance, on  the  line  S  B ;  a  third  at  246°  distance,  on  S  C  ;  and  the  next  at 
368°,  on  S  D.  This  last-mentioned  conjunction,  taking  place  nearly  in 
I  the  situation  of  the  first,  will  produce  nearly  a  repetition  of  the  first  effect 
ia  retarding  or  accelerating  the  planets ;  but  the  other  two,  being  in  the 
most  remote  situations  possible  from  the  first,  will  happen  under  entirely 
different  circumstances  as  to  the  position  of  the  perihelia  of  the  orbits. 
{Now,  we  have  seen  that  a  presentation  of  the  one  planet  to  the  other  in 


^.■^. 


.3>ii|>4- 

m 


3il 


4*. 


404 


OUTLINES  OF  ASTRONOMY. 


Fig.  103. 


i? 


conjunction,  in  a  variety  of  situations,  tends  to  produce  compensation ; 
and,  in  fact,  the  greatest  possible  amount  of  compensation  \vhich  can  be 
produced  by  only  three  conjunctions  is  when  they  are  thus  equally  dis- 
tributed round  the  centre.  Hence  we  see  that  it  is  not  the  whole  amount 
of  perturbation  which  is  thus  accumulated  in  each  triple  conjunction,  but 
only  that  small  part  which  is  left  uncompensated  by  the  intermediate 
ones.  The  reader,  who  possesses  already  some  acquaintance  with  the 
subject,  will  not  be  at  a  loss  to  perceive  how  this  consideration  is,  in  fact, 
equivalent  to  that  part  of  the  geometrical  investigation  of  this  inequality 
which  leads  us  to  seek  its  expressiou  in  terms  of  the  third  order,  or  in- 
volving the  cubes  and  products  of  three  dimensions  of  the  excentricitieg 
and  inclinations ;  and  how  the  continual  accumulation  of  small  quantities, 
during  long  periods,  corresponds  to  what  geometers  intend  when  thcj 
speak  of  small  terms  receiving  great  accessions  of  magnitude  by  the  intro- 
duction of  large  coefficients  in  the  process  of  integration. 

(726.)  Similar  considerations  apply  to  every  case  of  approximate  com- 
mensurability  which  can  take  place  among  the  mean  motions  of  any  two 
planets.  Such,  for  instance,  is  that  which  obtains  between  the  mean 
motion  of  the  earth  and  Venus, — 13  times  the  period  of  Venus  being  very 
nearly  equal  to  8  times  that  of  the  earth.  This  gives  rise  to  an  extremely 
near  coincidence  of  every  fifth  conjunction,  in  the  same  parts  of  each  orbit 
(within  jiljfth.  part  of  a  circumterence,)  and  therefore  to  a  correspondingly 
extensiv  accumulation  of  the  resulting  uncompensated  perturbation. 
But,  on  the  other  hand,  the  part  of  the  perturbation  thus  accumulated  is 
only  that  which  remains  outstanding  after  passing  the  equalizing  ordeal 
of  five  conjunctions  equally  distributed  round  the  circle ;  or,  in  the  lan- 
guage of  geometers,  is  dependent  on  powers  and  products  of  the  excen- 
tricities  and  inclinations  of  the  fifth  order.  It  is,  therefore,  extremely 
minute,  and  the  whole  resulting  inequality,  according  to  the  elaborate 
calcvlatioDS  of  Mr.  Airy,  to  whom  it  owes  its  detection,  amounts  to  no 


lONO   INEQUALITIES   OF   ELEMENTS. 


4l 


e  cotnpenaatlon; 

on  wliich  can  be 

thus  equally  dis- 

,he  whole  amount 

)  conjunction,  but 
tbe  intcnnediat* 

ftintance  with  tbe 

leration  is,  in  fact, 
of  this  inequality 

third  order,  or  in- 

the  excentricities 

,f  small  quantities, 

intend  Tvhen  they 

,itude  by  the  intro- 

m. 
approximate  com- 

jotions  of  any  t\TO 
[between  the  mean 
,f  Venus  being  very 
•ise  to  an  extremely 
5  parts  of  each  orbit 
to  a  correspondingly 
sated  perturbation, 
[thus  accumulated  is 
,e  equalizing  ordeal 
•cle;  or,inthelan- 
»ducts  of  the  excen- 
therefore,  extremely 
[ng  to  the  elaborate 
tion,  amounts  to  do 


more  than  a  few  seconds  at  its  maximum,  while  its  period  is  no  less  than 
240  years.  This  uxaniple  will  serve  to  show  to  what  minuteness  these 
inquiries  have  been  carried  to  the  planetary  theory. 

(727.)  That  variations  of  long  period  arising  in  the  way  above  described 
are  necessarily  accompanied  by  similarly  periodical  displacements  of  the 
upper  focus,  equivalent  in  their  effect  to  periodical  fluctuations  in  the 
magnitude  of  the  cxccnti-icity,  and  in  the  position  of  the  line  of  apsides, 
is  evident  from  what  has  been  already  said  respecting  the  motion  of  the 
upper  focus  under  the  influence  of  the  disturbing  forces.     In  the  case  of 
circular  orbits  the  mean  place  of  H  coincides  with  S  tbe  centre  of  the  sun, 
but  if  the  orbits  have  any  independent  ellipticity,  this  coincidence  will  no 
longer  exist  —  and  the  mean  place  of  the  upper  focus  will  come  to  be 
inferred  from  the  average  of  all  the  situations  which  it  actually  holds 
during  an  entire  revolution.     Now  the  fixity  of  this  point  depends  on  the 
equality  of  each  of  the  branches  of  the  cuspidated  curves,  and  consequent 
equality  of  excursion  of  the  focus  in  each  particular  direction,  in  every 
successive  situation  of  the  line  of  conjunction.     But  if  there  be  some 
one  line  of  conjunction  in  which  these  excursions  arc  greater  in  any  one 
particular  direction  than  in  another,  the  mean  place  of  the  focus  will  be 
displaced,  and  if  this  process  bo  repeated,  that  mean  place  will  continue 
to  deviate  more  and  more  from  its  original  position,  and  thus  will  arise  a 
circulation  of  the  mean  place  of  the  focns  fur  a.  revolution  about  another 
mean  situation,  the  average  of  all  the  former  mean  places  during  a  com- 
plete cycle  of  conjunctions.     Supposing  S  to  be  the  sun,  0  the  situation 
tbe  upper  focus  would  have,  had  these  inequalities  no  existence,  and  H  K 
the  path  of  the  upper  focus,  which  it- pursues  about  0  by  reason  of  them, 
then  it  is  evident  that  in  the  course  of  a  complete  cycle  of  the  inequality 
in  question,  the  excentricity  will  have  fluctuated  between  the  extreme 
limits  S  J  and  S  T  and  the  direction  of  the  longer  axis  between  the 
extreme  position  S  H  and  S  K,  and  that  if  we  suppose  ijhk  to  be  the 
corresponding  mean  places  of  the  focus,  ij  will  be  the  extent  of  the  fluctu- 
ation of  the  mean  excentricity,  and  the  angle  h  s  k,  that  of  the  longitude 
of  the  perigee. 

(728.)  The  periods  then  in  which  these  fluctuations  go  through  their 
phases  are  necessarily  equal  in  duration  with  that  of  the  inequality  in 
longitude,  with  which  they  stand  in  connexion.  But  it  by  no  means 
follows  that  their  maxima  all  coincide.  The  variation  of  the  axis  to  which 
that  of  the  mean  motion  corresponds,  depends  on  the  tangential  force  only 
whose  maximum  is  not  at  conjunction  or  opposition,  Hnt  at  points  remote 
from  either,  while  the  excentricity  depends  both  on  tlio  normal  and  tan- 
1  gcntial  forces,  the  maximum  of  the  former  of  which  is  at  the  conjunction 


,* 


■'3J'  «**•* 


mi! 


406 


OUTLINES  OP  ASTRONOMY. 
Fig.  104. 


'  •mi 

ft* 


That  particular  conjunction  therefore,  which  is  most  influential  on  the 
axis,  is  not  so  on  the  excentricity,  so  that  it  can  by  no  means  be  concluded 
that  either  the  maximum  value  of  the  axis  coincides  with  the  maximum, 
or  the  minimum  of  the  excentricity,  or  with  the  greatest  excursion  to  or 
fro  of  the  line  of  apsides  from  its  mean  situation,  all  that  can  be  safely 
asserted  is,  that  as  either  the  axis  or  the  excentricity  of  the  one  orbit 
varies,  that  of  the  other  will  vary  in  the  opposite  direction. 

(729.)  The  primary  elements  of  the  lunar  and  planetary  orbits,  which 
may  be  regarded  as  variable,  are  the  longitude   ^j"  the  node,  the  inclina- 
tion, the  axis,  excentricity,  longitude  of  the  pehhelicn,  and  epoch  (art. 
496).     In  the  foregoing  articles  we  have  shown  in  what  manner  each  of 
thr  first  five  of  these  elements  is  made  to  vary,  by  the  direct  action  of 
the  perturbing  forces.     It  remains  to  explain  in  what  manner  the  last 
comes  to  be  affected  by  them.     And  here  it  is  necessary,  in  the  first  in- 
stance, to  remove  some  degree  of  obscurity  which  may  be  thought  to  hang 
about  the  sense  in  which  the  term  itself  is  to  be  understood  in  speaking  of 
an  orbit,  every  other  element  of  which  is  regarded  as  in  a  continual  state 
of  variation.     Supposing,  then,  that  we  were  to  reverse  the  process  of 
calculation  described  in  arts.  499  and  500  by  which  a  planet's  heliocentric 
longitude  in  an  elliptic  orbit  is  computed  for  a  given  time ;  and  setting 
out  with  a  heliocentric  longitude  ascertained  by  observation,  all  the  other 
elements  being  known,  we  were  to  calculate  either  what  mean  longitude 
the  planet  had  at  a  given  epochal  time,  or,  which  would  come  to  the 
same  thing,  at  what  moment  of  time  (thenceforward  to  be  assumed  as 
an  epoch)  it  had  a  given  mean  longitude.     It  is  evident  that  by  this  I 
means  the  epoch,  if  not  otherwise  known,  would  become  known,  whether 
we  consider  it  as  the  moment  of  time  corresponding  to  a  convenient  mean  j 
longitude,  or  as  the  mean  longitude  corresponding  to  a  convenient  time. 
The  latter  way  of  considering  it  has  some  advantages  in  respect  of  general  I 
convenience,  and  astronomers  are  in  agreement  in  employing,  as  an  ele-l 


VARIATION  OF  THE   EPOCH. 


40T 


influential  on  tbe 
cans  be  concludca 
th  the  maximum, 
sst  excursion  to  or 
that  can  bo  safely 
y  of  tbe  one  orbit 

(tion. 

letary  orbits,  vrbch 

p  node,  tbe  inclina- 

:n,  and  epocb  (art. 

.at  manner  each  of 

ao  direct  action  of 

^t  manner  the  last 

sary,  in  tbe  first  in- 

be  tbougbt  to  bang 

itood  in  speaking  of 

in  a  continual  state 

lerse  tbe  process  o( 

planet's  beliocentric 

1  time }  and  setting 

[vation,  all  tbe  other 

-hat  mean  longitude 

would  come  to  the 

[d  to  be  assumed  as 

evident  that  by  tins 

|ome  known,  whether 

,0  a  convenient  mean 
;o  a  convenient  time. 
[in  respect  of  general 
employing,  as  an  ele- 


ment under  the  title  "  Epoch  of  the  mean  longitude,"  the  mean  longitude 
of  the  planet  so  computed  for  a  fixed  date;  as,  for  instance,  the  commence- 
ment of  the  year  1800,  mean  time  at  a  given  place.  Supposing  now  all 
elements  of  the  orbit  invariable,  if  wo  were  to  go  through  this  reverse 
process,  and  thus  ascertain  the  epoch  (so  defined)  from  any  number  of 
different  perfectly  correct  heliocentric  longitudes,  it  is  clear  we  should 
always  corao  to  the  same  result.  One  and  the  same  "epoch"  would  come 
out  from  all  the  calculations. 

(730.)  Considering  then  the  "epoch"  in  this  light,  as  merely  a  result 
of  this  reversed  process  of  calculation,  and  not  as  the  direct  result  of  an 
observation  instituted  for  tho  purpose  at  the  precise  epochal  moment  of 
time,  (which  would  be,  generally  speaking,  impracticable,)  it  might  be 
conceived  subject  to  variation  in  two  distinct  ways,  viz.  dependently  and 
independently.     Dependently  it  nmst  vary,  as  a  necessary  consequence  of 
the  variation  of  the  other  elements ;  because,  if  setting  out  from  one  and 
the  same  observed  heliocentric  longitude  of  tho  planet,  we  calculate  back 
to  the  epoch  with  two  different  sets  of  intermediate  elements,  the  one  set 
consisting  of  those  which  it  had  immediately  before  its  arrival  at  that 
longitude,  tho  other  that  which  it  takes  up  immediately  after  (^i.  e.  with 
an  unvaried  and  varied  system),  we  cannot  (unless  by  singular  accident  of 
mutual  counteraction)  arrive  at  the  same  result ;  and  the  difference  of  the 
results  is  evidently  the  variation  of  the  epoch.     On  the  other  hand,  how- 
ever, it  cannot  vary  independently  j  for  since  this  is  the  only  mode  in 
which  the  unvaried  and  varied  epochs  can  become  known,  and  as  both 
result  from  direct  processes  of  calculation  involving  only  given  data,  the 
results  can  only  differ  by  reason  of  the  difference  of  those  data.     Or  we 
may  argue  thus.     The  change  in  the  path  of  the  planet,  and  its  place  in 
that  path  so  changed,  at  any  future  time  (supposing  it  to  undergo  no  fur- 
ther variation),  are  entirely  owing  to  the  change  in  its  velocity  and  direc- 
tion, produced  by  the  disturbing  forces  at  the  point  of  disturbance  j  now 
these  latter  changes  (as  we  have  above  seen)  are  comj)l€tely  represented  by 
the  momentary  change  in  the  situation  of  the  upper  focus,  taken  in  com- 
bination with  the  momentary  variation  in  the  plane  of  the  orbit;  and  these 
therefore  express  the  total  effect  of  the  disturbing  forces.    There  is,  there- 
fore, no  direct  and  specific  action  on  the  epoch  as  an  independent  variable. 
It  is  simply  left  to  accommodate  itself  to  the  altered  state  of  things  in  the 
mode  already  indicated. 

(731.)  Nevertheless,  should  the  effects  of  perturbation  by  inducing 
changes  on  these  other  elements  affect  the  mean  longitude  of  the  planet 
in  any  other  way  than  can  be  considered  as  properly  taken  account  of,  by 
the  varied  periodic  time  due  to  a  change  of  axis,  such  effects  must  be  re- 


t^^ 

P 

zS^   1; 

*^TI      t 

-^:2l»       p 

■'^^ 

■f  %.« 

-'-!!         ^ 

■x> 

•*s 

*W  ''.r 

1, 

■^  ^■ 

*>'»      . 

58  .v; 

-f 

'^:% 

-.  ^- 

■» 

:i 

"'    ' 

i 

:^, 

1 

2^^ 

' 

408 


OUTLINES  OP  ASTRONOMY. 


<•■•*■ 
•  •»< 

to  «• 


•v.  c. : 

■fe^  ».V  It 

»■•■.,  ^   , 

EPM»» 


Sac 


gaiilcd  as  incident  on  tho  epoch.  This  is  the  case  with  a  very  curious 
class  of  perturbations  which  wo  are  now  to  consider,  and  which  have  their 
origin  in  an  alteration  of  tho  average  distance  at  which  the  disturbed  body 
id  found  at  every  instant  of  a  complete  revolution,  distinct  from,  and  not 
brought  about  by  tho  variation  of  the  major  semi-axis,  or  momrutary 
"  mean  distance"  which  is  an  imaginary  magnitude,  tc  '  o  carefully  distin- 
guished from  the  avcrgo  of  the  actual  distances  now  contemplated.  Per- 
turbations of  this  class  (like  the  moon's  variation,  with  which  they  arc 
intimately  connected)  are  independent  on  the  excentricity  of  tho  diiiturhed 
orbit;  for  which  reason  we  shall  simplify  our  treatment  of  this  part  of  tiio 
subject,  by  supposing  that  orbit  to  have  no  permanent  excentricity,  tlio 
upper  focus  in  its  successive  displacements  merely  revolving  about  a  mciin 
position  coincident  with  the  lower.  We  shall  also  suppose  M  very  dis- 
tant, as  in  the  lunar  theory. 

(732.)  Keferring  to  what  is  said  in  arts.  706  and  707,  and  to  the  figures 
accompanying  those  articles,  and  considering  first  the  effect  of  the  tangential 
force,  we  see  that  besides  the  elTect  of  that  force  in  changing  tho  length 
of  tho  axis,  and  consequently  tho  periodic  time,  it  causes  the  upper  focus 
H  to  describe,  in  each  revolution  of  P,  a  four-ousped  curve,  «,  i,  d,  e, 
about  S,  all  whose  intercuspidal  arcs  are  similar  and  equal.  This  supposes 
M  fixed,  and  at  an  invariable  distance, — suppositions  which  simplify  the 
relations  of  the  subject,  and  (as  we  shall  afterwards  show)  do  not  aifcct 
the  general  nature  of  the  conclusions  to  be  drawn.  In  virtue,  then,  of 
the  excentricity  thus  given  rise  to,  P  will  be  at  the  perigee  of  its  momen- 
tary ellipse  at  syzygies  and  in  its  apogee  at  quadratures.  Apart,  therefore, 
from  the  change  arising  from  the  variation  of  axis,  the  distance  of  P 
from  S  will  be  less  at  syzygies,  and  greater  at  quadratures,  than  in  the 
original  circle.  But  the  average  of  all  the  distances  during  a  whole  revo- 
lution will  be  unaltered ;  because  the  distances  of  a,  d,  b,  e,  from  S  beiug 
equal,  and  the  arcs  symmetrical,  the  approach  in  and  about  perigee  will 
be  equal  to  the  recess  in  and  about  the  apogee.  And,  in  like  manner,  the 
effect  of  the  changes  going  on  in  the  length  of  the  axis  itself,  on  the 
average  in  question,  is  nilj  because  tho  alternate  increases  and  decreases 
of  that  length  balance  each  other  in  a  complete  revolution.  Thus  we  see 
that  tho  tangential  force  is  excluded  from  all  influence  in  producing  the 
class  of  perturbations  now  under  consideration. 

(733.)  It  is  otherwise  with  respect  to  the  normal  forco.  In  virtue  of 
the  action  of  that  force  the  upper  focus  describes,  in  each  revolution  of  P, 
the  four-cusped  curve  (fig.  art.  707),  whose  intercuspidal  arcs  are  alter- 
nately of  very  unequal  extent,  arising,  as  we  have  seen,  from  the  longer 
duration  and  greater  energy  of  the  outward  than  of  the  inward  action  of 


tho  disti 
apogee  « 
opproucl 
wliolo  n 
distance 
orbit.     J 
change  ii 
produce. 
(734.) 
velocity  i 
effect  of  t 
motion  roi 
The  avern 
crease  wit 
higher  rati 
areas,  is  in 
being  (in  t 
turb  that  e 
of  a  whole  ; 
of  conjpleti 
than  in  tho 
reference  to 
or  "  mean  n 
out  (as  is  ea 
perturbation 
disturbed  or 
a  retardation 
tho  average  i 
/735.)  Tl 
principles,  of 
alteration  of 
of  the  outwa; 
—  nearly  as  ' 
formed  into  i 
diameter  as  tc 
ponderant  fon 
't  is  clear  thai 
attractions  on 
centre,  the  fo 
centre  is  man 
any  one  direct 


INEQUALITIES   INCIDENT   ON   THE   EPOCH. 


409 


;uriou8 
•c  tbcir 
id  body 
ind  not 
nn\to)-y 
y  distin- 
l.     Vor- 
tliey  arc 
I'wturbed 
kvt  i>f  the 
•icity,  t\»c 
it  a  mciin 
very  dis- 

tbe  figures 

tangential 

tho  length 

ippcr  focu8 

,  0,  h  ''>  c, 

is  supposes 

implify  the 

0  not  affect 

ic,  then,  of 
its  TOomen- 
!,  therefore, 
tanco  of  P 
jan  in  the 
whole  revo- 
cm  S  being 
perigee  will 
manner,  the 
self,  on  the 
|d  decreases 
'hu3  we  see 
oducing  the 

In  virtue  of 

llution  of  P, 

Is  are  alter- 

the  longer 

Id  action  of 


tho  disturbing  force.  Altiiough,  thorofnro,  in  perigee  at  syzygios  and  in 
apogee  at  quadratures,  the  apogeal  recess  is  iimch  greater  than  tho  pcrigoal 
approach,  inasmuch  a^  S  (/  greatly  exceeds  S  *i.  On  tho  average  of  n 
whole  revolution,  then,  tho  recesses  will  preponderate,  and  tho  average 
disianco  will  therefore  bo  greater  in  tho  disturbed  than  in  tho  undisturbed 
orbit.  And  it  is  manifest  that  this  conclu.sioii  is  quite  independent  of  any 
change  in  tho  length  of  tho  axis,  which  tho  normal  force  has  no  power  to 
produce. 

(734.)  But  neither  does  tho  normal  force  operate  any  change  of  linear 
velocity  in  tho  disturbed  body.     When  carried  out,  therefore,  by  tho 
cffet'tof  that  force  to  a  greater  distance  from  8,  the  angular  velocity  of  its 
motion  round  S  will  be  diminished  :  and  contniriwiso  when  brought  nearer. 
The  average  of  all  tho  momentary  angular  motions,  therefore,  will  de- 
crease with  the  increase  in  that  of  tho  momentary  distances ;  and  in  a 
higher  ratio,  since  tho  angular  velocity,  under  an  equable  description  of 
areas,  is  inversely  as  tho  square  of  tho  distance,  and  the  disturbing  force, 
being  (in  tho  case  supposed)  directed  to  or  from  tho  centre,  does  not  dis- 
turb that  equable  description  (art.  G16).     Consequently,  on  the  average 
of  a  whole  revolution,  the  angular  motion  is  slower,  and  therefore  tho  tirao 
of  completing  a  revolution,  and  returning  to  the  same  longitude,  longer 
than  in  tho  undisturbed  orbit,  and  that  independent  of  and  without  any 
reference  to  tho  length  of  the  momentary  axis,  and  tho  "  periodic  tirao  " 
or  "mean  motion"  dependent  thereon.     Wo  leave  to  the  reader  to  follow 
out  (as  is  easy  to  do)  tho  same  train  of  reasoning  in  tho  cases  of  planetary 
perturbation,  when  M  is  not  very  remote,  and  when  it  is  interior  to  the 
disturbed  orbit.     In  ihe  latter  case  tho  preponderant  effect  changes  from 
a  retardation  of  angular  velocity  to  an  acceleration,  and  tho  dilatation  of 
the  average  dimensions  of  P's  orbit  to  a  contraction. 

(735.)  The  above  is  an  accurate  analysis,  according  to  strict  dynamical 
principles,  of  an  effect  which,  speaking  roughly,  may  be  assimilated  to  an 
alteration  of  M's  gravitation  towards  S  by  the  mean  preponderant  amount 
of  the  outward  and  inward  action  of  the  normal  forces  constantly  exerted 
— nearly  as  would  be  tho  case  if  the  mass  of  the  disturbing  body  were 
formed  into  a  ring  of  uniform  thickness,  concentric  with  S,  and  of  such 
diameter  as  to  exert  an  action  on  P  everywhere  equal  to  such  mean  pre- 
ponderant force,  and  in  the  same  direction  as  to  inwards  or  outwards.  For 
it  is  clear  that  the  action  of  such  n  ring  on  P,  will  bo  the  diflFerence  of  its 
attractions  on  the  two  points  P  and  S,  of  which  the  latter  occupies  its 
centre,  the  former  is  excentric.  Now  the  attraction  of  a  ring  on  its 
1  centre  is  manifestly  cqucl  in  all  directions,  and  therefore,  estimated  in 
I  any  one  direction,  is  zero.     On  the  other  hand,  on  a  point  P  out  of  its 


'^t.laS 


^1 


It' 


410 


OUTLINES   OF  ASTRONOMY. 


''.  *iaui 


■'«•? 


«J;; 


ilr-^ 


i     '■■■■> 


^K, 


«ii« 


centre,  if  within  the  ring,  the  resulting  attraction  will  always  be  outwards, 
towards  the  nearest  point  of  the  ring,  or  directly  from  the  centre.'  But 
if  P  lie  without  the  ring,  the  resulting  force  will  act  always  inwards, 
urging  P  towards  its  centre.  Hence  it  appears  that  the  mean  effect  of 
the  radial  force  of  the  ring  will  be  different  in  its  direction,  according  as 
the  orbit  of  the  disturbing  body  is  exterior  or  interior  to  that  of  the  dis- 
turbed. In  the  former  case  it  will  act  in  diminution,  in  the  latter  in 
augmentation  of  the  central  gravity. 

(736.)  Regarding,  still,  only  the  mean  effect,  as  produced  in  a  great 
number  of  revolutions  of  both  bodies,  it  is  evident  that  such  an  increase 
of  central  force  will  be  accompanied  with  a  diminution  of  periodic  time 
and  distance  of  a  body  revolving  with  a  stated  velocity,  and  vice  vcrsd. 
This,  as  we  have  shown,  is  the  first  and  most  obvious  effect  of  the  radial 
part  of  the  disturbing  force,  when  exactly  analyzed.  It  alters  permanently, 
and  by  a  certain  mean  amount,  the  distances  and  times  of  revolution  of 
all  the  bodies  composing  the  planetary  system,  from  what  they  would  be, 
did  each  planet  circulate  about  the  sun  uninfluenced  by  the  attraction  of 
the  rest;  the  angular  motion  of  the  interior  bodies  of  the  system  being 
thus  rendered  less,  and  those  of  tho  exterior  greater,  than  on  that  suppo- 
sition. The  latter  effect,  indeed,  might  be  at  once  concluded  from  this 
obvious  consideration,  —  that  all  the  planets  revolving  interiorly  to  any 

»  As  this  is  a  proposition  which  the  equilibrium  of  Saturn's  ring  renders  not  merely 
speculative  or  illustrative,  it  will  be  well  to  demonstrate  it;  which  may  be  done  very 
eimply,  and  without  the  aid  of  any  calculus.    Conceive  a  spherical  shell,  and  a  point 
within  it :  every  line  passing  through  the  point,  and  terminating  both  ways  in  the  shell, 
will,  of  course,  be  equally  inclined  to  its  surface  at  either  end,  being  n  chord  of  a  sphe- 
rical surface,  and  therefore  symmetrically  related  to  all  its  parts.    Now,  conceive  a 
small  double  cone,  or  pyramid,  having  its  apex  at  the  point,  and  formed  by  the  conical 
motion  of  such  a  line  round  the  point.     Then  will  the  two  portions  of  the  spherical 
shell,  which  form  the  bases  of  both  the  cones,  or  pyramids,  bo  similar  and  equally  in- 
clined to  their  axes.    Therefore  their  areas  will  be  to  each  other  as  the  squares  of  their 
distances  from  the  common  apex.    Therefore  their  attractions  on  it  will  be  equal,  be- 
cause the  attraction  is  as  the  attracting  mutter  directly,  and  the  square  of  its  distance 
inversely.     Now,  these  attractions  act  in  opposite  directions,  and  therefore  counteract 
each  other.    Therefore  the  point  is  in  equilibrium  between  them  ;  and  as  the  same  is  | 
true  of  every  such  pair  of  areas  into  which  the  spherical  shell  can  be  broken  up,  there- 
fore the  point  will  be  in  equilibrium  however  situated  within  such  a  spherical  shell,  j 
Now  take  a  ring,  and  treat  it  similarly,  breaking  its  circumference  up  info  pairs  of  ele- 
mtnts,  the  bases  of  triangles  formed  by  lines  passing  through  the  attracted  point, 
Here  the  attracting  elements  being  linet,  not  lurfaees,  are  in  the  simple  ratio  of  the  j 
distanccfi,  not  the  duplicate,  as  they  should  be  to  maintain  the  equilibrium.     Therefore 
it  will  not  be  maintained,  but  tho  nearest  elements  will  have  the  superiority,  and  the  I 
point  will,  on  the  whole,  be  urged  towards  the  nearest  part  of  the  ring.    The  sameisl 
true  of  every  linear  ring,  and  is  therefore  true  of  any  assemblage  of  concentric  onesj 
forming  a  flat  annulus,  like  the  ring  of  Saturn. 


INEQUALITIES   INCIDENT   ON  THE   EPOCH. 


411 


be  outwards, 
centre.'  But 
rays  imcards, 
nean  effect  of 
1,  according  as 
liat  of  the  dis- 
1  the  latter  in 

iced  in  a  great 
iuch  an  increase 
,f  periodic  time 
and  vice  versd. 
ect  of  the  radial 
Lcrs  permanently, 
of  revolution  of 
it  they  would  he, 
the  attraction  of 
the  system  heing 
mn  on  that  suppo- 
included  from  this 
interiorly  to  any 

ig  renders  not  merely 

,oh  may  be  done  very 

Ileal  shell,  and  a  point 

,0th  ways  in  the  shell, 

■ingachordofasphe. 

ft8  Now,  conceive  a 
formed  by  the  conical 
■tions  of  the  spherical 
limilar  and  equally  in- 
as  the  squares  of  their 

,n  it  will  be  equal,  be- 
square  of  its  distance 
,d  therefore  countcraci 
p  .  and  as  the  same  is 
In  be  broken  up,  there- 
,uch  a  spherical  shell 
icc  up  into  pairs  oleic 
,h  the  attracted  pomt. 
'the  simple  ratio  of  th« 
UiUbrium.    Theretore 
,e  superiority,  and  ihe 
Ithering.    The  same 
age  of  concentnc  one! 


orbit  may  be  considered  as  adding  to  the  general  aggregate  of  the  attract- 
ing matter  within,  which  is  not  the  less  efficient  for  being  distributed  over 
space,  and  maintained  in  a  state  of  circulation. 

(737.)  This  effect,  however,  is  one  which  we  have  no  means  of  mea- 
suring, or  even  of  detecting,  otherwise  than  by  calculation.  For  our 
knowledge  of  the  periods  of  the  planets  is  drawn  from  observations  made 
on  them  in  their  actual  state,  and  therefore  under  the  influence  of  this, 
which  may  be  regarded  as  a  sort  of  constant  part  of  the  perturbative 
action.  Their  observed  mean  motions  are  therefore  affected  by  the  whole 
amount  of  its  influence ;  and  we  have  no  means  of  distinguishing  this  by 
observation  from  the  direct  effect  of  the  sun's  attraction,  with  which  it  is 
blended.  Our  knowledge,  however,  of  the  masses  of  the  planets  assures 
us  that  it  is  extremely  small ;  and  this,  in  fiict,  is  all  which  it  is  at  all 
important  to  us  to  know,  in  the  theory  of  their  motions. 

(738.)  The  action  of  the  sun  upon  the  moon,  in  like  manner,  tends,  by 
its  mean  influence  during  many  successive  revolutions  of  both  bodies,  to 
increase  permanently  the  moon's  distance  and  periodic  time.  But  this 
general  average  is  not  established,  either  in  the  case  of  the  moon  or 
planets,  without  a  series  of  subordinate  fluctuations,  which  we  have  pur- 
posely neglected  to  take  account  of  in  the  above  reasoning,  and  which 
obviously  tend,  in  the  average  of  a  great  multitude  of  revolutions,  to 
neutralize  each  other.  In  the  lunar  theory,  however,  some  of  these  sub- 
ordinate fluctuations  are  very  sensible  to  observation.  The  most  conspi- 
cuous of  these  is  the  moon's  annual  equation ;  so  called  because  it  consists 
in  an  alternate  increase  and  decrease  in  her  longitude,  corresponding  with 


Fig.  105. 


^ 


the  earth's  situation  in  its  annual  orbit  j  i.  e.  to  its  angular  distance  from 
the  perihelion,  and  therefore  having  n  year  instead  of  a  month,  or  aliquot 
part  of  a  month,  for  its  period.  To  understand  the  mode  of  its  produc- 
tion, let  us  suppose  the  sun,  still  holding  a  fixed  position  in  longitude,  to 
approach  gradually  nearer  to  the  earth.  Then  will  all  its  disturbing  forces 
be  gradually  increased  in  a  very  high  ratio  compared  with  the  diminution 
of  the  distance  (being  inversely  as  its  cube ;  so  that  its  effects  of  every 
kind  are  three  times  greater  in  respect  of  any  change  of  distance,  than 


'f 

y«?«* 

'l». 

>MBar 

IN. 

'«Ml>«   y^ 

1.1 

«.fl»- 

'*, 

n^iw 

■if 

*;» 

?" 

' 

ft»@' 

%.•> 

'•*■! 

'•45 

f^^^ 

»•*(■» 

* 

■'«!* 

■■^^ 

^ 

1 

-M 

..h     -If 


.jiii't 


412 


OUTLINES   OF   ASTRONOMY. 


'I 


•».*" 
^•i* 


,i^-^ 


fcVlUt 


.'/ 


If'*'*-*. 


a»» 


** 


I- 

If:;?: 


they  would  be  by  the  simple  law  of  proportionality).  Hence,  it  is  obvious 
that  the  focus  H  (art,  707)  in  the  act  of  describing  each  intercuspidal  arc 
of  the  curve  a,  d,  b,  c,  will  be  continually  carried  out  farther  and  farther 
from  S ;  and  the  curve,  instead  of  returning  into  itself  at  the  end  of  each 
revolution,  will  open  out  into  a  sort  of  cuspidated  spiral,  as  in  the  figure 
annexed.  Retracing  now  the  reasoning  of  art.  733,  as  adapted  to  this 
state  of  things,  it  will  be  seen  that  so  long  as  this  dilatation  goes  on,  so 
long  will  the  difference  between  M's  recess  from  S  in  aphclio  and  its 
approach  in  perihelio  (which  is  equal  to  the  diflference  of  consecutive  long 
and  short  semidiameters  of  this  curve)  also  continue  to  increase,  and  with 
it  the  average  of  the  distances  of  M  from  S  in  a  whole  revolution,  and 
consequently  also  the  time  of  performing  such  a  revolution.  The  reverse 
process  will  go  on  as  the  sun  again  recedes.  Thus  it  appears  that,  as  the 
sun  approaches  the  earth,  the  mean  angular  motion  of  the  moon  on  the 
average  of  a  whole  revolution  will  diminish,  and  the  duration  of  each 
lunation  will  therefore  exceed  that  of'  the  foregoing,  and  vice  vcrsd. 

(739.)  The  moon's  orbit  bein^  supposed  circular,  the  sun's  orbitual 
motion  will  have  no  other  effect  than  to  keep  the  moon  longer  under  the 
influence  of  every  gradation  of  the  disturbing  force,  than  would  hpvc  been 
the  case  had  his  situation  in  longitude  remained  unaltered  (art.  711.)  The 
effects,  therefore,  will  take  place  only  on  an  increased  scale  in  the  propor- 
tion of  the  increased  time ;  i.  e.  in  the  proportion  of  the  synodic  to  the 
sidereal  revolution  of  the  moon.  Observation  confirms  these  results,  and 
assigns  to  the  inequality  in  question  a  maximum  value  of  between  10'  and 
11',  by  which  the  moon  is  at  one  time  in  advance  of,  and  at  another  be- 
hind, its  mean  place,  in  consequence  of  this  perturbation. 

(740.)  To  this  class  of  inequalities  we  must  refer  one  of  great  import- 
ance, and  extending  over  an  immense  period  of  time,  known  by  the  name 
of  the  secular  acceleration  of  the  moon's  mean  motion.  It  had  been 
observed  by  Dr.  Halley,  on  comparing  together  the  records  of  the  most 
ancien'o  lunar  eclipses  of  the  Chaldean  astronomers  with  those  of  modern 
times,  that  the  period  of  the  moon's  revolution  at  present  is  sensibly 
shorter  than  at  that  remote  epoch ;  and  this  result  was  confirmed  by  a 
further  comparison  of  both  sets  of  observations  with  those  of  the  Arabian 
astronomers  of  tho  eighth  and  ninth  centuries.  It  appeared,  from  these 
comparisons,  that  the  rate  at  which  the  moon's  mean  motion  increases  is 
about  11  seconds  per  century,  —  a  quantity  small  in  itself,  but  becoming 
considerable  by  its  accumulation  during  a  succession  of  ages.  This  re- 
markable ftict,  like  the  great  equation  of  Jupiter  and  Saturn,  had  been 
long  the  subject  of  toilsome  investigation  to  geometers.  Indeed,  so 
difficult  did  it  appear  to  render  any  exact  account  of,  that  while  some 


ANNUAL  INEQUALITY  OP  THE   MOON. 


418 


were  on  the  point  of  again  declaring  the  theory  of  gravity  inadequate  to 
its  exphmation,  others  were  for  rejecting  altogether  the  evidence  on  which 
it  rested,  although  quite  as  satisfactory  as  that  on  which  most  historical 
events  are  credited.  It  was  in  this  dilemma  that  Laplace  once  more 
stepped  i  i  to  rescue  physical  astronomy  from  its  reproach,  by  pointing  out 
the  real  cause  of  the  phaenomenon  in  question,  which,  when  so  explained, 
is  one  of  the  most  curious  and  instructive  in  the  whole  range  of  our  sub- 
ject,—  one  which  leads  our  speculations  farther  into  the  past  and  future, 
and  points  to  longer  vistas  in  the  dim  perspective  of  changes  which  our 
system  has  undergone  and  is  yet  to  undergo,  than  any  other  which  obser- 
vation assisted  by  theory  has  developed. 

(741.)  The  year  is  not  an  e.xact  number  of  lunations.     It  consists  of 
twelve  and  a  fraction.     Supposing  then  the  sun  and  moon  to  set  ou«,  from 
conjunction  together;  at  the  twelfth  conjunction  subsequent  the  sun  will 
not  have  returned  precisely  to  the  same  point  of  its  annual  orbit,  but  will 
fall  somewhat  short  of  it,  and  at  the  thirteenth  will  have  overpassed  it. 
Hence  in  twelve  lunations  the  gain  of  longitude  during  the  first  half  year 
will  be  somewhat  under  and  in  thirteen  somewhat  over-compensated.    In 
twenty-six  it  will  be  nearly  twice  as  much  over-compensated,  in  thirty-nine 
not  quite  so  nearly  three  times  as  much,  and  so  on,  until,  after  a  certain 
number  of  such  multiples  of  a  lunation  have  elapsed,  the  sun  will  be 
found  half  a  revolution  in  advance,  and  in  place  of  receding  farther  at  the 
expiration  of  the  next,  it  will  have  begun  to  approach.     From  this  time 
every  succeeding  cycle  will  destroy  some  portion  of  that  over-eompensa- 
tion,  until  a  complete  revolution  of  the  sun  in  excess  shall  be  accom- 
plished.    Thus  arises  a  subordinate  or  rather  supplementary  inequality, 
having  for  its  period  as  many  years  as  is  necessary  to  multiply  the  defi- 
cient arc  into  a  whole  revolution,  at  the  end  of  which  time  a  much  more 
exact  compensation  will  have  been  operated,  and  so  on.     Thus  after  a 
moderate  number  of  years  an  almost  perfect  compensation  will  be  effected, 
and  if  we  extend  our  views  to  centuries  we  may  consider  it  as  quite  so. 
Such  at  least  would  be  the  case  if  the  solar  ellipse  were  invariable.     But 
that  ellipse  is  kept  in  a  continual  but  excessively  slow  state  of  change  by 
the  action  of  the  planets  on  the  earth.     Its  axis,  it  is  true,  remains  unal- 
tered; but  its  excentricity  is,  and  has  been  since  the  earliest  ages,  dimin- 
ishing; and  this  diminution  will  continue  (there  is  little  reason  to  doubt) 
—till  the  excentricity  is  annihilated  altogether,  and  the  earth's  orbit  becomes 
itself,  but    e  m  ^^^^^^  circle ;  after  which  it  will  again  open  out  into  an  ellipse,  the 

n  of  ages.       ,  ,    _  ■excentricity  will  again  increase,  attain  a  certain  moderate  amount,  and 
d  Saturn,  ^"  HtheQ  again  decrease.     The  time  required  for  these  evolutions,  though 

[meters,     i"  ^    '     ■calculable,  has  not  been  calculated,  further  than  to  saiisfy  us  that  it  is 
of,  that  while  soBOF 


tee,  it  is  obvious 
ntercuspidal  arc 
■ther  and  farther 
the  end  of  each 
,  as  in  the  figure 

adapted  to  this 
tation  goes  on,  so 
I  aphclio  and  its 
:  consecutive  long 
increase,  and  with 
le  revolution,  and 
tion.    The  reverse 
ppcars  that,  as  the 
■  the  moon  on  the 
3  duration  of  each 
id  vice  versd. 
the  sun's  orbitual 
on  longer  under  the 
an  would  h?vve  been 
ered(art.7U.)The 
scale  in  the  propor- 

the  synodic  to  the 
ms  these  results,  and 

of  between  10'  and 

and  at  another  be-  , 

lion. 

lone  of  great  import- 
known  by  the  name 
Mon.    It  bad  been 
records  of  the  most 
nth  those  of  modern 
present  is  sensibly 
was  confirmed  by  a 
Ithose  of  the  Arabian 

ippeared,  from  these 
motion  increases  i3 
becoming 
This  re- 
had  been  | 
Indeed,  so  l 


•«■    >:.r 


' '   '!  ■ 

•III,; 

*%; 
|9m 


V. 


]l\ 


i 


414 


OUTLINES   OF  ASTRONOMY. 


■mtwA 

■'  rn li- 
te*. 


if 


**iNi 


^* 


not  to  be  reckoned  by  hundreds  or  by  thousands  of  years.  It  is  a  period, 
in  short,  in  which  the  whole  history  of  astronomy  and  of  the  human  race 
occupies  but  as  it  were  a  point,  during  which  all  its  changes  are  to  be 
regarded  as  uniform.  Now,  it  is  by  this  variation  in  the  cxccntricity  of 
the  earth's  orbit  that  the  secular  acceleration  of  the  moon  is  caused.  The 
compensation  above  spoken  of  (even  after  the  lapse  of  centuries)  will  now, 
we  see,  be  only  imperfectly  effected,  owing  to  this  slow  shifting  of  one 
of  the  essential  data.  The  steps  of  restoration  are  no  longer  identical 
with,  nor  equal  to,  those  of  change.  The  struggle  up  bill  is  not  main- 
tained on  equal  terms  with  the  downward  tendency.  The  ground  is  all 
the  while  slowly  sliding  beneath  the  feet  of  the  antagonists.  During  the 
whole  time  that  the  earth's  excentricity  is  diminishing,  a  preponderance 
is  given  to  the  reaction  over  the  action ;  and  it  is  not  till  that  diminution 
shall  cease,  that  the  tables  will  be  turned,  and  the  process  of  ultimate 
restoration  will  commence.  Meanwhile,  a  minute,  outstanding,  and  un- 
compensated effect  in  favour  of  acceleration  is  left  at  each  recurrence,  or 
near  recurrence,  of  the  same  configurations  of  the  sun,  the  moon,  and  the 
solar  perigee.  These  accumulate,  and  at  length  affect  the  moon's  longi- 
tude to  an  extent  not  to  be  overlooked. 

(742.)  The  phaenomenon,  of  which  we  have  now  given  an  account,  is 
another  and  very  striking  example  of  the  propagation  of  a  periodic  change 
from  one  part  of  a  system  to  another.  The  planets,  with  one  exception, 
have  no  direct  appreciable  action  on  the  lunar  motions  as  referred  to  the 
earth.  Their  masses  are  too  small,  and  their  distances  too  great,  for  their 
difference  of  action  on  the  moon  and  earth  ever  to  become  sensible.  Yet 
their  effect  on  the  earth's  orbit  is  thus,  we  see,  propagated  through  the 
sun  to  that  of  the  moon ;  and,  what  is  very  remarkable,  the  transmitted 
effect  thus  indirectly  produced  on  the  angle  described  by  the  moon  round 
the  earth  is  more  sensible  to  observation  than  that  directly  produced  by 
them  on  the  angle  described  by  the  earth  round  the  sun. 

(743.)  Referring  to  the  reasoning  of  art.  738,  we  shall  perceive  that 
if,  owing  to  any  other  cause  than  its  elliptic  motion,  the  sun's  distance 
from  *he  earth  be  subject  to  a  periodical  increase  and  decrease,  that  varia- 
tior  vill  give  rise  to  a  lunar  inequality  of  equal  period  analogous  to  the 
annual  equation.  It  thus  happens  that  very  minute  changes  impressed 
on  the  orbit  of  the  earth,  by  the  direct  action  of  the  planets,  (provided 
their  periods,  though  not  properly  speaking  secular,  be  of  considerable 
length,)  may  make  themselves  sensible  in  the  lunar  motions.  The  longi- 
tude of  that  satellite,  as  observed  from  the  earth,  is,  in  fact,  singularly 
sensible  to  this  kind  of  reflected  action,  which  illustrates  in  a  striking 
manner  the  principle  of  forced  vibrations  laid  dowJ  in  art.  650.    Th» 


INDIRECT  ACTION   OF  VENUS  ON  THE  MOON. 


415 


It  is  a  period, 
be  human  race 
ages  arc  to  bo 
eccentricity  of 
s  caused.     The 
.uries)  mW  now, 
shifting  of  one 
longer  identical 
ill  is  not  main- 
ae  ground  is  all 
sts.    During  the 
a  preponderance 
1  that  diminution 
rocess  of  ultimate 
standing,  and  un- 
sach  recurrence,  or 
the  moon,  and  the 
b  the  moon's  longi- 

riven  an  account,  is 

If  a  periodic  change 

vith  one  exception, 

as  referred  to  the 

too  great,  for  their 

ome  sensible.  Yet 
igated  through  the 
,le,  the  transmitted 
by  the  moon  round 
irectly  produced  by 

shall  perceive  that 
the  sun's  distance 
decrease,  that  varia- 
,od  analogous  to  the 
changes  impressed 
planets,  (provided 
be  of  considerable 
lotions.    The  longi- 
5,  in  fact,  singularly 
,trates  in  a  striking 
in  art.  650.    Th« 


reason  of  this  will  be  readily  apprehended,  if  we  consider  that  however 
trifling  the  increase  of  her  longitude  which  would  arise  in  a  single  revolu- 
tion, from  a  minute  and  almost  infinitesimal  increase  of  her  mean  angu- 
lar velocity,  that  increase  is  not  only  repeated  in  each  subsequent  revolu- 
tion, but  is  reinforced  during  each  by  a  similar  fresh  accession  of  angular 
motion  generated  in  its  lapse.     This  process  goes  on  so  long  as  the  angu- 
lar motion  continues  to  increase,  and  only  begins  to  be  reversed  when 
lapse  of  time,  bringing  round  a  contrary  action  on  the  angular  motion, 
shall  have  destroyed  the  excess  of  velocity  previously  gained,  and  begun 
to  operate  a  retardation.    In  this  respect,  the  advance  gained  by  the  moon 
on  her  undisturbed  place  may  be  assimilated,  during  its  increase,  to  the 
space  described  from  rest  under  the  action  of  a  continually  accelerating 
force.     The  velocity  gained  in  each  instant  is  not  only  effective  in  carry- 
ing the  body  forward  during  each  subsequent  instant,  but  new  velocities 
are  every  instant  generated,  and  go  on  adding  their  cumulative  effects  to 
those  before  produced. 

(744.)  The  distance  of  the  earth  from  the  sun,  like  that  of  the  moon 
from  the  earth,  may  be  affected  in  its  average  value  estimated  over  long 
periods  embracing  many  revolutions,  in  two  modes,  conformably  to  the 
theory  above  delivered.     1st,  it  may  vary  by  a  variation  in  the  length  of 
the  axis  major  of  its  orbit,  arising  from  the  direct  action  of  some  tangen- 
tial disturbing  force  on  its  velocity,  and  thereby  producing  a  change  of 
mean  motion  and  periodic  time  in  virtue  of  the  Keplerian  law  of  periods, 
which  declares  that  the  periodic  times  are  in  the  sesquiplicate  ratio  of  the 
mean  distances.     Or,  2dly,  it  may  vary  by  reason  of  that  peculiar  action 
on  the  average  of  actual  distances  during  a  revolution,  which  arises  from 
variations  of  exccntrieity  and  perihelion  only,  and  which  produces  that 
sort  of  change  in  the  mean  motion  which  we  have  characterized  as  inci- 
dent on  the  epoch.    The  change  of  mean  motion  thus  arising,  has  nothing 
whatever  to  do  with  any  variation  of  the  major  axis.     It  does  not  depend 
on  the  change  of  distance  by  the  Keplerian  law  of  periods,  but  by  that 
of  ureas.    The  altered  mean  motion  is  not  sub-sesquiplicate  to  the  altered 
axis  of  the  ellipse,  which  in  fact  does  not  alter  at  all,  but  is  suh-diipli- 
cate  to  the  altered  average  of  distances  in  a  revolution;  a  distinction 
which  must  be  carefully  borne  in  mind  by  every  one  who  will  clearly  un- 
derstand either  the  subject  itself,  or  the  force  of  Newton's  explanation 
of  it  in  the  6th  Corollary  of  his  celebrated  66th  Proposition.     In  which- 
ever mode,  however,  an  alteration  in  the  mean  motion  is  effected,  if  we 
accommodate  the  general  sense  of  our  language  to  the  specialities  of  the 
iCasc,  it  remains  true  that  every  change  in  the  mean  motion  is  accompa- 
Died  with  a  corresponding  change  in  the  mean  distance. 


il 


"*<.'; 


%im9 


'& 


•,'.t.   ,^r 
■•t    , 

■J'                 i 
''  '"'                  1 

Pi:             1 

'*"*           1 

•i.t«              n 

416 


OUTLINES   OF  ASTRONOMY. 


tt:;» 


•M 


(745.)  Now  we  have  seen  (art.  726),  that  Venus  produces  in  the  earth 
a  perturbation  in  lengitude,  of  so  long  a  period  (240  years),  that  it  can- 
not well  be  regarded  without  violence  to  ordinary  language,  otherwise  than 
as  un  equation  of  the  mean  motion.  Of  course,  therefore,  it  follows  that 
during  that  half  of  this  long  period  of  time,  in  which  the  earth's  motion 
is  retarded,  the  distance  between  the  sun  and  earth  is  on  the  increase,  and 
vic<i  versd.  Minute  as  is  the  ei*uation  in  question,  and  consequent  altera- 
tion of  solar  distance,  and  almost  inconceivably  minute  as  is  the  effect 
produced  on  the  moon's  mean  angular  velocity  in  a  single  lunation,  yet 
the  great  number  of  lunations  (1484),  during  which  the  effect  goes  on 
accumulating  in  one  direction,  causes  the  moon,  at  the  moment  whon  that 
accumulation  has  attained  its  maximum  to  be  very  sensibly  in  advance  of 
its  undisturbed  place  (viz.  by  23"  of  longitude),  and  after  1484  more 
lunations,  as  mm;h  in  arrear.  The  calculations  by  which  this  curious 
result  has  been  established,  formidable  from  their  length  and  intricacy, 
are  due  to  the  industry,  as  the  discovery  of  its  origin  is  to  the  sagacity, 
of  Professor  Hansen. 

(746.)  The  action  of  Venus,  just  explained,  is  indirect,  being  as  it 
were  a  sort  of  reflection  of  its  influence  on  the  earth's  orbit.  But  a  very 
remarkable  instance  of  its  influence,  in  actually  perturbing  the  moon's  mo- 
tions by  its  direct  attraction,  has  been  pointed  out,  and  the  inequality  due 
to  it  computed  by  the  same  eminent  geometer.'  As  the  details  of  his 
processes  have  not  yet  appeared,  we  can  here  only  explain,  in  gciieiai 
terms,  the  principle  on  which  the  result  in  question  depends,  and  the 
nature  of  the  peculiar  adjustment  of  the  mean  angular  velocities  of  the 
earth  ?nd  Venus  which  render  it  effective.  The  disturbing  forces  of 
Venus  on  the  moon  are  capable  of  being  represented  or  expressed  (as  is 
indeed  generally  the  case  with  all  the  forces  concerned  in  producing  pla- 
netary disturbance)  by  the  substitution  for  them  of  a  series  of  other  forces, 
each  having  a  period  or  cycle  within  which  it  attains  a  maximum  in  one 
direction,  decreases  to  nothing,  reverses  its  action,  attains  a  maximum  in 
the  opposite  direction,  again  decreases  to  nothing,  again  reverses  its  action, 
and  rcattains  its  former  magnitude,  and  so  on.  These  cycles  differ  for 
each  particular  constituent  or  term,  as  it  is  called,  of  the  total  forces  con- 
sidered as  so  broken  up  into  partial  ones,  md,  generally  speaking,  every 
combination  which  can  be  formed  by  subtracting  a.  multiple  of  the  mean 
motion  of  one  of  the  bodies  concerned  from  a  multiple  of  that  of  the 
other,  and  when  there  are  three  bodies  disturbing  one  another,  every  such 
triple  combination  becomes,  under  the  technical  name  of  an  argument, 
the  cyclical  representative  of  a  force  acting  in  the  manner  and  according 
*  Astronoinische  Nachrichten,  No.  597. 


(  ■-  -.'1-TirT   t 


DIRECT  ACTION   OF   VENUS   ON  THE   MOON. 


417 


a  in  the  earth 
j),  that  it  can- 
otherwise  than 
it  follows  that 
earth's  motion 
le  increase,  and 
isequent  altcra- 
as  is  the  effect 
;le  lunation,  yet 
3  effect  goes  on 
)ment  whon  that 
ly  in  advance  of 
after  1484  more 
lich  this  curious 
th  and  intricacy, 
a  to  the  sagacity, 

lirect,  heing  as  it 
orbit.    But  a  very 
ng  the  moon's  nio- 
the  inequality  tluc 
the  details  of  liis 
xplain,  in  gei»fral 
depends,  and  the 
XX  velocities  of  tbe 
[sturhing  forces  of 
or  expressed  (as  is 
'  in  producing  pla- 
-ries  of  other  forces, 
a  maximum  in  one 
dns  a  maximum  in 
reverses  its  action, 
se  cycles  differ  for 
the  total  forces  con- 
illy  speaking,  every 
altiple  of  the  mean 
liple  of  that  of  the 
another,  every  such 
,e  of  an  argument, 
inner  and  according 


to  the  law  described.     Each  of  these  periodically  acting  forces  produces 
its  perturbative  effect,  according  to  the  law  of  the  superposition  of  small 
motions,  as  if  the  others  had  no  existence.     And  if  it  happen,  as  in  an 
immense  majority  of  cases  it  does,  that  the  cycle  of  any  particular  one  of 
these  partial  forces  has  no  relation  to  the  periodic  time  of  the  disturbed 
body,  so  as  to  bring  it  to  the  same,  or  very  nearly  the  same  point  of  its 
orbit,  or  to  any  situation  favourable  to  any  particular  form  of  disturbance, 
over  and  over  again  when  the  force  is  at  its  maximum ;  that  force  will,  in 
a  few  revolutions,  neutralize  its  own  effect,  and  nothing  but  fluctuations 
of  brief  duration  can  result  from  its  action.     The  contrary  will  evidently 
be  the  case,  if  the  cycle  of  the  force  coincide  so  nearly  with  the  cycle  of 
the  moon's  anomalistic  revolution,  as  to  bring  round  the  maximum  of  the 
force  acting  in  one  and  the  same  direction  (whether  tangential  or  normal) 
either  accurately,  or  very  nearly  indeed  to  some  definite  point,  as,  for  ex- 
ample, the  apogee  of  her  orbit.     Whatever  the  effect  produced  by  such  a 
force  on  the  angular  motion  of  the  moon,  if  it  be  not  exactly  compen- 
sated in  one  cycle  of  its  action,  it  will  go  on  accumulating,  being  repeated 
over  and  over  again  under  circumstances  very  nearly  the  same,  for  many 
successive  revolutions,  until  at  length,  owing  to  the  want  of  precise  accu- 
racy in  he  adjustment  of  that  cycle  to  the  anomalistic  period,  the  maxi- 
mum of  tl'.G  force  (in  the  same  phase  of  its  action)  is  brought  to  coincide 
with  a  point  in  tbe  orbit  (as  the  perigee),  determinative  of  an  opposite 
effect,  and  thus,  at  length  a  compensation  will  be  worked  out;  in  a  time, 
however,  so  much  the  longer  as  the  difference  between  the  cycle  of  the 
force  and  the  moon's  anomalistic  period  is  less. 

(747.)  Now,  in  fact,  in  the  case  of  Venus  disturbing  the  moon,  there 
exists  a  cyclical  combination  of  this  kind.  Of  course  the  disturbing  f  jrce 
of  Venus  on  the  moon  varies  with  her  distance  from  the  earth,  and  this 
distance  again  depends  on  her  configuration  with  respect  to  the  earth  and 
the  sun,  taking  into  account  the  ellipticity  of  both  their  orbits.  Among 
the  combinations  which  take  their  rise  from  this  latter  consideration,  and 
which,  as  may  oasily  be  supposed,  are  of  great  complexity,  there  is  a  term 
(an  exceedingly  minute  one),  whose  argument  or  cycle  is  determined  by 
subtracting  16  times  the  mean  motion  of  the  earth  from  18  times  that  of 
Venus.  The  difference  is  so  very  nearly  the  mean  motion  of  the  moon 
in  her  anomalistic  revolution,  that  whereas  the  latter  revolution  is  com- 
pleted in  27*  13"  18-  32 -3',  the  cycle  of  the  force  is  completed  in  27" 
IS''  7'"  Zb-Q*,  differing  from  the  other  by  no  more  than  10"  56-7',  or 
about  one  3625th  part  of  a  complete  period  of  the  moon  from  apogee  to 
I  apogee.  During  half  of  this  very  long  interval  (that  is  to  say,  during 
I  about  136i  years),  the  perturbations  produced  by  a  force  of  this  character, 
27 


'"U.r. 


Iili: 


».^ 


-;3 


^ 


■«Ji, 


2r*: 


t»fll 


418 


OUTLINES   OP   ASTRONOMY. 


W  r»«,. 


ir 


K: 


•<*•< 


*«*i 


8ii 


go  on  increasing  and  accumulating,  and  are  destroyed  in  another  equal  in- 
terval. Although  therefore  excessively  niinuto  in  their  actual  eftoct  on 
tlie  angular  motion,  this  minuteness  is  compensated  by  the  number  of  re- 
peated acts  of  accumulation,  and  by  the  length  of  time  during  which  they 
continue  to  act  on  the  longitude.  Accordingly  M.  Hansen  has  found  the 
total  amount  of  fluctuation  to  and  fro,  or  the  value  of  the  equation  of  the 
moon's  longitude  so  arising,  to  be  274".  It  is  exceedingly  interesting  to 
observe  that  the  two  equations  considered  in  these  latter  paragraphs', 
account  satisfactorily  for  the  only  remaining  material  differences  between 
theory  and  observation  in  the  modern  history  of  this  hitherto  rebellious 
satellite.  We  have  not  thought  it  necessary  (indeed  it  would  have  required 
a  treatise  on  the  subject)  to  go  into  a  special  account  of  the  almost  innu- 
merable other  lunar  inequalities  which  have  been  computed  and  tabulated, 
and  which  are  necessary  to  be  taken  into  account  in  every  computation 
of  her  place  from  the  tables.  Many  of  them  are  of  very  much  larger 
amount  than  these.  We  ought  not,  however,  to  pass  unnoticed,  that  the 
parallactic  inequality,  already  explained  (art.  712),  is  interesting,  as  afford- 
ing a  measure  of  the  sun's  distance.  For  this  equation  originates,  as  there 
shown,  in  the  fact  that  the  disturbing  forces  are  not  precisely  alike  in  the 
two  halves  of  the  moon's  orbit  nearest  to  and  most  remote  fr^n  the  sun, 
all  their  values  being  greater  in  the  former  half.  As  a  knowledge  of  the 
relative  dimensions  of  the  solar  and  lunar  orbits  enables  us  to  calculate  a 
priori,  the  amount  of  this  inequality,  so  a  knowledge  of  that  amount 
deduced  by  the  comparison  of  a  great  number  of  observed  places  of  the 
moon  with  tables  in  which  every  inequality  but  this  should  be  included, 
would  enable  us  conversely  to  ascertain  the  ratio  of  the  distances  in  ques- 
tion. Owing  to  the  smallness  of  the  inequality,  this  is  not  a  very  accu- 
rate mode  of  obtaining  an  element  of  so  much  importance  in  astronomy 
as  the  sun's  distance,  but  were  it  larger  (i.  e.  were  the  moon's  orbit  con- 
siderably larger  than  it  actually  is),  this  would  be,  perhaps,  the  most 
exant  method  of  any  by  which  it  could  be  concluded. 

(7'^8.)  The  greatest  of  all  the  lunar  inequalities,  produced  by  pertur- 
bation, is  that  called  the  evecf.ion      It  arises  directly  from  the  variation 
of  the  exc€ntricity  of  her  orbit,  and  from  the  fluctuation  to  and  fro  in  the 
general  progress  of  the  line  of  apsides,  caused  by  the  different  situation 
of  the  sun,  with  respect  to  that  line  (arts.  685,  691).     Owing  to  these 
causes  the  moon  is  alternately  in  advance,  and  in  arrear  of  her  elliptic  | 
place  by  about  1°  20'  20".     This  equation  was  known  to  the  ancients, 
having  been  discovered  by  Ptolemy,  by  the  comparison  of  a  long  series! 
of  observations,  handed  down  to  him  from  the  earliest  ages  of  astronomy.  [ 
The  mode  in  which  the  effects  of  these  several  sources  of  inequality  be-j 


EFFECT   or  THE   EARTIl'S   SPHEROIDAL   FIGURE. 


410 


motlicr  equal  in- 
actual  effect  ou 
lie  number  of  rc- 
uring  which  they 
sen  has  found  the 
le  equation  of  the 
igly  interesting  to 
latter  paragraplis, 
ifferences  between 
hitherto  rebellious 
■ould  have  required 
f  the  almost  innu- 
uted  and  tabulated, 
every  computuiion 
'  very  much  larger 
unnoticed,  that  the 
Qteresting,  as  afford- 
[\  originates,  as  there 
recisely  alike  in  the 
•emote  fr^^-n  the  sun, 
,  a  knowledge  of  the 
)le8  us  to  calculate  a 
idge  of  that  amount 
(served  places  of  the 
should  be  included, 
he  distances  in  ques- 
is  not  a  very  accu- 
>rtance  in  astronomy 
[he  moon's  orbit  con- 
,e,  perhaps,  the  most 

produced  by  pertur- 
Ily  from  the  variation 
Ition  to  and  fro  in  the 
Ihe  different  situation 
[l).     Owing  to  these 
1  arrear  of  her  elliptic 
[own  to  the  ancients, 
^•ison  of  a  long  series 
£st  ages  of  astronomy.  [ 
frees  of  inequality  be-l 


come  grouped  together  under  one  prir'- pal  argument,  common  to  them 
all,  belongs,  for  its  explanation,  rather  to  works  specially  treating  of  the 
lunar  theory  than  to  a  treatise  of  this  kind. 

(749.)  Some  small  perturbations  are  produced  in  the  lunar  orbit  by 
the  protuberant  matter  of  the  earth's  equator.    The  attraction  of  a  sphere 
is  tbo  same  as  if  all  its  matter  were  condensed  into  a  point  in  its  centre ; 
but  that  is  not  the  case  with  a  spheroid.     The  attraction  of  such  a  mass 
is  neither  exactly  directed  to  its  centre,  nor  does  it  exactly  follow  the  law 
of  the  inverse  squares  of  the  distances.     Hence  will  arise  a  scries  of 
perturbations,  extremely  small  in  amount,  but  still  perceptible  in  the 
lunar  motions,  by  which  the  node  and  the  apogee  will  be  affected.     A 
more  remarkable  consequence  of  this  cause,  however,  is  a  small  nutation 
of  the  lunar  orbit,  exactly  analogous  to  that  which  the  moon  causes  in 
the  plane  of  the  earth's  equator,  by  its  action  on  the  same  elliptio  protu- 
berance.   And,  in  general,  it  may  be  observed,  that  in  the  systems  of 
planets  which  have  satellites,  the  elliptic  figure  of  the  primary  has  a  ten- 
dency to  bring  the  orbits  of  the  satellites  to  coincide  with  its  equator, — a 
tendency  which,  though  small  in  the  case  of  the  earth,  yet  in  that  of  Jupiter, 
whose  ellipticity  is  very  considerable,  and  of  Saturn  especially,  where  the 
cllipticity  of  the  body  is  reinforced  by  the  attraction  of  the  rings,  becomes 
predominant  over  every  external  and  internal  cause  of  disturbance,  and 
produces  and  maintains  an  almost  exact  coincidence  of  the  planes  in 
question.     Such,  at  least,  is  the  case  with  the  nearer  satellites.     The 
More  distant  are  compa'-tively  less  effected  by  this  cause,  the  difference 
of  attractions  between  a  sphere  and  spheroid  diminishing  with  great  ra- 
pidity as  the  distance  increases.    Thus,  while  the  orbits  of  all  the  interior 
satellites  of  Saturn  lie  almost  exactly  in  the  plane  of  the  ring  and  equator 
of  the  planet,  that  of  the  external  satellite,  whose  distance  from  Saturn 
is  between  sixty  and  seventy  diameters  of  the  planet,  is  inclined  to  that 
plane  considerably.     On  the  other  hand,  this  considerable  distance,  while 
it  permits  the  satellite  to  retain  its  actual  inclination,  prevents  (by  parity 
of  reasoning)  the  ring  and  equator  of  the  planet  from  being  perceptibly 
disturbed  by  its  attraction,  or  being  subjected  to  any  appreciable  move- 
ments analogous  to  our  nutation  and  precession.     If  such  exist,  they 
must  be  much  slower  than  those  of  the  earth ;  the  mass  of  this  satellite 
being,  as  far  as  can  be  judged  by  its  apparent  size,  a  much  smaller  frac- 
tion of  that  of  Saturn  than  the  moon  is  of  the  earth ;  while  the  solar 
precession,  by  reason  of  the  immense  distance  of  the  sun,  must  be  quite 
imperceptible. 

(750.)  The  subject  of  the  tides,  though  rather  belonging  to  terrestrial 
physics  than  properly  to  astronomy,  is  yet  so  directly  connected  vrith  the 


4 


m 

Mm 


*l 

■if: 


^.1 


ll 


|i 


420 


OUTLINES  OP  ASTRONOMY. 


.•2* 


••f. 


fe 


theory  of  the  lunar  perturbations,  that  we  cannot  omit  some  explanatory 
notice  of  it,  especially  since  many  persons  find  a  strange  difficulty  in  con- 
ceiving the  manner  in  which  they  are  produced.  That  the  sun,  or  moon, 
should  by  its  attraction  heap  up  the  waters  of  the  ocean  under  it,  seems 
to  them  very  natural.  That  it  should  at  the  same  time  heap  them  up  on 
the  opposite  side  seems,  on  the  contrary,  palpably  absurd.  The  error  of 
this  class  of  objectors  is  of  the  same  kind  with  that  noticed  in  art.  723, 
and  consists  in  disregarding  the  attraction  of  the  disturbing  body  on  the 
mass  of  the  earth,  and  looking  on  it  as  wholly  effective  on  the  superficial 
water.  Were  the  earth  indeed  absolutely  fixed,  held  in  its  place  by  an 
external  force,  and  the  water  left  free  to  move,  no  doubt  the  eflFect  of  the 
disturbing  power  would  be  to  produce  a  single  accumulation  vertically 
under  the  disturbing  body.  But  it  is  not  by  its  whole  attraction,  but  by 
the  difference  of  its  attractions  on  the  superficial  water  at  both  sides,  and 
on  the  central  mass,  that  the  waters  are  raised :  just  as  in  the  theory  of 
the  moon,  the  difference  of  the  sun's  attractions  on  the  moon  and  on  the 
earth  (regarded  as  moveable  and  as  obeying  that  amount  of  attraction 
which  is  due  to  its  situation)  gives  rise  to  a  relative  tendency  in  the  moon 
to  recede  from  the  earth  in  conjunction  and  opposition,  and  to  approach 
it  in  quadratures.  Referring  to  the  figure  of  art.  675,  instead  of  sup- 
posing A  D  B  C  to  represent  the  moon's  orbit,  let  it  be  supposed  to  repre- 
sent a  section  of  the  (comparatively)  thin  film  of  water  reposing  on  the 
globe  of  the  earth,  in  a  great  circle,  the  plane  of  which  passes  through 
the  disturbing  body  M,  which  we  shall  suppose  to  be  the  moon.  The 
disturbing  force  on  a  particle  at  P  will  then  (exactly  as  in  the  lunar 
theory)  be  I'epresented  in  amount  and  direction  by  N  S,  on  the  same  scale 
on  which  S  M  represents  the  moon's  whole  attraction  on  a  particle  situ- 
ated at  S.  This  force,  applied  at  P,  will  urge  it  in  the  direction  PX 
parallel  to  N  S ;  and  therefore;  when  compounded  with  the  direct  force  of 


\\ 


gravity  which  (neglecting  as  of  no  account  in  this  theoiy  the  spheroidal 


OF  THE   TIDES. 


421 


ne  explnnatory 
lifficulty  in  con- 
le  Bun,  or  moon, 
under  it,  seems 
leap  them  up  on 
I.    The  error  of 
ticed  in  art.  723, 
bing  body  on  the 
on  the  superficial 
in  its  place  by  an 
;  the  effect  of  the 
miation  vertically 
attraction,  but  by 
at  both  sides,  and 
IS  in  the  theory  of 
e  moon  and  on  the 
lount  of  attraction 
idency  in  the  moon 
an,  and  to  approach 
75,  instead  of  sup- 
supposed  to  repro- 
ver reposing  on  the 
[icb  passes  through 
the  moon.    The 
^ly  as  in  the  lunar 
i,  on  the  same  scale 
on  a  particle  situ- 
the  direction  PX 
the  direct  force  of 


leory  the  spheroidal 


form  ot'  the  earth)  urges  P  towards  S,  will  bo  equivalent  to  a  single  force 
deviating  from  the  direction  P  S  towards  X.     Suppose  P  T  to  be  the  di- 
rection of  this  forco,  which,  it  is  easy  to  see,  will  be  directed  towards  a 
point  in  D  S  produced,  at  un  extremely  small  distance  below  S,  because 
of  the  excessive  minuteness  of  the  disturbing  force  compared  to  gravity.' 
Then  if  this  be  done  at  every  point  of  the  quadrant  A  D,  it  will  bo  evi- 
dent that  the  direction  P  T  of  the  resultant  force  will  be  always  that  of  a 
tangent  to  the  small  cuspidated  curve  advX  T,  to  which  tangent  the  sur- 
face of  the  ocean  at  P  nuist  everywhere  be  perpendicular,  by  reason  of 
that  law  of  hydrostatics  which  requires  the  direction  of  gravity  to  be 
everywhere  perpendicular  to  the  surface  of  a  fluid  in  equilibrio.     The 
form  of  the  curve  D  P  A,  to  which  the  surface  of  the  ocean  will  tend  to 
conform  itself,  so  as  to  place  itself  everywhere  in  equilibrio  under  two 
acting  forces,  will  bo  that  which  always  has  P  T  for  its  radius  of  curva- 
ture.    It  will  therefore  be  slightly  less  curved  at  D,  and  more  so  at  A, 
being  in  fact  no  other  than  an  ellipse,  hut'ing  S  for  its  centre,  da  for  its 
auhdCy  and  S  /> ,  S  D  for  its  longer  and  shorter  semi-axes  respectively ;  so 
that  the  whole  uuifuce  (supposing  it  covered  with  water)  will  tend  to  as- 
sume, as  its  form  of  equilibrium,  that  of  an  oblongated  ellipsoid,  having 
its  longer  axis  directed  towards  the  disturbing  body,  and  its  shorter  of 
course  at  right  angles  to  that  direction.     The  difference  of  the  longer  and 
shorter  semi-axes  of  this  ellipsoid  due  to  the  moon's  attraction  would  be 
about  58  inches :  that  of  the  ellipsoid,  similarly  formed  in  virtue  of  the 
sun,  about  2J^  times  less,  or  about  23  inches. 

(751.)  Let  us  suppose  the  moon  only  to  act,  and  to  have  no  orbitual 

motion ;  then  if  the  earth  also  had  no  diurnal  motion,  the  ellipsoid  of 

[equilibrium  would  be  quietly  formed,  and  all  would  be  thenceforward 

tranquil.     There  is  never  time,  however,  for  this  spheroid  to  be  fully 

formed.     Before  the  waters  can  take  their  level,  the  moon  has  advanced 

Id  her  orbit,  both  diurnal  and  monthly,  (for  in  this  theory  it  will  answer 

Ithe  purpose  of  clearness  better,  if  we  suppose  the  earth's  diurnal  motion 

[transferred  to  the  sun  and  moon  in  the  contrary  direction,)  the  vertex  of 

Ithe  spheroid  has  shifted  on  the  earth's  surface,  and  the  ocean  has  to  seek 

la  new  bearing.     The  effect  is  to  produce  an  immensely  broad  and  exces- 

lavely  flat  wave  (not  a  circulating  current),  which  follows,  or  endeavours 

'  According  to  Newton's  calculation,  the  maximum  disturbing  force  of  the  sun  on  the 
"fater  does  not  exceed  one  2573C400th  part  of  its  gravity.  That  of  the  moon  will 
lliercforo  be  to  this  fraction  as  ihe  cube  of  the  sun's  distance  to  that  of  the  moon's  di- 
■ecily,  and  as  the  mass  of  the  sun  to  that  of  the  moon  inversely,  t.  e.  as  (400)'  X  0012517 
1354936,  which,  reduced  to  numbers,  gives,  for  the  moon's  maximum  of  power  to  dis- 
prb  the  waters,  about  one  11400000th  of  gravity,  or  somewhat  less  than  2i  times  the 
Inn's. 


"fmmm 


■^ 


•'.r 


1' 

M.  ■ 

•♦■ 

I 

■lif 

'■;l 


422 


OUTLINES   OF  ASTRONOMY. 


»c  ■■'■-'<■. 


t 


to  follow,  tho  apparent  motions  of  tho  moon,  and  must,  in  fuct,  by  the 
principle  of  forced  vibrations,  imitate,  by  oi|ual  though  not  by  iti/nrhroiwiiH 
periods,  oil  tho  periodical  inequalities  of  that  motion.  When  the  highor 
or  lower  parts  of  this  wave  strike  our  coasts,  they  experience  what  wo 
call  high  and  low  water. 

(752.)  Tho  sun  also  produces  precisely  such  a  wave,  whose  vertex  tends 
to  follow  the  apparent  motion  of  tho  sun  in  the  heavens,  and  also  to  imi- 
tate its  periodic  inequalities.  This  solar  wave  co-exists  with  the  lunar — 
is  sometimes  superposed  on  it,  sometimes  transverse  to  it,  so  as  to  partly 
neutralize  it,  according  to  the  monthly  synodical  configuration  of  the  two 
luminaries.  This  alternate  mutual  reinforcement  and  destruction  of  the 
solar  and  lunar  tides  cause  what  are  called  tho  spring  and  neap  tides — the 
former  being  their  sum,  the  latter  their  diiferencc.  Although  tho  real 
amount  of  either  tide  is,  at  present,  hardly  within  the  reach  of  exact  cal- 
culation, yet  their  proportion  at  any  one  place  is  probably  not  very  remote 
from  that  of  the  ellipticities  which  would  belong  to  their  respective  sphe- 
roids, could  an  equilibrium  be  attained.  Now  these  ellipticities,  for  the 
solar  and  lunar  spheroids,  are  respectively  about  two  and  five  feet ;  so  that 
the  average  spring  tide  will  be  to  tho  neap  as  7  to  3,  or  thereabouts. 

(753.)  Another  effect  of  the  combination  of  the  solar  and  lunar  tides 
is  what  is  called  the  priming  and  lagyiwj  of  the  tides.  If  the  moon 
alone  existed,  and  moved  in  the  plane  of  the  equator,  the  tide-day  (i*.  e. 
the  interval  between  two  successive  arrivals  at  the  same  place  of  the  same 
vertex  of  the  tide-wave)  would  be  the  lunar  day  (art.  143),  formed  by 
the  combination  of  the  moon's  sidereal  period  and  that  of  the  earth's 
diurnal  motion.  Similarly,  did  the  sun  alone  exist,  and  move  always  on 
the  equator,  the  tide-day  would  be  the  mean  solar  day.  The  actual  tide- 
day,  then,  or  the  interval  of  the  occurrence  of  two  successive  maxima  of 
their  superposed  waves,  will  vary  as  the  separate  waves  approach  to  or  re- 
cede from  coincidence ;  because,  when  the  vertices  of  two  waves  do  not 
coincide,  their  joint  height  has  its  maximum  at  a  point  intermediate  be- 
tween them.  This  variation  from  uniformity  in  the  lengths  of  successive  i 
tide-days  is  particularly  to  be  remarked  about  tho  time  of  the  new  and  | 
full  moon. 

(754.)  Quite  different  in  its  origin  is  that  deviation  of  the  time  of  higli  j 
and  low  water  at  any  port  or  harbour,  from  the  culmination  of  the  lumi- 
naries, or  of  the  theoretical  maximum  of  their  superposed  spheroids,  which  j 
is  called  the  "establishment"  of  that  port.  If  the  water  were  without | 
inertia,  and  free  from  obstruction,  either  owing  to  the  friction  of  the  bodi 
of  the  sea,  the  narrowness  of  channels  along  which  the  wave  has  to  travail 
before  reaching  the  port,  their  length,  &c.,  &c.,  the  times  above  distiuj 


OF  THE  TIDES. 


423 


^  iu  fact,  by  the 
I  by  ni/ucliro»oiiK 
^icn  tho  higher 
)orienco  Vfbat  wo 

hoso  vortex  tends 
I,  onil  alao  to  imi- 
with  the  lunar— 
t,  80  aa  to  partly 
iration  of  tho  two 
destruction  of  the 
id  neap  tides— the 
Although  the  real 
reach  of  exact  cal- 
bly  not  very  remote 
eir  respective  sphc- 
cllipticities,  for  the 
nd  five  feet  J  so  that 

or  thereabouts. 
)lar  and  lunar  tides 
tides.    If  the  moon 
,r,  the  tide-day  («'.  <•■ 
le  place  of  the  same 
irt.  143),  formed  by 
that  of  the  earth's 
md  move  always  on 
ly.     The  actual  tide- 
iccessive  maxima  of 
res  approach  to  or  re- 
>f  two  waves  do  not 
jint  intermediate  be- 
[lengths  of  successive  I 
time  of  the  new  and 

L  of  the  time  of  high 
Lation  of  thelumi- 
Led  spheroids,  wW 
>  vyater  were  without  | 
L  friction  of  the  U 
the  wave  has  to  travel 
L  times  above  distiu-l 


guished  would  be  identical.  IJiit  all  thcHO  causes  tend  to  create  a  dif- 
ference, and  to  make  that  diU'orciico  not  alike  at  all  portn.  Tho  observa- 
tion of  the  establishments  of  harbours  is  a  point  of  great  maritime  im- 
portance; nor  is  it  of  loss  consequence,  theoretically  speaking,  to  a 
knowledge  of  tho  true  distribution  of  tho  tide-waves  over  tho  globe.  In 
making  such  observations,  care  must  be  taken  not  to  confound  the  time 
of  "slack  water,"  when  the  current  caused  by  the  tide  ceases  to  flow 
vi-sibly  one  way  or  the  other,  and  that  of  Jn'i/h  or  low  nutter,  when  the 
level  of  the  surface  ceases  to  rise  or  fall.  Tlioso  are  totally  distinct  phw- 
nomena,  and  depend  on  entirely  dift'orent  causes,  though  it  is  true  they 
may  sometimes  coincide  iu  point  of  timo.  They  are,  it  is  feared,  too  often 
mistaken  one  for  the  other  by  practical  men  ;  a  circumstance  which, 
whenever  it  occurs,  must  produce  the  greatest  confusion  in  any  attempt  to 
reduce  tho  system  of  the  tides  to  distinct  and  intelligible  laws. 

(755.)  The  declination  of  the  sun  and  moon  materially  affects  the  tides 
at  any  particular  spot.  As  the  vertex  of  the  tide-wave  tends  to  place 
itself  vertically  under  the  luminary  which  produces  it,  when  this  vertical 
changes  it's  point  of  incidence  on  the  surface,  the  tide-wave  must  tend  to 
shift  accordingly,  and  thus,  by  monthly  and  annual  periods,  must  tend  to 
increase  and  diminish  alternately  the  principal  tides.  The  period  of  tho 
moon's  nodes  is  thus  introduced  into  this  subject;  her  excursions  in  de- 
clination in  one  part  of  that  period  being  29",  and  in  another  only  17", 
on  cither  side  the  equator. 

(750.)  Geometry  demonstrates  that  tho  efficacy  of  a  luminary  in  raising 
tides  is  inversely  proportional  ^o  the  cube  of  its  distance.  The  sun  and 
moon,  however,  by  reas<i»n  uf  the  ellipticity  of  their  orbits,  are  alternately 
nearer  to  and  farther  from  the  earth  than  their  mean  distances.  Tn  con- 
sequence of  this,  the  efficacy  of  the  sun  will  fluctuate  between  the  ex- 
tremes 19  and  '21,  taking  20  for  its  mean  value,  and  that  of  the  moon 
between  43  and  59.  Taking  into  account  this  cause  of  difference,  the 
highest  spring  tide  will  be  to  tho  lowest  neap  as  5J>  +  21  lo  43  — 19,  or 
as  80  to  24,  or  10  to  3.  Of  all  the  causes  of  differences  n  the  height 
of  tides  however,  local  situation  is  the  most  influential.  Ir;  soujo  places 
the  tide-wave,  rushing  up  a  narrow  channel,  is  suddenly  raised  to  an  ex- 
traordinary height.  At  Annapolis,  for  instance,  in  the  Bay  of  Fundy,  it 
is  said  to  rise  120  feet.  Even  at  Bristol  the  diftereuce  of  high  and  low 
water  occasionally  amounts  to  50  feet. 

(757.)  It  is  by  means  of  the  perturbations  of  the  planets,  as  ascertained 
by  observation  and  compared  with  theory,  that  we  arrive  at  a  knowledge 
of  the  masses  of  those  planets  which  having  no  satellites,  offer  no  other 
hold  upon  them  for  this  purpose.     Kvery  planet  produces  an  amount  of 


►•# 


1 1 


'..it  I 


424 


OUTLINES   OF  ASTRONOMY. 


IP 


»«•«*" 


'"»»-\ 

'-><•■ 


fc  'f»  "A 


•V. 


jr 


perturbation  in  the  motions  of  every  other,  proportioned  to  its  mass,  and 
to  the  degree  of  advantage  or  purchase  which  its  situation  in  the  system 
gives  it  over  their  movements.  The  latter  is  a  subject  of  exact  calcula- 
tion ;  the  former  is  unknown,  otherwise  than  by  observation  of  its  effects. 
In  the  determination,  however,  of  the  masses  of  the  planets  by  this 
means,  theory  lends  the  greatest  assistance  to  observation,  by  pointing  out 
the  combinations  most  favourable  for  eliciting  this  knowledge  from  the 
confused  mass  of  superposed  inequalities  which  affect  every  observed  place 
of  a  planet ;  by  poiuting  out  the  laws  of  each  inequality  in  its  periodical 
rise  and  decay ;  and  by  showing  how  every  particular  inequality  depends 
for  its  magnitude  on  the  mass  producing  it.  It  is  thus  that  the  mass  of 
Jupiter  itself  (employed  by  Laplace  in  his  investigations,  and  interwoven 
with  all  the  planetary  tables)  has  been  ascertained,  by  observations  of  the 
derangements  produced  by  it  in  the  motions  of  the  ultra-zodiacal  planets, 
to  have  been  insuflficiently  determined,  or  rather  considerably  mistaken, 
by  relying  too  much  on  observations  of  its  satellites,  made  long  ago  by 
Pound  and  others,  with  inadequate  instrumental  means.  The  same  con- 
clusion has  been  arrived  at,  and  nearly  the  same  mass  obtained,  by  means 
of  the  perturbations  produced  by  Jupiter  on  Encke's  comet.  The  error 
was  one  of  great  importance ;  the  mass  of  Jupiter  being  by  far  the  most 
influential  element  in  the  planetary  system,  after  that  of  the  sun.  It  is 
satisfactory,  then,  to  have  ascertained,  as  Mr.  Airy  has  done,  the  cause  of 
the  error ;  to  have  traced  it  up  to  its  source,  in  insufficient  micrometric 
measurements  of  the  greatest  elongations  of  the  satellites ;  and  to  have 
found  it  disappear  when  measures,  taken  with  more  care  and  with  infinitely 
superior  instruments,  are  substituted  for  those  before  employed. 

(758.)  In  the  same  way  that  the  perturbations  of  the  planets  lead  us 
to  a  knowledge  of  their  masses,  as  compared  with  that  of  the  sun,  so  the 
perturbations  of  the  satellites  of  Jupiter  have  led,  and  those  of  Saturn's 
attendants  will  no  doubt  hereafter  lead,  to  a  knowledge  of  the  proportion 
their  masses  bear  to  their  respective  primaries.  The  system  of  Jupiter's 
satellites  has  been  elaborately  treated  by  Laplace ;  and  it  is  from  his 
theory,  compared  with  innumerable  observations  of  their  eclipses,  that  the 
masses  assigned  to  them,  in  art.  540  have  been  fixed.  Few  results  of 
theory  are  more  surprising  than  to  see  these  minute  atoms  weighed  in  the 
same  balance,  which  we  have  applied  to  the  ponderous  mass  of  the  sun, 
which  exceeds  the  least  of  them  in  the  enormous  proportion  of  65,000,000 
tol. 

(759.)  The  mass  of  the  moon  is  concluded,  Ist,  from  the  proportion  of 
the  lunar  to  the  solar  tide,  as  observed  at  various  stations,  the  effects  being 
separated  from  each  other  by  a  long  series  of  observations  of  the  relative 


MASS   OF  THE   MOON   DISCOVERED. 


425 


;o  its  mass,  and 
in  the  system 

f  exact  calcula- 

on  of  its  effects. 

planets  by  this 

^  by  pointing  out 

pledge  from  the 

ry  observed  place 

^  in  its  periodical 

lequality  depends 

that  the  mass  of 

8,  and  interwoven 

,bservations  of  the 

•a-zodiacal  planets, 

iderably  mistaken, 

made  long  ago  by 

I.     The  same  con- 

Dbtained,  by  means 
comet.     The  error 

ling  by  far  the  most 
of  the  sun.     It  is 

I  done,  the  cause  of 
ifficient  micrometric 
llites;  and  to  have 
e  and  with  infinitely 

smployed. 

the  planets  lead  us 
t  of  the  sun,  so  the 
i  those  of  Saturn's 
re  of  the  proportion 
system  of  Jupiter's 
and  it  is  from  his 
.eir  eclipses,  that  the 

>d.    Few  results  of 
itoms  weighed  in  the 

w  mass  of  the  sun, 
portion  of  65,000,000 

jom  the  proportion  of 
Ls,  the  effects  being 
lations  of  the  relative 


heights  of  spring  and  neap  tides  which,  we  have  seen,  (art.  752,)  depends 
on  the  proportional  influence  of  the  two  luminaries.  2dly,  from  the 
phaenornenon  of  nutation,  which,  being  the  result  of  the  moon's  attraction 
alone,  aflFords  a  means  of  calculating  her  mass,  independent  of  any  know- 
ledge of  the  sun's.  Both  methods  agree  in  assigning  to  our  satellite  a 
mass  about  one  seventy-fifth  that  of  the  earth.' 

(760. )  Not  only,  however,  has  a  knowledge  of  the  perturbations  pro- 
duced on  other  bodies  of  our  system  enabled  us  to  estimate  the  mass  of  a 
disturbing  body  already  known  to  exist,  and  to  produce  disturbance.     It 
has  done  much  more,  and  enabled  geometers  to  satisfy  themselves  of  the 
existence,  and  even  to  indicate  the  situation  of  a  planet  previously  un- 
known, with  such  precision,  as  to  lead  to  its  immediate  discovery  on  the 
very  first  occasion  of  pointing  a  telescope  to  tlie  place  indicated.     We 
have  already  (art.  506,)  had  occasion  to  mention  in  general  terras  this 
great  discovery ;  but  its  importance,  and  its  connexion  with  the  subject 
before  us,  calls  for  a  more  specific  notice  of  the  circumstances  attending  it. 
When  the  regular  observation  of  Uranus,  consequent  on  its  discovery  in 
1781,  had  afforded  some  certain  knowledge  of  the  elements  of  its  orbit,  it 
became  possible  to  calculate  backwards  into  time  past,  with  a  view  to 
ascertain  whether  certain  stars  of  about  the  same  apparent  magnitude, 
observed  by  Flamsteed,  and  since  reported  as  missing,  might  not  possibly 
be  this  planet.     No  less  than  six  ancient  observations  of  it  as  a  supposed 
star  were  thus  found  to  have  been  recorded  by  that  astronomer,  —  one  in 
1690,  one  in  1712,  and  four  in  1715.     On  further  inquiry,  it  was  also 
ascertained  to  have  been  observed  by  Bradley  in  1753,  by  Mayer  in  1756, 
and  no  less  than  twelve  times  by  Le  Monnier,  in  1750,  1764, 1768, 1769, 
and  1771,  all  the  time  without  the  least  saspicion  of  its  planetary  nature. 
The  observations,  however,  so  made,  being  all  circumstantially  registered, 
and  made  with  instruments  the  best  that  their  respective  dates  admitted, 
were  quite  available  for  correcting  the  elements  of  the  orbit,  which,  as 
will  be  easily  understood,  is  done  with  so  much  the  greater  precision  the 
larger  the  arc  of  the  ellipse  embraced  by  the  extreme  observations  em- 
ployed.     It  was,  therefore,  reasonably  hoped  and  expected,  that,  by 
making  use  of  the  data  thus  afforded,  and  duly  allowing  for  the  perturba- 
tions produced  since  1690,  by  Saturn,  Jupiter,  and  the  inferior  planets, 
elliptic  elements  would  be  obtained,  which,  taken  in  conjunction  with 
I  those  perturbations,  would  represent  not  only  all  the  observations  up  to 
the  time  of  executing  the  calculations,  but  also  all  future  observations,  in 
I  as  satisfactory  a  manner  as  those  of  any  of  the  other  planets  are  actually 
I  represented.     This  expectation,  however,  proved  delusive.     M.  Bouvard^ 

*  Laplace,  Expos,  du  Syst.  du  Monde,  pp.  285,  SCO. 


J— urn 


tMba 


'.1- 

;* 

I*: 

'1 


%. 


426 


OUTLINES   OF   ASTRONOMY. 


I: 


lie: 

*  — 


C 


k-;  •*  "w 


7^.  •<t-»« 


H-* 


^*^;c 


one  of  the  most  expert  and  laborious  calculators  of  whom  astronomy  has 
had  to  boast,  and  to  whose  zeal  and  indefotigable  industry  we  owe  the 
tables  of  Jupiter  and  Saturn  in  actual  use,  having  undertaken  the  task  of 
constructing  similar  tables  for  Uranus,  found  it  impossible  to  reconcile 
the  ancient  observationa  above  mentioned  with  those  made  from  1781  to 
1820,  so  as  to  represent  both  series  by  means  of  the  same  ellipse  and  the 
same  system  of  perturbations.  He  therefore  rejected  altogether  the  ancient 
series,  and  grounded  his  computations  solely  on  the  modern,  although 
evidently  not  without  serious  misgivings  as  to  the  grounds  of  such  a  pro- 
ceeding, and  "  leaving  it  to  future  time  to  determine  whether  the  difficulty 
of  reconciling  the  two  series  arose  from  inaccuracy  in  the  older  observa- 
tions, or  whether  it  depend  on  some  extraneous  and  unperceivcd  influence 
which  may  have  acted  on  the  planet." 

(761.)  But  neither  did  the  tables  so  calculated  continue  to  represent, 
with  due  precision,  observations  subsequently  made.  The  "  error  of  the 
tables"  after  attaining  a  certain  amount,  by  which  the  true  longitude  of 
Uranus  was  in  advance  of  the  computed,  and  which  advance  was  steadily 
maintained  from  about  the  year  1795  to  1822,  began,  about  the  latter 
epoch,  rapidly  to  diminish,  till,  in  1830-31,  the  tabular  and  observed 
longitudes  agreed.  But,  far  from  remaining  in  accordance,  the  planet, 
still  losing  ground,  fell,  and  continued  to  fall  behind  its  calculated  place, 
and  that  with  such  rapidity  as  to  make  it  evident  that  the  existing  tables 
could  no  longer  be  received  as  representing,  with  any  tolerable  precision, 
the  true  laws  of  its  motion. 

(762.)  The  reader  will  easily  understand  the  nature  and  progression  of 
these  discordancies  by  casting  his  eye  on  fig.  1,  Plate  A,  in  which  the 
horizontal  line  or  abscissa  is  divided  into  equal  parts,  each  representiDg 
50°  of  heliocentric  longitude  in  the  motion  of  Uranus  round  the  sun,  and 
in  which  the  distances  between  the  horizontal  lines  represent  each  100" 
of  error  in  longitude.  The  result  of  each  year's  observation  of  Uranus 
(or  of  the  mean  of  all  the  observations  obtained  during  that  year)  in  lon- 
gitude, is  represented  by  a  black  dot  placed  above  or  below  the  point  of 
the  abscissa,  corresponding  to  the  mean  of  the  observed  longitudes  for  the 
year  above,  if  the  observed  longitude  be  in  excess  of  the  calculated,  below 
if  it  fall  short  of  it,  and  on  the  line  if  they  agree ;  and  at  a  distance  from 
the  line  corresponding  to  their  difference  on  the  scale  above  mentioned.' 


'  The  points  are  laid  down  from  M.  Lcverrier's  comparison  of  liie  whole  scries  of 
observations  of  Uranus,  with  an  ephemeris  of  his  own  calculation,  founded  on  a  com- 
plete and  searching  revision  of  the  tables  of  Bouvard,  and  a  rigorous  computation  of 
the  perturbations  caused  by  all  the  known  planets  capable  of  exercising  any  influence 
on  it.  The  diflerences  of  longitude  aie  geocentric;  but  for  our  present  purpose  it 
matters  not  in  the  least  whether  we  consider  the  errors  in  heliocentric  or  in  geocentric 
longitude.  .  i 


PERTURBATION   OF   URANUS. 


427 


astronomy  bus 
ry  we  owe  the 
:en  the  task  of 
)le  to  reconcile 
,Q  from  1781  to 
ellipse  and  the 
atlier  the  ancient 
odern,  although 
Is  of  such  a  pro- 
her  the  difficulty 
he  older  observa- 
5rceived  influence 

inue  to  represent, 
Che  "  error  of  the 
true  longitude  of 
vancc  was  steadily 
,  about  the  latter 
ular  and  observed 
:dance,  the  planet, 
ts  calculated  place, 
the  existing  tables 
tolerable  precision, 

and  progression  of 
be  A,  in  which  the 
L  each  representing 
[round  the  sun,  and 
represent  each  100" 
ervation  of  Uranus 
[g  that  year)  in  lon- 
I  below  the  point  of 
Id  longitudes  for  the 
[he  calculated,  below 
Id  at  a  distance  from 
above  mentioned.' 

mof  ihewbole  series  oi 

liion,  founded  on  acorn- 

•iBoroufl  computation  ol 

Lxercising  any  influence 

lour  present  purpose  u 

locentric  or  in  geocen«'« 


Thus  in  Flamsteed's  earliest  observations  in  1690,  the  dot  so  marked  is 
placed  above  the  line  at  65"-9  above  the  line,  the  observed  longitude  being 
so  much  greater  than  the  calculated. 

(763.)  If,  neglecting  the  individual  points,  we  draw  a  curve  (indicated 
in  the  figure  by  a  fine,  unbroken  line,)  through  their  general  course,  we 
shall  at  once  perceive  a  certain  regularity  in  its  undulations.     It  presents 
two  great  elevations  above,  and  one  nearly  as  great  intermediate  depres- 
sion below  the  medial  line  or  abscissa.     And  it  is  evident  that  these  un- 
dulations would  be  very  much  reduced,  and  the  errors  in  consequence 
greatly  palliated,  if  each  dot  were  removed  in  the  vertical   direction 
through  a  distance  and  in  the  direction  indicated  by  the  corresponding 
point  of  the  curve  A,  B,  C,  D,  E,  F,  G,  H,  intersecting  the  abscissa  at 
points  180°  distant,  and  making  equal  excursions  on  either  side.     Thus 
the    point  a  for  1750  being  removed   upwards  or  in  the  direction  to- 
wards h  through  a  distance   equal  to  ch,  would  be  brought  almost  to 
precise  coi:<  "''•ncc  with  the  point  e  in  the   abscissa.     Now,  this  is  a 
clear  indica  .       ■  jat  a  very  large  part  of  the  differences  in  question  are 
due,  not  to  j;..,ivarbation,  but  simply  to  error  in  the  elements  of  Uranus, 
which  have   been   assumed  as  the   basis  of  calculation.     For  such  ex- 
cesses and  defects  of  longitude  alternating  over  arcs  of  180°  are  pre- 
cisely what  would  arise  from  error  in  the  excentricity,  or  in  the  place 
of  the  perihelion,  or  in  both.     In  ellipses  slightly  excentric,  the  true  lon- 
gitude alternately  exceeds  and  falls  short  of  the  mean  during  180°  for 
each  deviation,  and  the  greater  the  excentricity,  the  greater  these  alternate 
fluctuations  to  and  fro.     If  then  the  excentricity  of  a  planet's  orbit  be 
assumed  erroneously  (suppose  too  great)  the  observed  longitudes  will  ex- 
hibit a  less  amount  of  such  fluctuation  above  and  below  the  mean  than 
the  computed,  and  the  difference  of  the  two,  instead  of  being,  as  it  ought 
to  be,  always  nil,  will  be  alternately  +  and  —  over  arcs  of  180°.  If  then 
a  difference  be  observed  following  such  a  law,  it  may  arise  from  erro- 
neously assumed  excentricity,  provided  always  the  longitudes  at  which 
they  agree  (supposed  to  differ  by  180°)  be  coincident  with  those  of  the 
perihelion  and  aphelion ;  for  in  elliptic  motion  nearly  circular,  these  are 
the  points  where  the  mean  and  true  longitudes  agree,  so  that  any  fluctua- 
tion of  the  nature  observed,  if  this  condition  be  not  satisfied,  cannot  arise 
from  error  of  excentricity.     Now  the  longitude  of  the  perihelion  of 
Uranus  in  the  element^  employed  by  Bouvard  is  (neglocting  fractions  of 
a  degree)  168°,  and  of  the  aphelion  348°.     These  points,  then,  in  our 
figure,  fall  at  n  and  a,  respectively,  that  is  to  say,  nearly  half  way  between 
A  C,  C  E,  E  Gr,  &c.     It  is  evident,  therefore,  that  it  is  not  to  error  or 
excentricity  that  the  fluctuation  in  question  is  mainly  due. 


I 


428 


OUTLINES   OF  ASTRONOMY. 


0 


■  .<i»  ,3* 


fci  •'»  •'19 


■I     ■^sv 


'•fr 


(764.)  Let  us  now  consider  the  effect  of  an  erroneous  assumption  of 
the  place  of  the  perihelion.  Suppose  in  fig.  2,  Plate  A,  o  a;  to  represent 
the  longitude  of  a  planet,  and  xi/  the  excess  of  its  true  above  its  mean 
longitude,  e  to  ellipticity.  Then  if  R  be  the  place  of  the  perihelion, 
and  P,  or  i,  the  aphelion  in  longitude,  y  will  always  lie  iu  a  certain  un- 
dulating curve  P  Q  Rfi  T,  above'  P  T,  betvireen  R  and  T,  and  below  it 
between  P  and  R.  Now  suppose  the  place  of  the  perihelion  shiftci  for- 
ward to  r,  or  the  whole  curve  shifted  bodily  forward  into  the  situation 
pqrst,  then  at  the  same  longitude  ox,  the  excess  of  the  true  above  the 
mean  longitude  will  be  a:;y0i:ly;  in  other  words,  this  excess  will  have 
diminished  by  the  quantity  i/i/'  below  its  former  amount.  Take  therefore 
in  oN  (Jitj.  3,  PI.  A,)  01/  =  ox  and  1/9/  always  =yj/  in  fi(j.  2,  and 
having  thus  constructed  the  curve  K  L  M  N  0,  the  ordinate  yj/  will 
always  represent  the  effect  of  the  supposed  change  of  perihelion.  It  iS 
evident  (the  excentricity  being  always  supposed  small),  that  this  curve 
will  consist  also  of  alternate  superior  and  inferior  waves  of  180°  each  in 
amplitude,  and  the  points  L,  N  of  its  intersection  with  the  axis,  will 
occur  at  longitudes  corresponding  to  X,  Y,  intermediate  between  the 
maxima  Q,  q ;  and  S,  s  of  the  original  curves,  that  is  to  say  (if  these  in- 
tervals Qg',  S  .s,  or  Rr,  to  which  both  are  equal,  be  very  small,)  very 
nearly  at  90°  from  the  perihelion  and  aphelion.  Now  this  agrees  with 
the  conditions  of  the  case  in  hand,  and  we  are  therefore  authorised  to 
conclude  that  the  major  portion  of  the  errors  in  question  has  arisen  from 
error  in  the  place  of  the  perihelion  of  Uranus  itself,  and  not  from  pertur- 
bation, and  that  to  correct  this  portion,  the  perihelion  must  be  shifted 
somewhat  forward.  As  to  the  amount  of  this  shifting,  our  only  object 
being  explanation,  it  will  not  be  necessary  here  to  inquire  into  it.  It  will 
suflSce  that  it  must  be  such  as  shall  make  the  curve  ABCDEFG  as 
nearly  as  possible  similar,  equal,  and  opposite  to  the  curve  traced  out  by 
the  dots  on  the  other  side.  And  this  being  done,  we  may  next  proceed 
to  lay  down  a  curve  of  the  residual  differences  between  observation  and 
theory  in  the  mode  indicated  in  art.  (763.)      '. 

(765.)  This  being  done,  by  laying  off  at  each  point  of  the  line  of 
longitudes  an  ordinate  equal  to  the  difference  of  the  ordinates  of  the  tuo 
curves  in  fig.  1.  when  on  opposite,  and  their  sum  when  on  the  same  side 
of  the  abscissa,  the  result  will  be  as  indicated  by  the  dots  in  fig.  4.  And 
here  it  is  at  once  seen  that  a  still  farther  reduction  of  the  differences  under 
consideration  would  result,  if,  instead  of  taking  the  lino  A  B  for  the  line 
of  longitudes,  a  line,  a  h,  slightly  inclined  to  it,  were  substituted,  in  which 
case  the  whole  of  the  differences  between  observation  and  theory,  from 

*  The  curves,  Rgi.  2.  3,  are  inverted  in  the  engraving. 


PERTURBATIONS  OF  URANUS  BY  NEPTUNE. 


429 


ssumption  of 
X  to  represent 
)ove  its  mean 
he  perihelion, 
ii  a  certain  un- 
',  and  below  it 
ion  sbiftei  for- 
0  the  situation 
true  above  the 
sxccss  will  have 

Take  therefore 
/  in  fiU-  2,  an^i 
rdinate  ?//  ^^^^ 
jcrihelion.     It  .3 
:,  that  this  curve 
of  180°  each  in 
th  the  axis,  will 
liate  between  the 
0  say  (if  these  in- 
very  small,)  very 
L  this  agrees  with 
[fore  authonsed  to 
jn  has  arisen  from 
[d  not  from  pertur- 

.  must  be  shifted 

.g,  our  only  object 

lire  into  it.    It  ^i^^ 
^BCDEFO  as 

|rve  traced  out  by 
may  next  proceed 
.n  observation  and 

lint  of  the  line  of 
Irdinates  of  the  t^>0 
on  the  same  side 
lots  in  fig.  4.  And 
L  differences  under 
[o  A  B  for  the  line 
Ustituted,  in  which 

and  theory,  from 
Graving. 


1712  to  1800,  would  be  annihilated,  or  at  least  so  far  reduced  ns  hardly 
to  exceed  the  ordinary  error?  of  observation ;  and  as  respects  the  observa- 
tion of  1690,  the  still  outstanding  difference  of  about  35"  would  not  be 
more  than  might  be  attributed  to  a  not  very  careful  observation  at  so  early 
an  epoch.  Now  the  assumption  of  such  a  new  line  of  longitudes  as  the 
correct  one,  is  in  efiect  equivalent  to  the  admission  of  a  slight  amount  of 
error  in  the  periodic  time  and  epoch  of  Uranus;  for  it  is  evident  that  by 
reckoning  from  the  inclined  instead  of  the  horizontal  line,  we  in  efiect 
alter  all  the  apparent  outstanding  errors  by  an  amount  proportional  to  the 
t.  ne  before  or  after  the  date  at  which  the  two  lines  intersect  (viz.  nbout 
Vi2d).  As  to  the  direction  in  which  this  correction  should  be  made,  it  is 
obvious  by  inspection  of  the  course  of  the  dots,  that  if  we  reckon  from 
A  B,  or  any  lino  parallel  to  it,  the  observed  planet  on  the  long  run  keeps 
fulling  more  and  more  behind  the  calculated  one ;  i.  e.  its  assigned  mean 
angular  velocity  by  the  tables  is  too  great,  and  must  be  diminished,  or  its 
periodic  time  requires  to  be  increased. 

(706.)  Let  this  increase  of  period  be  made,  and  in  correspondence  with 
that  change  let  the  longitudes  be  reckoned  on  a  h,  and  the  residual  diffe- 
rences from  that  line  instead  of  A  B,  and  we  shall  have  then  done  all  tha* 
can  be  done  in  the  way  of  reducing  and  palliating  these  differences,  and 
that,  with  such  success,  that  up  to  the  year  1804  it  might  have  been  safely 
asserted  that  positively  no  ground  whatever  existed  for  suspecting  any 
disturbing  influence.     But  with  this  epoch  an  action  appears  to  have 
commenced,  and  gone  on  increasing,  producing  an  acceleration  of  the 
motion  in  longitude,  in  consequence  of  which  Uranus  continually  gains  on 
its  elliptic  place,  and  continued  to  do  so  till  1822,  when  it  ceased  to  gain, 
and  the  excess  of  longitude  was  at  its  maximum,  %fter  which  it  began 
rapidly  to  lose  ground,  and  has  continued  to  do  so  up  m  the  present  time. 
It  is  perfectly  clear,  then,  that  in  this  interval  some  extraneous  cause  must 
have  come  into  action  which  was  not  so  before,  or  not  in  sufficient  power 
to  manifest  itself  by  any  marked  effect,  and  that  that  cause  must  have 
ceased  to  act,  or  rather  begun  to  reverse  its  action,  in  or  about  the  year 
1822,  the  reverse  action  being  even  more  energetic  than  the  direct. 

(767.)  Such  is  the  phoenomenon  in  the  simplest  form  we  are  noiv  able 
to  present  it.  Of  the  various  hypotheses  formed  to  account  for  it,  during 
the  progress  of  its  developement,  none  seemed  to  have  any  degree  of  ra- 
tional probability  but  that  of  the  existence  ^f  an  exterior,  and  hitherto 
undiscovered,  planet,  disturbing,  according  to  the  received  laws  of  plan- 
I  etary  disturbance,  the  motion  of  Uranus  by  its  attraction,  or  rather  super- 
posing its  disturbance  on  those  produced  by  Jupiter  and  Saturn,  the  only 
two  of  the  old  planets  which  exercise  any  sensible  disturbing  action  on 


"2"'' 

■»mmt 


is? 


v^ 


'V 

;t 


430 


OUTLINES   OF  ASTRONOMY. 


SMM^jM. 


''Sim* 

s 


fcv  ll*  •'« 

if* 


yrvm 


thrt  planet.  Accordingly,  this  was  the  explanation  which  naturally,  and 
almost  of  necessity,  suggested  itself  to  those  conversant  with  the  plane- 
tary perturbations  who  considered  the  subject  with  any  degree  of  atten- 
tion. Tl'"  idea,  however,  of  setting  out  from  the  observed  anomalous 
deviatiouf  id  employing  them  as  data  to  ascertain  the  distance  and  situ- 
ation of  o  uuknown  body,  or,  in  other  words,  to  resolve  the  inverse 
problem  of  perturbations,  "  f/ivcii  the  disturbances  to  find  the  orbit,  and 
place  in  that  orbit  of  the  distnrbimj  planet"  appears  to  have  occurred 
only  to  two  mathematicians,  Mr.  Adams  in  England  and  M.  Leverrier  in 
France,  with  sufficient  distinctness  and  hopefulness  of  success  to  induce  them 
to  attempt  its  solution.  Both  succeeded,  and  their  solutions,  arrived  at  with 
perfect  independence,  and  by  each  in  entire  ignorance  of  the  other's  at- 
tempt, were  found  to  agree  in  a  surprising  manner  when  the  nature  and 
difficultj  of  the  problem  is  considered ;  the  calculations  of  M.  Leverrier 
assigning  for  the  heliocentric  longitude  of  the  disturbing  planet  for  the 
23d  Sept.  1846,  326°  0',  and  those  of  Mr.  Adams  (brought  to  the  same 
date)  329°  19',  differing  only  3°  19' ;  the  plane  of  its  orbit  deviating  very 
slightly,  if  it  all,  from  that  of  the  ecliptic. 

(768.)  On  the  day  above  mentioned — a  day  for  ever  memorable  in  the 
annals  of  astronomy — Dr.  CTalle,  one  of  the  astronomers  of  the  Royal 
Observatory  at  Berlin,  received  a  letter  from  M.  Leverrier,  announcing  to 
him  the  result  he  had  arrived  at,  and  requesting  him  to  look  for  the  dis- 
turbing planet  in  or  near  the  place  assigned  by  his  calculation.  He  did 
so,  and  on  that  very  night  actualhj  found  it.  A  star  of  the  eighth  mag- 
nitude was  seen  by  him  and  by  M.  Encke  in  a  situation  where  no  star 
was  marked  as  existing  in  Dr.  Bremiker's  chart,  then  recently  published 
by  the  Berlin  Academy.  The  next  night  it  was  found  to  have  moved 
from  its  place,  and  was  therefore  assuredly  a  planet.  Subsequent  obser- 
vations and  calculations  have  fully  demonstrated  this  planet,  to  which  tlio 
name  of  Neptune  has  been  assigned,  to  be  really  that  body  to  whose  dis- 
turbing attraction,  according  to  the  Newtonian  law  of  gravity,  the  observed 
anomalies  in  the  motion  of  Uranus  were  owing.  The  geocentric  longi- 
tude determined  by  Dr.  Galle  from  this  observation  was  325°  63',  whicli, 
converted  into  heliocentric,  gives  326°  52',  differing  0°  52'  from  M.  Lc- 
verrier's  place,  2°  27'  from  that  of  Mr.  Adams,  and  only  47'  from  a 
mean  of  the  two  calculations. 

(769.)  It  would  be  quite  beyond  the  scope  of  this  work,  and  far  in 
advance  of  the  amount  of  mathematical  knowledge  we  have  assumed  our  i 
readers  to  possess,  to  attempt  giving  more  than  a  superficial  idea  of  the  | 
course  followed  by  these  geometers  in  their  arduous  investigations.    Suf- 
fice it  to  say,  that  it  consisted  in  regarding,  as  unknown  quantities,  to  be 


PERTURBATI  NS  OP  URANUS  BY  NEPTUNE. 


431 


li  naturally,  and 
with  the  plane- 
degree  of  atton- 
erved  anomalous 
iistance  and  situ- 
jolve  the  inverse 
Ind  tlie  orbit,  and 

to  have  occurred 
id  M.  Leverrier  iu 
eess  to  induce  them 
ons,  arrived  at  witU 
J  of  the  other's  at- 
letx  the  nature  and 
ms  of  M.  Leverrier 
Ding  planet  for  the 
brought  to  the  same 

orbit  deviating  very 

rer  memorable  in  tbo 
■omers  of  the  Koyal 
errier,  announcing  to 
ji  to  look  for  the  dis- 
calculation.     He  did 
r  of  the  eighth  mag- 
[uation  where  no  star 
m  recently  published 
,und  to  have  moved 
Subsequent  obser- 
,  planet,  to  which  tk 
^at  body  to  whose  dis- 
f  gravity,  the  observed 

The  geocentric  longi- 
'vya8  325°53',whieb, 

L  0°  52'  from  M.  Lc- 
and  only  47'  from  a 

Ithis  work,  and  far  in 
1  we  have  assumed  our 
I  superficial  idea  of  the 

3  investigations.    Suf- 
kown  quantities,  to  be] 


determined,  the  mass,  and  all  the  elements  of  the  unknown  planet  (sup- 
posed to  revolve  in  the  same  plane  and  the  same  direction  with  Uranus), 
except  its  major  semiaxis.     This  was  assumed  in  the  first  instance  (in 
conformity  with  "  Bode's  law,"  art.  (^05),  and  certainly  at  the  time  with 
a  high  primd  facie  probability,)  to  bo  double  that  of  Uranus,  or  38-364 
radii  of  the  Earth's  orbit.     Without  some  assumption  as  to  the  value  of 
this  element,  owing  to  the  peculiar  form  of  the  analytical  expression  of 
the  perturbations,  the  analytical  investigation  would  have  presented  difii- 
"ilties  apparently  insuperable.     But  besides  these,  it  was  also  necessary 
to  regard  as  unknown,  or  at  least  as  liable  to  corrections  of  unknown 
magnitude  of  the  same  order  as  the  perturbations,  all  the  elements  of 
Uranus  itself,  a  circumstance  whose  necessity  will  be  easily  understood, 
when  we  consider  that  the  received  elements  could  only  be  regarded  as 
provisional,  and  must  certainly  be  erroneous,  the  places  from  which  they 
were  obtained  being  affected  by  at  least  some  portions  of  the  very  pertur- 
bations in   question.     This   consideration,         .gh  indispensable,  added 
vastly  both  to  the  complication  and  the  labour  of  the  inquiry.     The  axis 
(and  therefore  the  mean  motion)  of  the  one  orbit,  then,  being  known  very 
nearly,  and  that  of  the  other  thus  hypothetically  assumed,  it  became  prac- 
ticable to  express  in  terms,  partly  algebraic,  partly  numerical,  the  amount 
of  perturbation  at  any  instant,  by  the  aid  of  general  expressions  delivered 
by  Laplace  in  his  "  3Uc.a)iiqne  Ciltstc'^  and  elsewhere.     These,  then, 
together  with  the  corrections  due  to  the  altered  elements  of  Uranus  itself, 
being  applied  to  the  tabular  longitudes,  furnished,  when  cohapared  with 
those  observed,  a  series  of  equations,  in  which  the  elements  and'mass  of 
Neptune,  and  the  corrections  of  those  of  Uranus  entered  as  the  nnknown 
quantities,  and  by  who.se  resolution  (no  slight  effoit  of  analytical  skill)  all 
their  values  were  at  length  obtained.    The  calculations  were  then  repeated, 
reducing  at  the  same  time  the  value  of  the  assumed  distance  of  the  new 
planet,  the  discordances  between  the  given  and  calculated  results  indicating 
it  to  have  been  assumed  too  large  when  the  results  were  found  to  agree 
better,  and  the  solutions  to  be,  in  fact,  more  satisfactory.     Thus,  at  length, 
elements  were  arrived  at  for  the  orbit  of  the  unknown  planet,  as  below. 


Leverrier. 

Adams. 

Epoch  of  Elements 

Jan.  1,  1847. 

318°  47'  4" 
36-1539 
0-107610 

284°  45'  8" 

000010727 

Oct.  6,  1846. 
323°  2' 
37-2474 
0-120615 
299°  11' 
0-00015003 

Mean  longitude  in  Epoch 

Semiuxis  Mnjor 

Excentricity  

Longitude  of  Perihelion 

'  Miiss  (the  Sun  being  1) 

KM 

fc.l'J 


432 


OUTLINES  OF  ASTRONOMY. 


:!rr- 


fc,  ■*  ••« 


«lt.v    *•    .1... 


The  elements  of  M.  Lcverrier  were  obtained  from  a  consideration  of  the 
observations  up  to  the  year  1845,  those  of  Mr.  Adams  only  as  far  as 
1840.  On  subsequently  taking  into  account,  however,  those  of  the  five 
years  up  to  1845;  the  latter  was  led  to  conclude  that  the  semiaxis  ought 
to  be  still  much  further  diminished,  and  that  a  mean  distance  of  33-33 
(being  to  that  of  Uranus  as  1 :  0*574)  would  probably  satisfy  all  the  obser- 
vations very  nearly.' 

(770.)  On  the  actual  discovery  of  the  planet,  it  was,  of  course,  assidu- 
ously observed,  and  it  was  soon  ascertained  that  a  mean  distance,  even  less 
than  Mr.  Adams's  last  presumed  value,  agreed  better  with  ita  motion ; 
and  no  sooner  were  elements  obtained  from  direct  observation,  sufficiently 
approximate  to  trace  back  its  path  in  the  heavens  for  a  considerable  inter- 
val of  time,  than  it  was  ascertained  to  have  been  observed  as  a  stur  by 
Lalande  on  the  8th  and  10th  of  May,  1795,  the  latter  of  the  two  obser- 
vations, however,  having  been  rejected  by  him  as  faulty,  by  reason  of  its 
non-agreement  with  the  former  (a  consequence  of  the  motion  of  the 
planet  in  the  interval.)  From  these  observations,  combined  with  those 
since  accumulated,  the  elements  calculated  by  Prof.  Walker,  U.  S.,  result 
as  follows: — 


Epoch  of  Elements 

IVIean  longitude  at  Epoch 

Semiaxis  major 

Excentricity 

Longitude  of  the  Perihelion 

Ascending  Node 

Inclination 

Periodic  time 

Mean  annual  Motion 


Jan.  1,  1847,  M.  noon,  Greenwich. 
328°  32'  44" 2 
30-0367 

0  00871946 

47°  1-2'  6"-30 

130°4'20"-81 

l°46'58"-97 
164-6181  tropical  year. 

2°-18688 


(771.)  The  great  disagreement  between  these  elements  and  those  assigned 
either  by  M.  Leverrier  or  Mr.  Adams  will  not  fail  to  be  remarked ;  and  it 
will  naturally  be  asked  how  it  has  come  to  pass,  that  elements  so  widely 
different  from  the  truth  should  afford  anything  like  a  satisfactory  represen- 
tation of  the  perturbation  in  question,  and  that  the  true  situation  of  the 
planet  in  the  heavens  should  have  been  so  well,  and  indeed  accurately, 
pointed  out  by  them.  As  to  the  latter  point,  any  one  may  satisfy  himself 
by  half  an  hour's  calculation  that  both  sets  of  elements  do  really  place  the 
planet,  on  the  day  of  its  discovery,  not  only  in  the  longitudes  assigned  in 
art.  763,  i.  e.  extremely  near  its  apparent  place,  but  also  at  a  distance  from 
the  sun  very  much  more  approximately  correct  than  the  mean  distances  or 
semiaxes  of  the  respective  orbits.     Thus  the  radius  vector  of  Neptune, 

'  In  a  letter  to  the  Astronomer  Royal,  dated  Sept.  2, 1846, — i.  e.  three  weeks  previous  ■    '  Tj 
to  the  optical  discovery  of  the  planet.  |  object 


( 

CODJI 

mi 

lowil 

the 

durij 
oftlj 
as  tl 
tire 
at  tH 


PERTURBATIONS   OF   URANUS   BY  NEPTUNE. 


433 


ideration  of  the 
1  only  as  far  as 
hose  of  the  five 
3  semiaxis  ought 
istance  of  33-33 
isfy  all  the  obser- 

of  course,  assidu- 
listance,  even  less 
with  its  motion; 
vation,  sufficiently 
considerable  intcr- 
jerved  as  a  star  by 
f  of  the  two  obscr- 
-y?  ^y  reason  of  its 
the  motion  of  the 
)robined  with  those 
alker,  U.  S.,  result 

M.  noon,  Greenwich. 


ical  year. 

ts  and  those  assigned 
je  remarked ;  and  it 
elements  so  widely 
satisfactory  represen- 
true  situation  of  the 
id  indeed  accurately, 
3  may  satisfy  himself 
ts  do  really  place  the 
ongitudes  assigned  in 
ilso  at  a  distance  from 
ihe  wean  distances  or 
[a  vector  of  Neptune, 
ke.  three  weeks  previous 


calculated  from  M.  Loverrier's  elements  for  the  day  in  question,  instead 
of  36-1539  (the  mean  distance)  comes  out  almost  exactly  33;  and  indeed, 
if  wo  consider  that  the  excentricity  assigned  by  those  elements  gives  for 
the  perihelion  distance  32-2634,  tho  longitude  assigned  to  the  perihelion 
brings  the  whole  arc  of  the  orbit  (more  than  83°),  described  in  tho  in- 
terval from  1806  to  1847  to  lie  within  42°  one  way  or  the  other  of  the 
perihelion,  and  therefore,  during  the  whole  of  that  interval,  the  hypothe- 
tical planet  would  be  moving  within  limits  of  distance  from  the  sun,  32-6 
and  33-0.  The  following  comparative  tables  of  the  relative  situations  of 
Uranus,  the  real  and  hypothetical  planet,  will  exhibit  more  clearly  than 
any  lengthened  statement,  the  near  imitation  of  tho  motion  of  the  former 
by  the  latter  within  that  interval.     Tho  longitudes  are  heliocentric' 


A.D. 

Uranus. 

Neptune. 

Leverrior. 

Adnms. 

Long. 

Long. 

Raa.  Vec. 

Long. 

Bad.  Vec. 

Long. 

Rad.  Vec. 

1805-0 

197°-8 

235°-9 

30-3 

2410-2 

33-1 

2460-5 

34-2 

1810-0 

220-9 

247-0 

30-3 

261-1 

32-8 

255-9 

33-7 

1815-0 

243-2 

258-0 

30-3 

261-2 

.S2-5 

265-5 

33-3 

1820-0 

264-7 

268-8 

30-2 

271-4 

32-4 

275-4 

33-1 

1821-0 

269-0 

271-0 

.30-2 

273-5 

32-3 

277-4 

33-0 

1S22-0 

273-3 

273-2 

30-2 

275-0 

32-3 

279-5 

330 

1823-0 

277-6 

275-3 

30-2 

277-6 

32-3 

281-5 

.32-9 

1824-0 

281-8 

277-4 

30-2 

27»-7 

32-3 

283-6 

32-9 

1825-0 

285-8 

279-6 

30-2 

281-8 

32-3 

285-6 

32-8 

1830-0 

306-1 

290-5 

30-1 

292-1 

32-3 

296-0 

32-8 

1835-0 

320-0 

301-4 

no-1 

302-5 

32-4 

306-3 

32-8     1 

1810-0 

345-7 

312-2 

30-1 

312-6 

32-6 

316-3 

32-9 

18450 

365-3 

323-1 

30-0 

322-6 

32-9 

326-0 

33-1 

1847-0 

373-3 

327-6 

30-0 

326-5 

33-1 

329-3 

33-2 

(772.)  From  this  comparison  it  will  be  seen  that  Uranus  arrived  at  its 
conjunction  with  Neptune  at  or  immediately  before  the  commencement  of 
1822,  with  tho  calculated  planet  of  Leverrier  at  the  beginning  of  the  fol- 
lowing year  1823,  and  with  that  of  Adams  about  the  end  of  1824.  Both 
the  theoretical  planets,  and  especially  that  of  M.  Leverrier,  therefore, 
during  the  whole  of  the  above  interval  of  time,  so  far  as  the  directions 
of  their  attractive  forces  on  Uranus  are  concerned,  would  act  nearly  on  it 
as  the  true  planet  must  have  done.  As  regards  the  intensi  ^v  of  the  rela- 
tive disturbing  forces,  if  we  estimate  these  by  the  principles  of  art.  (612) 
at  the  ep»>chs  of  conjunction,  and  for  the  commencement  of  1805  and 

'  The  caloulations  are  carried  only  to  tenths  of  degrees,  as  quite  sufRcient  for  tho 
object  in  view. 

28  > 


vmm 

■••• 

VB0' 


.ir 


1 4. 1 


484 


OUTLINES   OF   ASTUONOMY. 


I 


J:-*' 


*««5; 


1845,  wo  fiud  for  the  respective  dcnoniinatora  of  the  fractions  of  the  sun's 
attraction  on  Uranus  regarded  as  unity,  which  express  the  total  disturbing 
force,  N  S,  in  each  case,  as  below : 


Nepluno  with 


I 

1f3  2  2 


1808. 

Conjunction. 

1R45. 

27540 

7508 

32390 

•20244 

5519 

23810 

20837 

5193 

1993r. 

Pierce's  mass 
Struve's  mass 
Levcrrier's  theoretical  Planet,  mass 

The  masses  here  assigned  to  Neptune  are  those  respectively  deduced  by 
Prof.  Pcirce  and  M.  Struve  from  observations  of  the  satellite  discovered 
by  3Ir.  Lassell  made  with  the  large  telescopes  of  Fraunhofer  in  the  obser- 
vatories of  Cambridge,  U.  S.  and  Pulkova  respectively.  These  it  will  bo 
perceived  differ  very  considerably,  as  might  reasonably  be  expected  in  the 
results  of  raicrometrical  measurements  of  such  difficulty,  and  it  is  not  pes- 
Bible  at  present  to  say  to  which  the  preference  ought  to  be  given.  As 
compared  with  the  mass  assigned  by  M.  Struve,  an  agreement  on  the 
v.'lv>lo  more  satisfactory  could  not  have  been  looked  for  within  the  interval 
in.      liatcly  in  question. 

(773.)  Subject  then  to  this  uncertainty  as  to  the  real  mass  of  Neptune, 
the  theoretical  planet  of  Leverrier  must  bo  considered  as  representing  with 
quite  as  much  fidelity  as  could  possibly  be  expected  in  a  research  of  such 
exceeding  delicacy,  the  particulars  of  its  motion  and  perturbative  action 
during  the  forty  years  elapsed  from  1805  to  1845,  an  interval  which  (as 
is  obvious  from  the  rapid  diminution  of  the  forces  on  either  side  of  the 
conjunction  indicated  by  the  numbers  here  set  down)  comprises  all  the 
most  influential  range  of  its  action.     This  will,  however,  be  placed  in  full 
evidence  by  the  construction  of  curves  representing  the  normal  and  tan- 
gential forces  on  the  principles  laid  down  (as  far  as  the  normal  constituent 
is  concerned)  in  art  717,  one  slight  change  only  being  made,  which,  for 
the  purpose  in  view,  conduces  greatly  to  clearness  of  conception.    Tiie 
force  L  s  (in  the  figure  of  that  article)  being  supposed  applied  at  P  in  the 
direction  l  s,  we  here  construct  the  curve  of  the  normal  force  by  erecting 
at  P  (Jig.  5,  Plate  A)  P  W  always  perpendicular  to  the  disturbed  orbit, 
A  P,  at  P,  measured  from  P  in  the  same  direction  that  S  lies  from  L,  and 
equal  in  length  to  L  S.     P  W  will  then  always  represent  both  the  direc- 
tion and  magnitude  of  the  normal  force  acting  at  P.     And  in  like  man- 
ner, if  we  take  always  P  Z  on  the  tangent  to  the  disturbed  orbit  at  P, 
equal  to  N  L  of  the  former  figure,  and  measured  in  the  same  direction 
from  P  that  L  is  from  N,  P  Z  will  represent  both  in  magnitude  and  direc- 
tion the  tangential  force  acting  at  P.     Thus  will  be  traced  out  the  two  | 
curious  ovals  represented  in  our  figure  of  their  proper  forms  and  propor- 
tions for  the  case  in  question.    That  expressing  the  normal  force  is  formed  I 


PERTURBATIONS   OF   URANUS   BY   NEPTUNE. 


435 


ons  of  the  sun's 
total  disturbing 

Junction.         I****- 
7508  a^'-^yo 

5519  23«1« 

5193  19^35 

ively  deduced  by 
.tellito  discovcrt'il 
lofer  in  the  obscr- 
Thcsc  it  will  be 
)e  expected  in  the 
^  and  it  is  not  pos- 
to  be  given.     As 
agreement  on  tbc 
within  the  interval 

d  mass  of  Neptune, 
IS  representing  witli 
1  a  research  of  such 

perturbative  action 
1  interval  which  (as 
,n  either  side  of  tlic 
\)  comprises  all  the 

rer,  be  placed  in  full 
the  normal  and  tau- 
le  normal  constituent 
Lg  made,  vfhich,  for 

of  conception.  Tbc 
Jd  applied  at  P  in  tie 
[mal  force  by  erecting 

)  the  disturbed  orbit, 

[at  S  lies  from  L,  and 

•esent  both  the  direc- 
And  in  like  man- 
Jisturbed  orbit  at  W 
\n  the  same  direction 

magnitude  and  direc- 
[e  traced  out  the  t^vo 

,er  forms  and  proper- 

lormal  force  is  formed 


of  four  lobes,  having  a  common  point  in  S,  viz.,  SWwXSaSwSiSW 
and  that  expressing  the  tangential,  A  Z  c/B  rdYAZ,  consisting  of  four 
mutually  intersecting  loops,  surrounding  and  touching  the  disturbed  orbit 
in  four  points,  A  B  c  d.     The  normal  force  acts  outward  over  all  that  part 
of  the  orbit,  both  in  conjunction  and  opposition,  corresponding  to  the  por- 
tions of  the  lobes  m,  n,  exterior  to  the  disturbed  orbit,  and  inwards  in 
every  other  part.     The  figure  sets  in  a  clear  light  the  great  disproportion 
between  the  energy  of  this  force  near  the  conjunction,  and  in  any  other 
configuration  of  the  planets ;  its  exceedingly  rapid  degradation  as  P  ap- 
proaches the  point  of  neutrality  (whose  situation  is  35°  5'  on  either  side 
of  the  conjunction,  an  arc  described  synodically  by  Uranus  in  1Gj'-72)  j 
and  the  comparatively  short  duration  and  consequent  inefficacy  to  produce 
any  great  amount  of  perturbation,  of  the  more  intense  part  of  its  inward 
action  in  the  small  portions  of  the  orbit  corresponding  to  the  lobes  a,  b, 
in  which  the  lino  representing  the  inward  force  exceeds  the  radius  of  the 
circle.     It  exhibits,  too,  with  no  less  distinctness,  the  gradual  develope- 
ment,  and  rapid  degradation  and  extinction  of  the  tangential  force  from 
its  neutral  points,  c,  d,  on  either  side  up  to  the  conjunction,  where  its 
action  is  reversed,  being  accelerative  over  the  arc  d  A,  and  retardativo 
over  A  c,  each  of  which  arcs  has  an  amplitude  of  71"  20',  and  is  de- 
scribed by  Uranus  synodically  in  3-l>00.     The  insignificance  of  the  tan- 
gential force  in  the  configurations  remote  from  conjunction  throughout  the 
arc  cBdia  also  obviously  expressed  by  the  small  comparative  develone- 
raent  of  the  loops  e, /.  .  , 

(774.)  Let  us  now  consider  how  the  action  of  thes6  forces  results  in 
the  production  of  that  peculiar  character  of  perturbation  which  is  exhi- 
bited in  our  curve,  Jii/.  4,  Plate  A.  It  is  at  once  evident  that  the  increase 
of  the  longitude  from  1800  to  1822,  the  cessation  of  that  increase  in 
1822,  and  its  conversion  into  a  decrease  during  the  subsequent  interval  is 
in  complete  accordance  with  the  growth,  rapid  decay,  extinction  at  conjunc- 
tion, and  subsequent  reproduction  in  a  reversed  sense  of  the  tangential 
force :  so  that  we  cannot  hesitate  in  attributing  the  greater  part  of  the 
perturbation  expressed  by  the  swell  and  subsidence  of  the  curve  between 
the  years  1800  and  1845, — all  that  part,  indeed,  which  is  symmetrical  on 
either  side  of  1822  —  to  the  oction  of  the  tangential  force. 

(775.)  But  it  will  be  asked,  —  has  then  the  normal  force  (which,  on 
the  plain  showing  of  Jij.  5,  is  nearly  twice  as  powerful  as  the  tangential, 
and  which  does  not  reverse  its  action,  like  the  latter  force,  at  the  point  of 
junction,  but,  on  the  contrary,  is  there  most  energetic,)  no  influence  in 
producing  the  observed  effects  ?  We  answer,  very  little,  within  the  period 
to  which  observation  had  extended  up  to  1845.    The  eflect  of  the  tan- 


1 

! 


W 


486 


OUTLINES   OP  ASTRONOMY. 


:cr> 


I 

•'  t 


!> 

C  '»"  -sv  1 

fc,  '*  -»» ■ 

In-.    «.     ., 

»fc',    •>   .  ■    , 

*«  ^       i 

•••■ 

P '<■•,«, 


gential  forco  on  tho  longitude  is  direct  and  immediate  (art.  GOO),  that  of 
the  normal  indirect,  cuuscquential,  und  cumulative  with  tho  progress  of 
time  (art.  734.)  Tho  effect  of  tho  tangential  force  on  the  mean  motion 
takes  place  through  tho  medium  of  the  change  it  produces  on  tho  axis, 
and  is  transient:  the  reversed  action  after  conjunction  (supposing  tho 
orbits  circular),  exactly  destroying  all  the  previous  effect,  and  leaving  tho 
mean  motion  on  tho  whole  unaffected.  In  the  passage  through  the  con- 
junction, then,  tho  tangential  force  produces  a  sudden  and  powerful  accel- 
eration, succeeded  by  an  e(]uully  powerful  and  equally  sudden  retardation, 
which  done,  its  action  is  completed,  and  no  trace  remains  in  tho  subse- 
quent motion  of  the  planet  that  it  ever  existed,  for  its  action  on  the  peri- 
helion and  excentricity  is  in  like  manner  also  nullified  by  its  reversal  of 
direction.  But  with  the  normal  force  the  case  is  far  otherwise.  Its  im- 
mediate  effect  on  the  angular  motion  is  nil.  It  is  not  till  it  has  acted 
long  enough  to  produce  a  perceptible  change  in  the  distance  of  the  dis- 
turbed planet  from  the  sun  that  tho  angular  velocity  begins  to  be  sensibly 
affected,  and  it  is  not  till  its  whole  outward  action  has  been  e.xcrtcd  (/.  «>. 
over  the  whole  interval  from  neutral  point  to  neutral  point)  that  itH  maxi- 
mum effect  in  lifting  the  disturbed  planet  away  from  the  sun  has  been 
produced,  and  the  full  amount  of  diminution  in  angular  velocity  it  is 
capable  of  causing  has  been  developed.  This  continues  to  act  in  pro- 
ducing a  retardation  in  longitude  long  after  the  normal  force  itself  has 
reversed  its  action,  and  from  a  powerful  outward  force  has  become  a  feeble 
inward  motion.  A  certain  portion  of  this  perturbation  is  incident  on  the 
epoch  in  the  mode  described  in  art.  (731.)  et  seq.,  and  permanently  dis- 
turbs the  mean  motion  from  what  it  would  have  been,  had  Neptune  no 
existence.  The  rest  of  its  effect  is  compensated  in  a  single  synodic 
revolution,  not  by  the  reversal  of  the  action  of  the  force  (for  that  reversed 
action  is  far  too  feeble  for  this  purpose),  but  by  the  effect  of  the  pcrmn- 
Dent  alteration  produced  in  the  excentricity,  which  (the  axis  being  un- 
changed) compensates  by  increased  proximity  in  one  part  of  the  revolu- 
tion, for  increased  distance  in  the  other.  Sufficient  time  has  not  yet 
elapsed  since  the  conjunction  to  bring  out  into  full  evidence  the  influence 
of  this  force.  Still  its  commencement  is  quite  unequivocally  marked  in 
the  more  rapid  descent  of  our  curve  /Iff.  4,  subsequent  to  the  conjunction 
than  ascent  previous  to  that  epoch,  which  indicates  the  commencement  of 
a  series  of  undulations  in  its  future  course  of  an  elliptic  character,  con- 
sequent on  the  altered  excentricity  and  perihelion  (the  total  and  ultimate 
effect  of  this  constituent  of  the  disturbing  force)  which  will  bo  maintained 
till  within  about  20  years  from  the  next  conjunction,  with  the  exception, 
perhaps,  of  some  trifling  inequalities  about  the  time  of  the  opposition, 


PERTUUnATIONS   OF    UKANUrt    IJY   NEPTUNB. 


487 


.  GOO),  that  of 
;ho  progress  of 
le  mean  w«<«'>h 
CCS  on  tho  axis, 
(supposing  tbo 
and  leaving  tho 
through  the  con- 
I  powerful  acccl- 
Iden  retardation, 
iins  in  tho  suhsc- 
jtion  on  the  peri- 
by  its  reversal  of 
icrwisc.     Its  "»• 
till  it  has  acted 
[stance  of  the  dis- 
rins  to  be  sensibly 
been  exerted  (/.  '•. 
int)  that  its  niaxi- 
the  sun  hiis  been 
rular  velocity  it  is 
aes  to  act  in  pro- 
lal  force  itself  has 
as  become  :i  feeble 
I  is  incident  on  the 
i  permanently  dis- 
1,  had  Neptune  no 
I  a  single   synodic 
e  (for  that  reversed 
iffect  of  the  perma- 
the  axis  being  ua- 
part  of  the  revolu- 
t  time  has  not  yet 
[idence  the  influence 
jivocally  marked  in 
It  to  the  conjunction 
commencement  of 
[ptic  character,  con- 
(e  total  and  ultimate 
will  bo  maintained 
with  the  exception, 
of  the  opposition, 


similar  in  character,  but  far  inferior  in  nmgnitudo  to  thoso  now  under 
discusHion. 

(770.)  PoHtcrity  will  hardly  credit  that,  with  a  full  knowledge  of  all 
tho  circumstances  attoiidin;^  this  great  diHcovery  —  of  tho  calculations  of 
Lovcrricr  and  Adams  —  of  tho  ooinniuuication  of  its  predicted  place  to 
Dr.  Oallo  — and  of  the  now  i>hinct  buitig  actually  found  by  him  in  that 
place,  in  the  remarkable  uiuinior  above  commemorated ;  not  only  have 
doubts  been  expressed  ns  to  tho  validity  of  tho  calculations  of  thoso 
geometers,  and  tho  legitimacy  of  their  conclusions,  but  those  doubts  have 
been  carried  so  far  as  to  lead  tlie  objectors  to  attribute  t^o  acknowledged 
fact  of  a  planet  previously  unknown  occupying  that  precise  place  in  tho 
heavens  at  that  precise  time,  to  sheer  accident !'  What  share  accident 
may  have  had  in  tho  successful  issue  of  tho  calculations,  w  ■  prcsuir"  tho 
reader,  after  what  has  boon  said,  will  have  little  difficulty  in  satisfying 
himself.  As  regards  tho  time  when  the  discovery  was  made,  much  has 
also  been  attributed  to  fortunate  cnincidcncc.  Tho  following  cor'idcra- 
tions  will,  wo  apprehend,  completely  dissipate  this  idea,  if  still  liiigoi\ng 
in  tho  mind  of  any  one  at  all  conversant  with  the  subject.  The  period 
of  Uranus  being  84-0140  years,  and  that  of  Neptune  1G4-6181,  their 
synodic  revolution  (art.  41 S.),  or  tho  interval  between  two  successive  con- 
junctions, is  171-58  years.  The  late  conjunction  having  taken  place 
about  tho  beginn.iig  of  1822;  that  next  preceding  must  have  happened 
in  1G49,  or  more  than  40  years  before  the  first  recorded  observation  of 

'  These  doubts  seem  to  have  originatrd  partly  in  tlie  great  disogreenienl  between  the 
predicted  and  reol  elements  of  Ncpimic,  |)iirtiy  in  the  near  {possibly  precise)  commen- 
surabihty  of  tho  mean  motions  of  Ntfituiie  niid  Urnnus.  Wo  conceive  them  however 
to  be  founded  in  a  total  niiscoiieepiion  of  liie  nature  of  tho  problem,  which  was  not, 
from  such  obviously  uncertain  indications  as  the  observed  disc  n-Jaiices  could  give,  to 
determine  as  astronomical  quantities  the  a.vis,  cxcentricity  and  -r  .ss  of  the  disturbing 
planet ;  but  practically  to  discover  whero  to  look  for  it :  when,  if  once  found,  these 
elements  would  be  far  bolter  ascertained.  To  do  this,  any  axis,  cxcentricity,  perihe' 
lion,  arid  mass,  however  wide  of  the  truth,  which  would  /i;present,  even  roughly  the 
amount,  but  with  tolerable  correctness  the  direction  of  tlio  disturbing  force  during  the 
very  moderate  interval  when  the  departures  fron  theory  were  really  considerable, 
would  equally  serve  their  purposed ;  and  with  an  excentricity,  mass,  and  perihelion  dis- 
posable, it  is  obvious  that  any  assumption  of  the  axis  between  the  limits  30  and  J8, 
nay,  even  with  a  much  wider  inferior  limit,  would  serve  the  purpose.  In  his  attempt 
to  assign  an  inferior  limit  to  the  axis,  and  in  the  volue  so  assigned,  M.  Leverrier,  it 
must  be  admitted,  wos  not  successful.  Mr,  Adams,  on  the  other  hand,  influenced  Ly 
no  considerations  of  the  kind  which  appeor  to  have  weighed  with  his  brother  geometer, 
fixed  ultimately  (as  wo  have  seen)  on  an  axis  not  very  egrcgiously  wrong.  Still  it  were 
to  be  wished,  for  tho  satisfaction  of  all  parties,  that  some  one  would  undertake  the 
problem  de  novo,  employing  formulae  not  liable  to  the  passage  through  infinity,  which, 
technically  speaking,  hampers,  or  may  be  supposed  to  hamper  the  continuous  applica- 
tion of  the  usual  perturbational  formulae  when  cases  of  commensurability  occur. 


»■<«"•    ,.0 


rni 


438 


OUTLINES   OF  ASTRONOMY. 


fcv  J  •>». ' 

■tt>.      >t 


Uranus  in  1690,  to  say  nothing  of  its  discovery  as  a  planet.  In  1690, 
then,  it  must  have  been  eflFectually  out  of  reach  of  any  perturbative  influ- 
ence worth  considering,  and  so  it  rcumined  during  the  whole  interval  from 
thence  to  1800.  From  that  time  the  eflfect  of  perturbation  began  to  be- 
come sensible,  about  1805  prominent,  and  in  1820  had  nearly  reached  its 
maximum.  At  this  epoch  an  alarm  was  sounded.  The  maximum  was 
not  attained, — the  event,  so  important  to  astronomy,  was  still  in  progress 
of  developement,  —  when  the  fact  (any  thing  rather  than  a  striking  one) 
was  noticed,  and  made  matter  of  complaint.  But  the  time  for  discussing 
its  cause  with  any  prospect  of  success  was  not  yet  come.  Every  thing 
turns  upon  the  precise  determination  of  the  epoch  of  the  maximum, 
when  the  perturbing  and  perturbed  planet  were  in  conjunction,  and  upon 
the  law  of  increase  and  diminution  of  the  perturbation  itself  on  either 
side  of  that  point.  Now  it  is  always  difficult  to  assign  the  time  of  the 
occurrence  of  a  maximum  by  observations  liable  to  errors  bearing  a  ratio 
far  from  inconsiderable  to  the  whole  quantity  observed.  Until  the  lapse 
of  some  years  from  1822  it  would  have  been  impossible  to  have  fixed  that 
epoch  with  any  certainty,  and  as  respects  the  law  of  degradation  and  total 
arc  of  longitude  over  which  the  sensible  perturbations  extend,  w  are 
hardly  yet  arrived  at  a  period  when  this  can  be  said  to  be  completely  de- 
terminable from  observation  alone.  In  all  this  we  see  nothing  of  acci- 
dent, unless  it  be  accidental  that  an  event  which  must  have  happened 
between  1781  and  1953,  actually  happened  in  1822;  and  that  we  live  iu 
an  age  when  astronomy  has  reached  that  perfection,  and  its  cultivators 
exercise  that  vigilance  which  neither  permit  such  an  event,  nor  its  scientific 
importance,  to  pass  unnoticed.  Tlie  blossom  had  been  watched  with  in- 
terest in  its  developement,  and  the  fruit  was  gathered  in  the  very  moment 
of  maturity.' 

'  The  student  who  may  wish  to  see  the  perturbations  of  Uranus  produced  by  Nep- 
tune, as  computed  from  a  knowledge  of  the  elements  and  mass  of  that  planet,  such 
as  we  now  know  to  be  pretty  near  the  truth,  will  find  them  stated  at  length  from  the 
calculations  of  Mr.  Walker,  (of  Washington,  U.  S.)  in  the  "  Proceedings  of  the  Amer- 
ican Academy  of  Arts  and  Sciences,"  vol.  i.  p.  334,  et  seq.  On  examining  the  com- 
parisons of  the  results  of  Mr.  Walker's  formulae  with  those  of  Mr.  Adam's  theory  in 
p.  342,  he  will  perhaps  be  surprised  at  the  enormous  difference  between  the  actions  ol 
Neptune  and  Mr.  Adam's  "hypothetical  planet"  on  the  longitude  of  Uranus.  This 
is  easily  explained.  Mr.  Adam's  perturbations  are  deviations  from  Bouvard's  orbit  ol 
Uranus,  as  it  stood  immediately  previous  to  the  late  conjunction.  Mr.  Walker's  are 
the  deviations  from  a  mean  or  undisturbed  orbit  freed  from  the  influence  of  the  long 
inequality  resulting  from  the  near  commensurability  of  the  motions. 


OF  SIDEREAL  ASTRONOMY. 


439 


anet.    In  1690, 
jrturbative  influ- 
ole  interval  from 
tion  began  to  bc- 
learly  reached  its 
10  maximum  was 
s  still  in  progress 
Q  a  striking  one) 
me  for  discussing 
ne.    Every  thing 
jf  the  maximum, 
unction,  and  upon 
n  itself  on  either 
nrn  the  time  of  the 
rors  bearing  a  ratio 
I.     Until  the  lapse 
5  to  have  fixed  that 
igradation  and  total 
,na  extend,  vi'^  are 
0  be  completely  de- 
see  nothing  of  acci- 
ust  have  happened 
and  that  we  live  iu 
and  its  cultivators 
ent,  nor  its  scientific 
en  watched  with  in- 
in  the  very  moment 

anus  produced  by  Nep- 
ass  of  that  planet,  such 
ued  at  length  from  the 
•oceedings  of  the  Amet- 
3n  examining  the  com- 
f  Mr.  Adam's  theory  in 
between  the  actions  of 
ritude  of  Uranus.    This 
from  Bouvard's  orbit  of 
ion.    Mr.  Walker's  are 
he  influence  of  the  long 
tons. 


PART  III. 

OP    SIDEREAL    ASTRONOMY. 
CHAPTER  XV. 

OF  THE  FIXED  STARS.  —  THEIR  CLASSIFICATION  BY  MAGNITUDES. — 
PHOTOMETRIC  SCALE  OP  MAGNITUDES. — CONVENTIONAL  OR  VULGAR 
SCALE. —  PHOTOMETRIC  COMPARISON  OP  STARS. —  DISTRIBUTION  OP 
STARS  OVER  THE  HEAVENS. — OP  THE  MILKY  WAY  OR  GALAXY. — 
ITS  SUPPOSED  FORM  THAT  OP  A  FLAT  STRATUM  PARTIALLY  SUB- 
DIVIDED.— ITS  VISIBLE  COURSE  AMONG  THE  CONSTELLATIONS. — ITS 
INTERNAL  STRUCTURE. —  ITS  APPARENTLY  INDEFINITE  EXTENT  IN 
CERTAIN  DIRECTIONS. — OP  THE  DISTANCE  OP  THE  FIXED  STARS. — 
THEIR  ANNUAL  PARALLAX.  —  PARALLACTIC  UNIT  OP  SIDEREAL 
DISTANCE. — EFFECT  OP  PARALLAX  ANALOGOUS  TO  THAT  OF  ABER- 
RATION.— HOW  DISTINGUISHED  FROM  IT.  —  DETECTION  OF  PARAL- 
LAX BY  MERIDIONAL  OBSERVATIONS. — HENDERSON'S  APPLICATION 
TO  a  CENTAURI. — BY  DIFFERENTIAL  OBSERVATIONS. — ^DISCOVERIES 
OF  BESSEL  AND  STRUVE.  —  LIST  OF  STARS  IN  WHICH  PARALLAX 
HAS  BEEN  DETECTED. — OP  THE  REAL  MAGNITUDES  OP  THE  STARS. — 
COMPARISON   OP  THEIR  LIGHTS  WITH   THAT   OP  THE   SUN. 

(777.)  Besides  the  bodies  we  have  described  in  the  foregoing  chap- 
ters, the  heavens  present  us  with  an  innumerable  multitude  of  other 
objects,  which  are  called  generally  by  the  name  of  stars.  Though  com- 
prehending individuals  differing  from  each  other,  not  merely  in  brightness, 
but  in  many  other  essential  points,  they  all  agree  in  one  attribute, — a 
high  degree  of  permanence  as  to  apparent  relative  situation.  This  has 
procured  them  the  title  of  "  fixed  stars ;"  an  expression  which  is  to  be 
understood  in  a  comparative  and  not  an  absolute  sense,  it  being  certain 
that  many,  and  probable  that  all,  are  in  a  state  of  motion,  although  too 
slow  to  be  perceptible  unless  by  means  of  very  delicate  observations,  con- 
tinued during  a  long  series  of  years. 

(778.)  Astronomers  are  in  the  habit  of  distinguishing  the  stars  into 


■■•nm 

'lESVff 
"m0m  ,.0 

Ml 

.Am' 


'M 

«•!! 

^ 


1» 


m 


440 


OUTLINES  OF  ASTRONOMY. 


"-if*} 


■^* 


»3    'k-v,. 


? 


'•li^Bl 


cm 

4f^ 


classes,  according  to  their  apparent  brightness.  These  are  termed  magni- 
tudes. The  brightest  stars  are  said  to  be  of  the  first  magnitude ;  those 
which  fall  so  far  short  of  the  first  degree  of  brightness  as  to  make  a 
strongly  marked  distinction  are  classed  in  the  second ;  and  so  on  down  to 
the  sixth  or  seventh,  which  comprise  the  smallest  stars  visible  to  the 
naked  eye,  in  the  clearest  and  darkest  night.  Beyond  these,  however, 
telescopes  continue  the  range  of  visibility,  and  magnitudes  from  the  8th 
down  to  the  16th  arc  familiar  to  those  who  are  in  the  practice  of  using 
powerful  instruments ;  nor  does  there  seem  the  least  reason  to  assign  a 
limit  to  this  progression ;  every  increase  in  the  dimensions  and  power  of 
instruments,  which  successive  improvements  in  optical  science  luue 
attained,  having  brought  into  view  multitudes  innumerable  of  objects 
invisible  before;  so  that,  for  any  thing  experience  has  hitherto  taught  us, 
the  number  of  the  stars  may  be  really  infinite,  in  the  only  sense  in  which 
we  can  assign  a  meaning  to  the  word. 

(779.)  This  classification  into  magnitudes,  however,  it  must  be  ob- 
served, is  entirely  arbitrary.  Of  a  multitude  of  bright  objects,  differing 
probably,  intrinsically,  both  in  size  and  in  splendour,  and  arranged  at 
unequal  distances  from  us,  one  must  of  necessity  appear  the  brightest,  one 
next  below  it,  and  so  on.  An  order  of  succession  (relative,  of  course,  to 
our  local  situation  among  them)  must  exist,  and  it  is  a  matter  of  absolute 
indifference,  where,  in  that  infinite  progression  downwards,  from  the  one 
brightest  to  the  invisible,  we  choose  to  draw  our  lines  of  demarcation.  All 
this  is  a  matter  of  pure  convention.  Usage,  however,  has  established 
such  a  convention ;  and  though  it  is  impossible  to  determine  exactly,  or 
d  priori,  where  one  magnitude  ends  and  the  next  begins,  and  although 
different  observers  have  differed  in  their  magnitudes,  yet,  on  the  whole, 
astronomers  have  restricted  their  first  magnitude  to  about  23  or  24  prin- 
cipal stars ;  their  second  to  50  or  60  next  inferior ;  their  third  to  about 
200  yet  smaller,  and  so  on  j  the  numbers  increasing  "very  rapidly  as  V!c 
descend  in  the  ,  ^ale  of  brightness,  the  whole  number  of  stars  already  regis- 
tered down  to  the  seventh  magnitude,  inclusive,  amounting  to  from  12000 
to  15000. 

(780.)  As  we  do  not  see  the  actual  disc  of  a  star,  but  judge  only  of  its 
brightness  by  the  total  impression  made  upon  the  eye,  the  apparent "  mag- 
nitude" of  any  star  will,  it  is  evident,  depend,  1st,  on  the  star's  distance 
from  us ;  2d,  on  the  absolute  magnitude  of  its  illuminated  surfixce ;  3d, 
on  the  intrinsic  brightness  of  that  surface.  Now,  as  we  know  nothing  or 
next  to  nothing,  of  any  of  these  data,  and  have  every  reason  for  believing 
that  each  of  them  may  differ  iu  different  individuals,  in  the  proportion  of 
many  millions  to  one,  it  is  clear  that  we  are  not  to  expect  much  satisfuc- 


**^  ■*•■ 


MAGNITUDES   OF  THE   STARS. 


441 


termed  magni- 
gnitude;  those 
as  to  make  a 
I  so  on  down  to 
s  visible  to  the 
these,  however, 
les  from  the  8th 
practice  of  using 
lason  to  assign  a 
IS  and  power  of 
al  science    ha\c 
jrablc  of  objects 
itherto  taught  us, 
\y  sense  in  which 

.J  it  must  be  ob- 

!  objects,  differing 

,  and  arranged  at 

:  the  brightest,  one 

ative,  of  course,  to 

matter  of  absolute 

ards,  from  the  one 

f  demarcation.   All 

has  established 

termine  exactly,  or 

.gins,  and  although 

yet,  on  the  whole, 

oout  23  or  24  prin- 

[heir  third  to  about 

•very  rapidly  as  wc 

fsUrs  already  regis- 

iting  to  from  12000 

kut  judge  only  of  its 
[the  apparent  "mag- 
I  the  star's  distance 
linated  surface;  3a, 
(we  know  nothing  or 
Treason  for  believing 
lin  the  proportion  of 
\pect  much  satisfac- 


tion in  any  conclusions  wo  may  draw  from  numerical  statements  of  the 
number  of  individuals,  which  have  been  arranged  in  our  artificial  classes 
antecedent  to  any  general  or  definite  principle  of  arrangement.     In  fact, 
astronomers  have  not  yet  agreed  upon  any  principle  by  which  the  magni- 
tudes may  be  photometrically  classed  d,  priori,  whether  for  example  a 
scale  of  brightnesses  decreasing   in   geometrical  progression  should  be 
adopted,  each  term  being  one-half  of  the  preceding,  or  one-third,  or  any 
othor  ratio,  or  whether  it  would  not  be  preferable  to  adopt  a  scale  decreas- 
ing as  the  squares  of  the  terms  of  an  harmonic  progression,  i.  e.  according 
to  the  series  1,  ;|,  -J-,  y'j,  tj'^,  &c.     The  former  would  be  a  purely  photo- 
metric sciile,  and  would  have  the  apparent  advantage,  that  the  light  of  a 
star  of  any  magnitude  would  bear  a  fixed  proportion  to  that  of  the  mag- 
nitude next  above  it,  an  advantage,  however,  merely  apparent,  as  it  is  cer- 
tain, from  many  optical  facts,  that  the  unaided  eye  forms  very  different 
judgments  of  the  proportions  existing  between  bright  lights,  and  those 
between  feeble  ones.     The  latter  scale  involves  a  physical  idea,  that  of 
supposing  the  scale  of  magnitudes  to  correspond  to  the  appearance  of  a 
first  magnitude  standard  star,  removed  successively  to  twice,  three  times,  &c., 
its  original  or  standard  distance.     Such  a  scale,  which  would  make  the 
nominal  magnitude  a  sort  of  index  to  the  prestnnahle  or  average  distance, 
on  the  supposition  of  an  equality  among  the  real  lights  of  the  stars, 
would  facilitate  the  expression  of  speculative  ideas  on  the  constitution  of 
the  sidereal  heavens.     On  the  other  hand,  it  would  at  first  sight  appear 
to  make  too  small  a  difference  between  the  lights  in  the  lower  magnitudes. 
For  example,  on  this  principle  of  nomenclature,  the  light  of  a  star  of  the 
seventh  magnitude  would  be  thirty-six  49ihs  of  that  of  one  of  the  sixth, 
and  of  the  tenth  81  hundredths  of  the  ninth,  while  between  the  first  and 
the  second  the  proportion  would  be  that  of  four  to  one.    So  far,  however, 
from  this  being  really  objectionable,  it  falls  in  well  with  the  general  tenor 
of  the  optical  facts  already  alluded  to,  inasmuch  as  the  eye  (in  the  ab- 
sence of  disturbing  causes)  does  aetually  discriminate  with  greater  preci- 
sion between  the  relative  intensities  of  feeble  lights  than  of  bright  ones, 
so  that  the  fraction  |^,  for  instance,  expresses  quite  as  great  a  step  down- 
wards (physiologically  speaking)  from  the  sixth  magnitude,  as  J  does  from 
the  first.   As  the  choice,  therefore,  so  far  as  we  can  see,  lies  between  these 
1  two  scales,  in  drawing  the  lines  of  demarcation  between  what  may  be 
j  termed  the  photometrical  magnitudes  of  the  stars,  we  have  no  hesitation 
in  adopting,  and  recommending  others  to  adopt,  the  latter  system  in  pre- 
ifcreuce  to  the  former. 

(781.)  The  conventional  magnitudes  actually  in  use  among  astrono- 
jmers,  so  far  as  their  usage  is  consistent  with  itself,  conforms  moreover 


iMIM 
"vmm 

<■» 


442 


OUTLINES  OF  ASTRONOMY. 


li 


'■'^^l 


•*    i*  "I 


very  much  more  nearly  tr^  this  than  to  the  geometrical  progression.  It  has 
been  shown,'  by  direct  photometric  measurement  of  the  light  of  a  consi- 
derable number  of  stars,  from  the  first  to  the  fourth  magnitude,  that  if  M 
be  the  number  expressing  the  magnitude  of  a  star  on  the  above  system, 
and  m  the  number  expressing  the  magnitude  of  the  same  star  in  the  loose 
and  irregular  language  at  present  conventionally  or  rather  provisionally 
adopted,  so  far  as  it  can  bw  collected  from  the   ionflicting  authorities  of 
difiFerent  observers,  the  difference  between  these  n\_mbers,  or  M  —  m,  is 
the  same  in  all  the  higher  parts  of  the  scale,  and  is  less  than  half  a  mag- 
nitude (0™-  414).     The  standard  star  assumed  as  the  unit  of  magnitude 
in  the  measurements  referred  to,  is  the  bright  southern  star  o  Centauri,  a 
star  somewhat  superior  to  Arcturus  in  lustre.     If  we  take  the  distance  of 
this  star  for  unity,  it  follows  that  when  removed  to  the  distances  14 14, 
2*414,  3-414,  &c.,  its  apparent  lustre  would  equal  those  of  average  stars 
of  the  1st,  2d,  3d,  &c.  magnitudes,  as  ordinarili/  reckoned,  respectively. 
(782.)  The  difference  of  lustre  between  stars  of  two  consecutive  mag- 
nitude**  is  so  considerable  as  to  allow  of  many  intermediate  "radations 
being  perfectly  well  distinguished.     Hardly  any  two  stars  of  the  first;  or 
of  the  second  magnitude,  would  be  judged  by  an  eye  practised  in  such 
comparisons  to  be  exactly  equal  in  brightness.     Hence,  the  necessity,  if 
anything  like  accuracy  be  aimed  at,  of  subdividing  the  magnitudes  and 
admitting  fractions  into  our  nomenclature  of  brightness.     When  this  ne- 
cessity first  began  to  be  felt,  a  simple  bisection  of  the  interval  was  recog- 
nized, and  the  mterraediate  degree  of  brightnesM  was  thus  designated,  viz. 
1.2  m,  2.3  m,  and  so  on.     At  present  it  is  not  unfrequent  to  find  the  in- 
terval trisected  thus :  1  m,  1.2  m,  2.1  m,  2  m,  &c.  where  the  expression 
1.2  m  denotes  a  magnitude  intermediate  between  the  first  and  second,  but 
nearer  1  than  2;  while  2.1  m  designates  a  magnitude  also  intermediate, 
but  nearer  2  than  1.     This  may  suffice  for  common  parlance,  but  as  this 
department  of  astronomy  progresses  towards  exactness,  a  decimal  subdi- 
vision will  of  necessity  supersede  these  rude  forms  of  expression,  and  the 
magnitude  will  be  expressed  by  an  integei  number,  followed  by  a  decimal 
fraction;  as,  for  instance,  2.51,  which  expresses  the  magnitude  of  y  Geini- 
norum  on  the  vulgar  or  conventional  scale  of  magnitudes,  by  which  we  at 
once  perceive  that  its  place  is  almost  exactly  half  way  between  t'le  2d  and 
3d  average  magnitudes,  and  that  its  light  is  to  that  of  an  average  first 
magnitude  star  in  that  scale  (of  which  a  Orionis  in  its  usual  or  normiil 
state^  may  be  taken  as  a  typical  specimen)  as  1*:  (2-51)'',  and  to  that  of 

'  See  "  Results  of  observations  made  at  the  Cape  of  Good  Hope,  &.c.  &c."  p.  371. 
By  the  Author. 

*  In  the  interval  from  1836  to  1839  this  star  underweni  conside'able  and  remarkable  | 
fluctuations  of  brightness. 


PHOTOMETRIC   SCALE   OF   MAGNITUDES. 


448 


ression.  Itbas 
ght  of  a  consi- 
tude,  that  if  M 

above  system, 
star  in  the  loose 
,er  provisionally 
tr  authorities  of 
's,  orM  — w>is 
than  half  a  mag- 
nit  of  magnitude 
5tar  o  Centauri,  a 
:e  the  distance  of 
,  distances  1*4U, 
3  of  average  stars 
ncd,  respectively. 

consecutive  mag- 
nediate  "radations 
tars  of  the  first,  or 
.  practised  in  such 
e  the  necessity,  if 
ie  laagnitudes  and 
gg.    AVhen  this  ne- 

interval  was  recog- 
hus  designated,  viz. 
^uenttofindthcin. 

"here  the  expression 
Ifirst  and  second,  hut 
|e  also  intermediate, 
variance,  but  as  tbis 
jss,  a  decimal  subdi- 
expression,  and  the 
Alowed  by  a  decimal 

magnitude  of  V  Gciw- 
tdes,  by  which  we  at 
.  between  t'le  2d  a«J 
ft  of  an  average  first 
its  usual  or  nonnal 
51)*,  and  to  that  of 

lHope,&c.&c."p.3'l. 
Lde-ablenndrematkabk 


a  Centauri  as  1*:  (2-924)*,  making  its  place  in  the  photometric  scale  (so 
defined)  2*924.  Lists  of  stars,  northern  and  southern,  comprehending 
those  of  the  vulgar  first,  second  and  third  magnitudes,  with  their  magni- 
tudes decimally  expressed  in  both  systems,  will  be  found  at  the  end  of 
this  work.  The  light  of  a  star  of  the  sixth  magnitude  may  be  roughly 
stated  as  about  the  hundredth  part  of  one  of  the  first.  Sirius  would  make 
between  three  and  four  hundred  stars  of  that  magnitude. 

(783.)  The  exact  photometrical  determination  of  the  comparative  in- 
tensities of  light  of  the  stars  is  attended  with  many  and  great  difiiculties, 
arising  partly  from  their  diftercnces  of  colour ;  partly  from  the  circum- 
stunce  that  no  invariable  standard  of  artificial  light  has  yet  been  disco- 
vered ;  partly  from  the  physiological  cause  above  alluded  to,  by  which  the 
eye  is  incapacitated  from  judgiijg  correctly  of  the  proportion  of  two  lights, 
and  can  only  decide  (and  that  with  not  verj  great  precision)  as  to  their 
equality  or  inequality  j  and  partly  from  other  physiological  causes.     The 
least  objectionable  mode  hitherto  proposed  would  appear  to  be  the  follow- 
ing.    A  natural  standard  of  comparison  is  in  the  first  instance  selected, 
brighter  than  any  of  the  stars,  so  as  to  allow,  of  being  equalized  with  any 
of  them  by  a  reduction  of  its  light  optically  efiiBcted,  and  at  the  same  time 
either  invariable,  or  at  least  only  so  variable  that  its  changes  can  be  \  .'c- 
actly  calculated  and  reduced  to  numerical  estimation.     Such  a  standard  is 
offered  by  the  planet  Jupiter,  which,  being  much  brighter  than  any  star, 
subject  to  n  J  phases,  and  variable  in  light  only  by  the  variation  of  its  dis- 
tance from  the  sun,  and  which,  moreover,  comes  in  succession  above  the 
horizon  at  a  convenidnt  altitude,  simultaneously  with  all  the  fixed  ttars, 
and,  in  the  abGonce  of  the  moon,  twilight,  and  other  disturbing  causes 
(which  fatally  affect  all  observations  of  this  nature),  combines  all  the  re- 
quisite conditions.     Let  us  suppose,  now,  that  Jupiter  being  at  A  and  the 
star  to  be  compared  with  it  at  B,  a  glass  prism,  0,  is  so  placed  that  the 
light  of  the  planet  deflected  by  total  internal  rcfkxion  at  its  base,  shall 
emerge  parallel  to  B  E,  the  direction  of  the  star's  visual  ray.     After  re- 
flexion let  it  be  received  on  a  lens,  D,  in  whose,  focus,  F,  it  will  form  a 
small,  bright,  star-like  image,  capable  of  being  viewed  by  an  eye  placed 
at  E,  so  far  out  of  the  axis  of  the  cone  of  diverging  rays  as  to  admit  d 
seeing  at  the  same  time,  and  with  the  same  eye,  and  so  comparing  this 
image  with  the  star  seen  directly.     By  bringing  the  eye  nearer  to  or 
further  from  the  focus,  F,  the  apparent  brightness  of  the  focal  point  will 
be  varied  in  the  inverse  ratio  of  the  square  of  the  distance,  E  F,  and 
therefore  may  be  equalized,  as  well  as  the  eye  can  judge  of  such  equali- 
ties, with  the  star.    If  this  be  done  for  two  stars  several  times  alternately, 
and  a  mean  of  the  results  taken,  by  measuring  E  F,  their  relative  bright- 


<».illW 

'ill 

'.13- 

I'M 

.1 1 

I* 


^ 


"^  .^^  w 


444 


OUTLINES   OF  ASTRONOMY. 


Fig.  107. 


m 


'  'rta.s  V 


!*1j 

'».« 

1 


b«  '■■'■■••'1 

MM  ':?>!»'»« 


t^iiAii* 


ness  will  1)0  ottained  :  that  of  Jupiter,  the  tomp  nary  staudart  f  com- 
parison, 'no'iug  altogether  eliminnied  from  the  re-mlt. 

(784.;  A  raoc'orate  number  of  well  selected  stars  being  thus  photometri- 
cally determ'aed  ]»j  repeated  and  careful  nieasurements,  so  as  to  aiFord  an 
ascertained  .wd  i^raduuicd  scale  of  brightness  among  the  stars  themselves, 
the  iuteruiediate  steps  or  grades  of  magnitude  may  be  filled  up,  by  insert- 
ing between  them,  according  to  the  judgment  ol  the  eye,  other  stars, 
forming  an  ascending  or  descending  sequence,  each  member  of  such  a 
sc<iuence  being  brighter  than  that  below,  and  less  bright  than  that 
abov(j  it;  and  thus  at  length,  a  scale  of  numerical  magnitudes  will 
beconae  established,  complete  in  all  its  members,  from  8irius,  the  brightest 
of  the  stars,  down  to  the  least  visible  magnitude.'  It  were  much  to  be 
wished  that  this  branch  of  astronomy,  which  at  present  can  hardly  be  said 
to  be  advanced  beyond  its  infancy,  were  perseveringly  and  systematically 
cultivated.  It  is  by  no  means  a  subject  of  mere  barren  curiosity,  as  will 
abundantly  appear  when  we  come  to  speak  of  the  phaenomena  of  variable 
stars,  and  being  moreover,  one  in  which  amateurs  of  the  science  may 
easily  chalk  out  for  themselves  a  useful  and  available  path,  may  naturally 
be  expected  to  receive  large  and  interesting  accessions  at  their  hands. 

(785.)  If  the  comparison  of  the  apparent  magnitudes  of  the  stars  with 
their  numbers  leads  to  no  immediately  obvious  conclusion,  it  is  otherwise 
when  we  view  them  in  connexion  with  their  local  distribution  over  the 
heavens.  If  indeed  we  confine  ourselves  to  the  three  or  four  brightest 
classes,  we  shall  find  them  distributed  with  a  considerable  approach  to 

•  For  the  method  of  combining  and  treating  such  sequences,  where  accumulated 
in  considerable  numbers,  so  as  to  eliminate  from  their  results  the  influence  of  erroneous 
judgment,  atmospheric  circumstances,  &c.,  which  often  give  rise  to  contradictory 
arrnngements  in  the  order  of  stars  differing  but  little  in  magnitude,  as  well  as  for  an 
account  of  a  series  of  photometric  comparisons  (in  which,  however,  not  Jupiter,  but 
the  moon  was  used  as  an  intermediate  standard),  see  the  work  above  cited,  note  on  p. 
353     (Results  of  Observations,  &c.) 


GENERAL  FORM  OF  THE  GALAXY. 


445 


st^ndarc' 


■f  coiu- 


g  thus  photometri- 

so  as  to  afford  an 

e  stars  -themselves, 

aUed  up,  by  insert- 

te  eye,  other  stars, 

member  of  such  a 

J  bright   th-an   that 

3,1   magnitudes  will 

Birius,  the  brightest 

fc  were  much  to  he 

t  can  hardly  he  said 

r  and  systematically 

ren  curiosity,  as  will 

_)nomena  of  variable 

of  the  science  may 

path,  may  naturally 

J  at  their  hands. 

des  of  the  stars  with 

ision,  it  is  otherwise 

listribution  over  the 

ee  or  four  brightest 

iderable  approach  to 

cea    where  accumulated 
he  influence  of  erroneous 

ive  rise  to  contradictory 
mtude.a9wella9foran 
lowever.notJupuer.but 
Ik  above  cited,  note  on  p. 


impartiality  over  the  sphere :  u  marked  preference  however  being  observa- 
ble, especially  in  the  southern  homisphere,  to  a  zone  or  belt,  following  the 
direction  of  a  great  circle  passing  through  t  Orionis  and  a  Crucis.  But 
if  wo  take  in  the  whole  amount  visible  to  the  naked  eye,  wo  shall  perceive 
a  great  increase  of  number  as  we  approach  the  borders  of  the  Milky  Way. 
And  when  we  come  to  telescopic  magnitudes,  vrc  find  them  crowded 
beyond  imagination,  along  the  extent  of  that  circle,  and  of  the  branches 
which  it  sends  off  from  it ;  so  that  in  fact  its  whole  light  is  composed  of 
nothing  but  stars  of  every  magnitude,  from  such  as  are  visible  to  the 
naked  eye  down  to  the  smallest  point  of  light  perceptible  with  the  best 
telescopes. 

(786.)  These  phaonomena  agree  with  the  supposition  that  the  stars  of 
our  firmament,  instead  of  being  scattered  in  all  directions  indifferently 
through  space,  form  a  stratum  of  which  the  thickness  is  small,  in  com- 
parison with  its  length  and  breadth;  and  in  which  the  earth  occupies  a 
place  somewhei'e  about  the  middle  of  its  thickness,  and  near  the  point 
where  it  subdivides  into  two  principal  laminae,  inclined  at  a  small  angle  to 
each  other  (art.  302).     For  it  is  certain  that,  to  an  eye  so  situated,  the 
apparent  density  of  the  stars,  supposing  them  pretty  equally  scattered 
through  the  space  they  occupy,  would  be  least  in  a  direction  of  the  visual 
ray  (as  S  A),  perpendicular  to  the  lamina,  and  greatest  in  that  of  its 
breadth,  as  S  B,  S  C,  S  D ;  increasing  rapidly  in  passing  from  one  to  the 
other  direction,  just  as  we  see  a  slight  haze  in  the  atmosphere  thickening 
into  a  decided  fog-bank  near  the  horizon,  by  the  rapid  increase  of  the 
mere  length  of  the  visual  ray.     Such  is  the  view  of  the  construction  of 
the  starry  firmament  taken  by  Sir  William  Herschel,  whose  powerful 


telescopes  first  effected  a  complete  analysis  of  this  wonderful  zone,  and 

demonstrated  the  fact  of  its  entirely  consisting  of  stars.'     So  crowded  are 

I  they  in  some  parts  of  it,  that  by  coxmting  the  stars  in  a  single  field  of  his 

'Thomas  Wright  of  Durham  (Theory  of  the  Universe,  London,  1750)  appears  so 
I  early  as  1734  to  have  entertained  the  same  general  view  as  to  the  consiitution  of  the 
1  Milky  Way  and  starry  firmament,  founded,  quite  in  the  spirit  of  just  astronomical 
I  speculation,  on  a  partial  resolution  of  a  portion  of  it  with  a  "  one-foot  reflector"  (a 
Iteflector  one  foot  in  focal  length).  See  an  account  of  this  rare  work  by  M.  de  Morgan 
I  in  Phil.  Mag.  Ser.  3.  xxxii.  p.  241.  et  seq. 


li 


mm 

**• 

it 

lift 


ti' 


446 


OUTLINES   OF  ASTRONOMY. 


■,m  ^wy  ■* 


««K.  ■*^'.  W..-i 


KV) 


-ji  ■(.« 


c 


telescope,  he  was  led  to  conclude  that  50,000  had  passed  under  his  review 
in  a  zone  two  degrees  in  breadth,  during  a  single  hour's  observation.  In 
that  part  of  the  milky  way  which  is  situated  in  lOA  30m  R  A  and  between 
the  147th  and  150th  degree  of  N  P  D,  upwards  of  5000  stars  have  been 
reckoned  to  exist  in  a  square  degree.  The  immense  distances  at  which 
the  remoter  regions  must  be  situated  will  sufficiently  account  for  the  vast 
predominance  of  small  magnitudes  which  are  observed  in  it. 

(787.)  The  course  of  the  Milky  Way  as  traced  through  the  heavens 
by  the  unaided  eye,  neglecting  occasional  deviations  and  following  the  lino 
of  its  greatest  brightness  as  well  as  its  varying  breadth  and  intensity  will 
permit,  conforms  nearly  to  that  of  a  great  circle  inclined  at  an  angle  of 
about  63"  to  the  equinoctial,  and  cutting  that  circle  in  11  A  OA  47m  and 
12A  47m,  so  that  its  northern  and  southern  poles  respectively  are  situated 
in  R.  A.  12^  47m  N  P  D  03°  and  R.  A.  OA  47m  N  P  D  117°.    Through- 
out  the  region  where  it  is  so  remarkably  bjbdivided  (art.  186),  this  great 
circle  holds  an  intermediate  situation  between  the  two  great  streams ;  with 
a  nearer  approximation  however  to  the  brighter  and  continuous  stream, 
than  to  the  fainter  and  interrupted  one.     If  we  trace  its  course  in  order 
of  right  ascension,  we  find  it  traversing  the  constellation  Cassiopeia,  its 
brightest  part  passing  about  two  degrees  to  the  north  of  the  star  5  of  that 
constellation,  i,  e.  in  about  62°  of  north  declination,  or  28°  N  P  D, 
Passing  thence  between  y  and  e  Cassiopeia)  it  sends  off  a  branch  to  the 
south-preceding  side,  towards  o  Persei,  very  conspicuous  as  far  as  that 
star,  prolonged  faintly  towards  «  of  the  same  constellation,  and  possibly 
traceable  towards  the  Hyades  and  Pleiades  as  remote  outliers.     The  main 
stream  however  (which  is  here  very  faint),  passes  on  thn  ugh  Auriga,  over 
the  three  remarkable  stars,  i,  Cj  «?>  of  that  constellation  preceding  Cupella, 
called  the  Hocdi,  preceding  Capella,  between  the  feet  of  Gemini  and  tlio 
horns  of  the  Bull  (where  it  inte.'sects  the  ecliptic  nearly  in  the  Solstitial 
Colure)  and  thence  over  the  club  of  Orion  to  the  neck  of  Monoceros, 
intersecting  the  equinoctial  in  R.  A.  6A  5^  m.     Up  to  this  point,  from 
the  offset  in  Perseus,  its  light  is  feeble  and  indefinite,  but  thenceforward 
it  receives  a  gradual  accession  of  brightness,  and  where  it  passes  througli 
the  shoulder  of  Monoceros  and  over  the  head  of  Canis  Major  it  presents 
abroad,  moderately  bright,  very  uniform,  and  to  the  naked  eye,  starless 
stream  up  to  the  point  where  it  enters  the  prow  of  the  ship  Argo,  nearly 
on  the  southern  tropic'     Here  it  again  subdivides  (about  the  star  m 

'■  In  reading  this  description  a  celestial  crlobe  will  be  a  necessary  companion.  It  may 
be  thought  needless  to  detail  the  course  of  the  Milky  Way  verbally,  since  it  is  mapped 
down  on  all  celestial  charts  and  globes.  But  in  the  generality  of  them,  indeed  in  all 
whicn  have  come  to  our  knowledge,  this  is  done  so  very  loosely  and  incorrectly,  as  by  | 
no  means  to  dispense  with  a  verbal  description. 


COURSE   OF  THE  VIA  LAOTEA  TRACED. 


447 


mder  his  review 
jbscrvation.  In 
tl  A  and  between 
I  stars  liavc  been 
jtancea  at  which 
sount  for  tho  vast 
lit. 

mgh  the  heavens 
following  the  line 
and  intensity  will 
2d  at  an  angle  of 
R  A  O/i  47w  ami 
ctively  are  situated 
D  117°-    Througli- 
rt.  186),  this  great 
great  streams ;  with 
continuous  stream, 
its  course  in  order 
atiou  Cassiopeia,  its 
of  the  star  8  of  that 
,n,  or  28°  N  P  D. 
off  a  branch  to  tbe 
iuous  as  far  as  that 
nation,  and  possibly 
outliers.    The  main 
thi- ugh  Auriga,  over 

m  preceding  Capella, 
of  Gemini  and  tbc 
sarly  in  the  Solstitial 
neck  of  Monoceros, 
,  to  this  point,  from 
,e,  but  thenceforward 
ere  it  passes  througli 
Qis  Major  it  presents 
,e  naked  eye,  starless  I 
the  ship  Argo,  nearly 
,g  (about  the  star  w 

Issary  companion.  Uniay 
Irbally.sinceitisrnappe 
Ity  of  them,  indeed  m  1 
lely  and  incorrectly,  as"? 


Puppis),  sending  off  a  narrow  and  winding  branch  on  the  preceding  side 
as  far  as  y  Argils,  where  it  terminates  abruptly.  The  main  stream  pur- 
sues its  southward  course  to  the  123d  parallel  of  N  P  D,  where  it  diffuses 
itself  broadly  and  again  subdivides,  opening  out  into  a  wide  fan-like  ex- 
panse nearly  20°  in  breadth  formed  of  interl  ing  branches,  all  which 
terminate  abruptly,  in  a  line  drawn  nearly  through  ».  and  y  Argfts. 

(788.)  At  this  place  the  continuity  of  the  Milky  Way  is  interrupted 
by  a  wide  gap,  and  where  it  recommences  on  the  opposite  side  it  is  by  a 
somewhat  similar  fan-shaped  assemblage  of  branches  which  converge  upon 
the  bright  star  tj  Argfts.     Thence  it  crosses  the  hind  feet  of  the  Centaur, 
forming  a  curious  and  sharply  defined   semicircular  concavity  of  small 
radius,  and  enters  the  Cross  by  u  very  bright  neck  or  isthmus  of  not  more 
than  3  or  4  degrees  in  breadth,  being  the  narrowest  portion  of  the  Milky 
Way.     After  this  it  immediately  expands  into  a  broad  and  bright  mass, 
enclosing  the  stars  a  and  ^  Crucis,  and  [3  Centauri,  and  extending  almost 
up  to  a  of  tho  latter  constellation.     In  the  midst  of  this  brigijt  mass,  sur- 
rounded by  it  on  all  sides,  and  occupying  about  half  its  breadth,  occurs  a 
singular  dark  poii  r-shapod  vacancy,  so  conspicuous  and  remarkable  as  to 
attract  the  notice  of  the  most  superficial  gazer,  and  to  have  acquired  among 
the  early  southern  navigators  the  uncouth  but  expressive  appellation  of 
tho  coal-mck.     In  this  vacancy  which  is  about  8°  in  length,  and  5°  broad, 
only  one  very  small  star  visible  to  the  naked  eye  occurs,  though  it  is  far 
from  devoid  of  telescopic  stars,  so  that  its  striking  blackness  is  simply  due 
to  the  effect  of  contrast  with  the  brilliant  ground  with  which  it  is  on  all 
sides  surrounded.     This  is  the  place  of  nearest  approach  of  the  Milky 
Way  to  the  South  Pole.    Throughout  all  this  region  its  brightness  is  very 
striking,  and  when  compared  with  that  of  its  more  northern  course  already 
traced,  conveys  strongly  the  impression  of  greater  proximity,  and  would 
almost  lead  to  a  belief  that  our  situation  as  spectators  is  separated  on  all 
sides  by  a  considerable  interval  from  the  dense  body  of  stars  composing 
the  Galaxy,  which  in  this  view  of  the  subject  would  come  to  be  considered 
as  a  fiat  ring  of  immense  and  irregular  breadth  and  thickness,  within 
which  we  are  excentrically  situated,  nearer  to  the  southern  than  to  the 
northern  part  of  its  circuit. 

(789.)  At  o  Centauri,  the  Milky  Way  again  subdivides',  sending  off  a 
great  branch  of  nearly  half  its  breadth,  but  which  thins  off  rapidly,  at  an 
angle  of  about  20°  with  its  general  direction,  towards  the  preceding  side, 
to  »j  and  d  Lupi,  beyond  which  it  loses  itself  in  a  narrow  and  faint  stream- 
let. The  main  stream  passes  on  increasing  in  breadth  to  y  Normae,  where 
it  makes  an  abrupt  elbow  and  again  subdivides  into  one  principal  and  con 
'  All  the  maps  and  globes  place  this  subdivision  at  j3  Centauri,  but  erroneously. 


""4W 
«.« 

'«« 

"131 
Jt 

J. 
••» 


H 


^ 


:4' 


448 


OUTLINES   OF  ASTRONOMY. 


'Cm 


mn 


•2?.'* 


.«;;• 


•;      HA 


fc.  i<e  ••iu  ■« 


.1..- 
H     -^  'iv  k' 


%2  '»^' 


■*M») 


tinuoua  stream  of  very  irregular  breadth  and  brigbtncsa  on  the  following 
side,  and  a  compliuatod  system  of  interlaced  streaks  and  masses  on  the 
preceding,  which  covers  the  tail  of  Scorpio,  and  terminates  in  a  vast  and 
faint  cilusion  over  the  whole  extensive  region  occupied  by  the  preceding 
leg  of  Ophiuchus,  extending  northwards  to  the  parallel  of  103"  N  P  D, 
beyond  which  it  cannot  bo  traced ;  a  wide  interval  of  14°,  free  from  all 
appearance  of  nebulous  light,  separating  it  from  the  great  branch  on  the 
north  side  of  the  equinoctial  of  which  it  is  usually  represented  as  a  con- 
tinuation. 

(790.)  Returning  to  the  point  of  separation  of  this  great  branch  from 
the  main  stream,  let  us  now  pursue  the  course  of  the  latter.  Making  an 
abrupt  bend  to  the  following  side,  it  passes  over  the  stars  »  Ara),  9  and  i 
Scorpii,  and  y  Tubi  to  y  Sagittarii,  where  it  suddenly  collects  into  a  vivid 
oval  mass  about  6°  in  length  and  4°  in  breadth,  so  excessively  rich  ia 
stars  that  a  very  moderate  calculation  makes  their  number  exceed  100,000. 
Northward  of  this  mass,  this  stream  crosses  the  ecliptic  in  longitude  about 
276°,  and  proceeding  along  the  bow  of  Sagittarius  into  Autinous  has  its 
course  rippled  by  three  deep  concavities,  separated  from  each  other  by 
remarkable  protuberances,  of  which  the  larger  and  brighter  (situated 
between  Flamstead's  stars  3  and  6  Aquilas)  forms  the  most  conspicuous 
patch  in  the  southern  portion  of  the  Milky  Way  visible  in  our  latitudes. 

(791.)  Crossing  the  equinoctial  at  the  19th  hour  of  right  ascension,  it 
next  runs  in  an  irregular,  patchy,  and  winding  stream  through  Aquila, 
Sagitta  and  Vulpecula  up  to  Cygnus ;  at  e  of  which  constellation  its  con. 
tiuuity  is  interrupted,  and  a  very  confused  and  irregular  region  commences, 
marked  by  a  broad  dark  vacuity,  not  unlike  the  southern  "  coal-sack," 
occupying  the  space  between  «,  a,  and  y  Cygni,  which  serves  aa  a  kind  of 
centre  for  the  divergence  of  three  great  streams;  one,  which  we  have 
already  traced ;  a  second,  the  continuation  of  the  first  (across  the  interval) 
from  a  northward,  between  Lacerta  and  the  head  of  Cepheus  to  the  point 
in  Cassiopeia  whence  we  set  out,  and  a  tbird  branching  off  from  y  Cygni, 
very  vivid  and  conspicuous,  running  off  in  a  southern  direction  through  ^ 
Cygni,  and  s  Aquiloo  almost  to  the  equinoctial,  where  it  loses  itself  in  a 
region  thinly  sprinkled  with  stars,  where  in  some  maps  the  modern  con- 
stellation Taurus  Poniatovii  is  placed.  This  is  the  branch  which,  if  con- 
tinued across  the  equinoctial,  might  bo  supposed  to  unite  with  the  great 
southern  effusion  in  "Ophiuchus  already  noticed  (art.  789).  A  considerable 
offset,  or  protuberant  appendage,  is  also  thi  >\vn  off  by  the  northern  stream 
from  the  head  of  Cepheus  directly  towards  the  pole,  occupying  the  greater 
part  of  the  quartile  formed  by  a,  /3,  t,  and  6  of  that  constellation. 


COURSE   OF  THE   VIA   J.ACTEA  TRACED. 


449 


n  the  following 
uiassca  ou  the 
3  in  a  vast  and 
y  the  preceding 
of  103°  NPD, 
4°,  free  from  all 
t  branch  ou  the 
caented  as  a  con- 

reat  branch  from 
fter.     Making  au 
ira  *  Arco,  9  and  i 
llccts  into  a  vivid 
xcessively  rich  in 
.r  exceed  100,000. 
in  longitude  about 
)  Autinous  has  its 
oui  each  other  by 
brighter  (situated 
,c  most  conspicuous 
[o  in  our  latitudes. 
'  right  ascension,  it 
m  through  Aquila, 
,ou8tellation  its  con. 
r  region  commences, 
ithern  "coal-sack," 
ser^'cs  as  a  kind  of 
me,  which  wc  have 
(across  the  interval) 
Depheus  to  the  point 
hg  off  from  y  Cyg"i, 
[  direction  through  3 
[re  it  loses  itself  in  a 
Laps  the  modern  con- 
.ranch  which,  if  con- 
unite  with  the  great 
;9).     A  considerable 
the  northern  stream 
.ccupying  the  greater 
Iconstellatiou. 


(702.)  Wo  have  been  somewhat  circumstantial  in  describing  the  course 
and  principal  features  of  the  Via  Lactea,  not  only  because  there  docs  not 
occur  anywhere  (so  far  as  we  know)  any  correct  account  of  it,  but  chiefly 
by  reason  of  its  high  interest  in  sidereal  astronotny,  and  that  the  reader 
may  perceive  how  very  difficult  it  must  necessarily  be  to  form  any  just 
conception  of  the  real,  solid  form,  as  it  exists  in  space,  of  an  object  so 
complicated,  and  which  we  see  from  a  point  of  view  so  unfavourable. 
The  difficulty  is  of  the  eamo  kind  which  wo  experience  when  we  set  our- 
selves to  conceive  the  real  shape  of  an  auroral  arch  or  of  the  clouds,  but 
far  greater  in  degree,  because  we  know  the  laws  which  regulate  the  forma- 
tion of  the  latter,  and  limit  them  to  certain  conditions  of  altitude  —  be- 
cause their  motion  presents  thorn  to  us  in  various  aspects,  but  chiefly 
because  wo  contemplate  them  from  a  station  considerably  below  their 
general  plane,  so  as  to  allow  of  our  raapjting  out  some  kind  of  ground- 
plan  of  their  shape.     All  these  aids  are  wanting  when  wc  attempt  to  map 
and  model  out  the  Galaxy,  and  beyond  the  obvious  conclusion  that  its 
form  must  be,  generally  speaking,  flat,  and  of  a  thickness  small  in  com- 
parison with  its  area  in  length  and  breadth,  the  laws  of  perspective  afford 
us  little  further  assistance  in  tho  inquiry.     Probability  may,  it  is  true, 
here  and  there  enlighten  us  as  to  certain  features.     Thus  when  wc  sec,  as 
in  tho  coal-sack,  a  sharply  defined  oval  space  free  from  stars,  insulated  in 
the  midst  of  a  uniform  band  of  not  much  more  than  twice  its  breadth,  it 
would  seem  much  less  probable  that  a  conical  or  tubular  hollow  traverses 
the  whole  of  a  starry  stratum,  continuously  extended  from  the  eye  out- 
wards, than  that  a  distant  mass  of  comparatively  moderate  thickness 
should  be  simply  perforated  from  side  to  side,  or  that  an  oval  vacuity 
should  be  seen  foreshortened  in  a  distant  foreshortened  area,  not  really 
cxcecdiu''  two  or  three  times  its  own  breadth.     Neither  can  we  without 
obvious  improbability  refuse  to  admit  that  the  long  lateral  oflsets  Vihidi  at 
so  many  places  quit  the  main  stream  and  run  out  to  great  distane  ,- ,  ire 
eitlier  planes  seen  edgeways,  or  the  convexities  of  curved  surfaccr!  ^  I"\sed 
tangentially,  rather  than  cylindrical  or  columnar  excrescences  biistliiig  up 
obliquely  from  the  general  level.     And  in  the  same  spirit  of  probable 
surmise  we  may  account  for  the  intricate  reticulations  above  described  as 
existing  in  the  region  of  Scorpio,  rather  by  the  accidental  crossing  of 
1  streaks  thus  originating,  at  very  different  distances,  or  by  a  cellular  struc- 
Iture  of  the  mass,  than  by  real  intersections.     Those  cirrous  clouds  which 
[are  often  seen  in  windy  weather,  convey  no  unapt  impression  cither  of  the 
Ikind  of  appearance  in  question,  or  of  the  structure  it  suggests.     It  is  to 
lother  indications  however,  and  chiefly  to  the  telescopic  examination  of  its 
liutimate  constitution,  and  to  the  law  of  the  distribution  of  stars,  not  ouly 
29 


«!« 

■mm 
■'mm 


i\ 


t 


I 


i; 


450 


OUTLINES   OP   ASTRONOMY. 


r 


•5»,»t 


to«i(r     r.. 


"«<i«3i: 


h^  1»  w  * 


•til 


6«»-»' 


•JUS* 


within  it8  bosom,  but  generally  over  the  heavens,  that  wo  niu«t  look  for 
more  definite  knowledge  respecting  its  true  form  and  extent. 

(708.)  It  is  on  ()bst'rvation,4  of  this  latter  class,  and  not  on  merely 
speculative  or  conjectural  vi(!ws,  that  the  generalization  in  Art.  780,  which 
refers  the  phrcnomena  of  the  starry  firmament  to  the  system  of  the  Gii. 
luxy  as  their  embodying  fact,  is  brought  to  depend.  Tho  process  of 
"gauging"  tho  heavens  was  devised  by  Sir  W.  Ucrschcl  for  this  purpose. 
It  consisted  in  simply  counting  the  stars  of  nil  magnitudes  which  occur  in 
single  fields  of  view,  of  15'  in  din  iioter,  visible  through  a  reflecting  tele- 
scope of  18  inches  aperture,  and  '20  feet  focal  length,  with  a  magnifying 
power  of  180°  :  the  points  of  observation  being  very  numerous  and  taken 
indiscriminately  in  every  part  of  the  surface  of  tho  sphere  visible  in  our 
latitudes.  On  a  comparison  of  many  hundred  such  "gauges"  or  local 
enumerations  it  appears  that  the  density  of  star-light  (or  the  number  of 
stars  existing  on  an  average  of  several  such  enumerations  in  any  one  im- 
mediate neighbourhood)  is  least  in  tho  polo  of  the  Galactic  circle,^  and 
increases  on  all  sides,  with  the  Galactic  polar  distance  (and  that  nearly 
equally  in  all  directions)  down  to  the  Milky  Way  itself,  where  it  attains 
its  maximum.  The  progressive  rate  of  increase  in  proceeding  from  the 
pole  is  at  first  slow,  but  becomes  more  and  more  rapid  as  we  approach  the 
plane  of  that  circle  according  to  a  law  of  which  the  following  numbers, 
deduced  by  M.  Struve  from  a  careful  analysis  of  all  the  gauges  in  ques- 
tion,  will  afford  a  correct  idea. 

Qolactio  9  North  Polar  DiBta&oe. 


0° 
15° 
30° 
45° 
60° 
75° 
90° 


ATcraKo  Number  of  Stars  in  a 
field  15'  in  Diameter. 

415 

4-68 

:      ...     6-52 

',     10-36 

rA    17-68      ' 

30-30 

122-00 


From  which  it  appears  that  the  mean  density  of  the  stars  in  the  galacti. 
circle  exceeds  in  a  ratio  of  very  nearly  30  to  1  that  in  its  pole,  and  in  a  I 
proportion  of  more  than  4  to  1  that  in  a  direction  15°  inclined  to  its  [ 
plane.  „'■'''  ■-'''"  '--  '■'■'  "-"^-         V     '■  ■■.-■''^■.i''.'^j''";  •-■! 

'  From  yaXo,  yaXuKTus,  milk;  meaning  the  great  circle  spoken  of  in  Art.  787,  to  | 
which  the  course  of  the  Vi:  Lactea  most  nearly  conforms.    Every  subject  has  its  tech- 
nical or  conventional  term  .  by  whose  use  circumlocution  is  avoided,  and  ideas  ren-j 
dcred  definite.    This  circle  is  (o  sidereal  what  the  invariable  ecliptic  is  to  planetaryl 
astronomy  —  a  plane  of  ultimate  reference,  the  ground-plane  of  the  sidereal  system, 

'  Etudes  d' Astronomic  Steltaire,  p,  71. 


LAW   OP  DISTRIBUTION   OP   THE   STARS. 


451 


FO  murtt  look  for 
tent. 

d  not  on  merely 
u  Art.  780,  whk-h 
By  stem  of  the  (J  a. 
Tho  process  of 
si  for  this  purpose. 
dc8  which  occur  in 
rh  a  reflecting  tele- 
with  a  magnifying 
lumcrous  and  tukon 
phero  visible  in  our 
u  gauges"  or  local 
(or  the  number  of 
tions  in  any  one  ini- 
Galactic  circle,^  and 
nee  (and  that  nearly 
elf,  where  it  attains 
proceeding  from  the 
i  as  we  approach  tlic 
following  numbers, 
tho  gauges  in  ques- 

umbor  of  Stars  in  a 
1&'  In  Dlamotor. 

415 

4-68 

6'52 

10-36 

17-68 

30-30 
122-00 

stars  in  the  galacti. 
in  its  pole,  and  in  a  I 
ml5°  inclined  to  its 

spoken  of  in  Art.  787,  to 
Every  subject  has  its  tech- 1 
is  avoided,  and  ideas  ren- 
,le  ecliptic  is  to  planetary 
of  the  sidereal  system.  I 


(704.)  These  numbers  fully  bear  out  tho  statement  in  Art.  786,  and 
even  draw  closer  the  resemblance  by  which  that  statonicnt  is  there  illus- 
trated. For  tho  rapidly  increasing  density  of  u  fog-bank  as  tho  visual  ray 
is  dcpro.sscd  towards  the  plane  of  the  horizon  is  a  conscquonce  not  only  of 
the  mere  increase  in  length  of  the  foggy  space  traversed,  but  also  of  an 
actual  increase  of  density  in  the  fog  itself  in  its  lower  strata.  Now  this 
very  conclusion  follows  from  a  comparison  inter  sc  of  tho  numbers  above 
^ct  down,  as  M.  Struve  has  clearly  shown  from  u  mathematical  analysis 
of  the  empirical  formula,  which  faithfully  represents  their  law  of  progres- 
sion, and  of  which  he  states  tho  result  in  the  following  table,  expressing 
the  densities  of  tho  stars  at  the  respective  distances,  1,  2,  '-\,  &c.,  from  tho 
galactic  plane,  taking  the  mean  density  of  the  stars  in  that  plane  Itself 
for  unity. 


DiRtancci  ft-om  tho 
Gttlactlc  I'luuo. 

Density  of  Stars. 

1 

Dixtancrs  from  tho 
<ialactic  i'lano. 

Density  of  Stars. 

0-00 
0-05 
0-10 
0-20 
0-30 
0-40 

1-00000 
0-18568 
0-33288 
0-23805 
0-17980 
0-13021 

0-50 

o-on 

0-70 
0-80 
0-866 

008640 
0-05510 
0-03070 
0-01414 
0-00532 

The  unit  of  distance,  of  which  tho  first  column  of  this  table  expresses 
fractional  parts,  is  the  distance  at  which  such  a  telescope  is  capable  of 
rendering  just  visible  a  star  of  average  magnitude,  or,  as  it  is  termed,  its 
fpacc-pcnctratiitg  power.  As  we  ascend  therefore  from  the  galactic  piano 
into  this  kind  of  stellar  atmosphere,  we  perceive  that  the  density  of  its 
parallel  strata  decreases  with  great  rapidity.  At  an  altitude  above  that 
plane  equal  to  only  one-twentieth  of  the  telescopic  limit,  it  has  already 
diminished  to  one-half,  and  at  an  altitude  of  0-866,  to  hardly  more  than 
oue-two-hundredth  of  its  amount  in  that  plane.  So  far  as  we  can  perceive 
there  is  no  flaw  in  this  reasoning,  if  only  it  be  granted,  1st,  that  the  level 
planes  are  continuous,  and  of  equal  density  throughout;  and,  2dly,  that 
im  ahsohite  and  definite  limit  is  set  to  tclcscojnc  vision,  heyond  Schick,  if 
stars  exist,  they  elude  our  sight,  and  are  to  ns  as  if  they  existed  not :  a 
I  postulate  whose  probability  the  reader  will  be  in  a  better  condition  to  esti- 
mate, when  in  possession  of  some  other  particulars  respecting  tho  consti- 
I  tution  of  tho  Galaxy  to  be  described  presently. 

(795.)  A  similar  course  of  observation  followed  out  in  the  southern 
I  hemisphere,  leads  independently  to  the  same  conclusion  as  to  the  law  of 
I  the  visible  distribution  of  stars  over  the  southern  galactic  hemisphere,  or 
I  that  half  of  the  celestial  surface  which  has  the  south  galactic  pole  for  its 
I  centre.    A  system  of  gauges,  extending  over  the  whole  surface  of  that 


■mm 

■  ■***■ 

km 

"•« 

'♦if 

a 

.'i>» 

I* 

It 


,f 


452 


OUTLINES  OF  ASTRONOMY. 


C: 


•?' 


it     -;»  .-u*. 

P '■>';!■  »* 


Average  Number  of  Stars 
per  Field  of  ly. 

605 


I'  I 


hemisphere  taken  with  the  same  telescope,  field  of  view  and  magnifying 
power  employed  in  Sir  William  Ilerschel's  gauges,  has  afforded  the  ave- 
rage numbers  of  stars  per  field  of  15'  in  diameter,  within  the  areas  of 
zones  encircling  that  pole  at  intervals  of  15°,  sec  down  in  the  following 
table. 

Zones  of  Oakctlc  South 
Polar  Distance. 

0°  to  15° 

15   to  30  6-62 

30   to  45  9-08 

45    to  60  13-49 

60    to  75  20-29 

75   to  90  5906 

(796.)  These  numbers  are  not  directly  comparable  with  those  of  M. 
Struve,  given  in  Art,  793,  because  the  latter  corresponds  to  the  limiting 
polar  distances,  while  these  are  the  averages  for  the  included  zones.  That 
eminent  astronomer,  however,  has  given  a  table  of  the  average  gauges  ap- 
propriate to  each  dcijree  of  north  galactic  polar  distance,'  from  which  it  is 
easy  to  calculate  averages  for  the  whole  extent  of  each  zone.  How  near 
a  parallel  the  results  of  this  calculation  for  the  northern  hemisphere  ex- 
hibit with  those  above  stated  for  the  southern,  will  be  seen  by  the  follow- 
ing table. 

Zones  of  Galactic  North 
Polar  Distance. 

0°  to  15°  4.32 

15   to  30  5-42 

30   to  45  8-21 

45   to  60  13-61 

60   to  75  24-09 

75   to  90  '                 53-43 

It  would  appear  from  this  that,  with  an  almost  exactly  similar  law  of  ap- 1 
parent  density  in  the  two  hemispheres,  the  southern  w  ^re  somewhat  richer 
in  stars  than  the  northern,  which  may,  and  not  improbably  docs,  arise  I 
from  our  situation  not  being  precisely  in  the  middle  of  its  thickness,  but  I 
somewhat  nearer  to  its  northern  surface. 

(797.)  When  examined  with  powerful  telescopes,  the  constitution  of  I 
this  wonderful  zone  is  found  to  be  no  less  various  than  its  aspect  to  the 
naked  eye  is  irregular.     In  some  regions  the  stars  of  which  it  is  wholly 
composed  are  scattered  with  remarkable  uniformity  o\er  immense  tracts, 
while  in  others  the  irregularity  of  their  (^.Istribution  is  quite  as  striking, 

'  Etudes  d'Astronomie  Stellaire,  p.  D4. 


Average  Number  of  Stars  per  Field 
of  15'  from  SI.  Struve's  Table. 


t 


TELESCOPIC   CONSTITUTION    OF   THE   GALAXY. 


453 


exhibiting  a  rapid  succession  of  closely  clustering  rich  patches  separated 
by  comparatively  poor  intervals,  and  indeed  in  some  instances  by  spaces 
absolutely  dark  and  complctdi/  void  of  any  star,  even  of  the  smallest 
tclescopic^agnitude.     In  some  places  not  more  than  40  or  50  stars  on 
an  average  occur  in  a  "gauge"  field  of  15',  while  in  others  a  similar 
average  gives  a  result  of  400  or  500.     Nor  is  less  variety  observable 
in  the  character  of  its  dificrent  regions  in  respect  of  the  magnitudes  of 
the  stars  they  exhibit,  and  the  proportional  numbers  of  the  larger  and 
smaller  magnitudes  associated  together,  than  in  respect  of  their  aggregate 
numbers.     In  some,  for  instance,  extremely  minute  stars,  though  never 
altogether  wanting,  occur  in  numbers  so  moderate  as  to  lead  us  irresistibly 
to  the  conclusion  that  in  these  regions  we  see  fairly  throxigli  the  starry 
stratum,  since  it  is  impossible  otherwise  (supposing  their  light  not  inter- 
cepted) that  the  numbers  of  the  smaller  magnitudes  should  not  go  on 
continually  increasing  ad  infinitum.     In  such  cases  moreover  the  ground 
of  the  heavens,  as  seen  between  the  stars,  is  for  the  most  part  perfectly 
dark,  which  again  would  not  be  the  case,  if  innumerable  multitudes  of 
stars,  too   minute  to  bo   individually  discernible,  existed   beyond.      In 
oth<;r  regions  we  are  presented  with  the  phenomenon  of  an  altiiost  uni- 
form degree  of  brightness  of  the  individual  stars,  accompanied  with  a 
I  very  even  distribution  of  them  over  the  ground  of  the  heavens,  both  the 
larger  and  smaller  magnitudes  being  strikingly  deficient.     In  such  cases 
it  is  equally  impossible  not  to  perceive  that  we  are  looking  through  a  sheet 
of  stars  nearly  of  a  size,  and  of  no  great  thickness  compared  with  the  dis- 
tance  which  separates  them  from  us.     Were  it  otherwise  we  should  be 
driven  to  suppose  the  more  distant  stars  uniformly  the  larger,  so  as  to 
I  compensate  by  thoir  greater  intrinsic  brightness  for  their  greater  distance, 
la  supposition  contrary  to  all  probability.     In  others  again,  and  that  not 
[unfrequently,  we  arc  presented  with  a  double  phaenomenon  of  the  same 
1,  viz.  a  tissue  as  it  were  of  large  stars  spread  over  another  of  very 
small  ones,  the  intermediate  magnitudes  being  wanting.     The  conclusion 
here  seems  equally  evident  that  in  such  cases  we  look  through  two  side- 
pi  sheets  separated  by  a  starless  interval. 
(798.)  Throughout  by  far  the  larger  portion  of  the  extent  of  the  Milky 
ay  in  both  hemispheres,  the  general  blackness  of  the  ground  of  the 
leavens  on  which  its  stars  are  projected,  and  the  r.bsence  of  that  innu- 
erable  multitude  and  excessive  crowding  of  the  smallest  visible  magni- 
u«u  .V"     :^^  jg  ^liolly  B'"'*^^*  and  of  glare  produced  by  the  aggregate  light  of  multitudes  too 
"mmense  tracts, ■"'^^1  to  affect  the  eye  singly,  which  the  contrary  supposition  would  appear 
*te  as  striking, ■"necessitate,  must,  we  +hink,  be  considered  unequivocal  indications  that 
^  V  ''^'ocnsions  in  directions  tchere  these  conditions  obtain,  are  not  only  not 

J4. 


and  magnifying 
afforded  the  ave- 
thin  the  areas  of 

in  the  following 

imljcr  of  Stars 
Bid  of  ly. 

B05 

6-62 

9-08 

.3-49 

JG-29 

3906 

e  with  those  of  M, 
,ond8  to  the  limiting 
icluded  zones.    That 
3  average  gauges  ap- 
ice,'  from  which  it  is 
ch  zone.     How  near 
hern  hemisphere  ex- 
^e  seen  by  the  follow- 

,bcr  of  stars  porFlcM 
M.  Struve'8  Table. 

4.32 

5-42 

8-21 
13-61 
24  09 
53-43 

tly  similar  law  of  ap- 
w-sre  somewhat  richer 
mprobably  does,  arise 
5  of  its  thickness,  but 

-  (. 
3,  the  constitution  of 
"Tthan  its  aspect  to  the 


'IH.IW 

■■4m 

I'M  It 
'M 


454 


OUTLINES   OF  ASTRONOMY. 


m-m  ,0 


K. 
It,     •■ 

it* 


is 


P 

s 


'W( 


infinite,  but  that  the  space-penetrating  power  of  our  telescopes  suflSces 
fairly  to  pierce  through  and  beyond  it.     It  is  but  right,  however,  to  warn 
our  readers  that  this  conclusion  has  been  controverted,  and  that  by  an 
authority  not  lightly  to  be  put  aside,  on  the  ground  of  certain  views  taken 
by  Olbers  as  to  a  defect  of  perfect  transparency  in  the  celestial  spaces,  in 
virtue  of  which  the  light  of  the  more  distant  stars  is  enfeebled  more  th.  n 
in  proportion  to  their  distance.     The  extinction  of  light  thus  originating, 
proceeding  in   geometrical  progression  while  the  distance  increases  in 
arithmetical,  a  limit,  it  is  argued,  is  placed  to  the  space-penetrating  powers 
of  telescopes,  far  within  that  which  distance  alone  apart  from  such  obscu- 
ration would  assign.     It  would  lead  us  too  far  aside  of  the  objects  of  a 
treatise  of  this  nature  to  enter  upon  any  discussion  of  the  grounds  (partly 
metaphysical)  on  which  these  views  rely.     It  must  suflSce  here  to  observe 
that  the  objection  alluded  to,  if  applicable  to  any,  is  equally  so  to  every 
part  of  the  galaxy.     We  are  not  at  liberty  to  argue  that  at  one  part  of  its 
circumference,  our  view  is  limited  by  this  sort  of  cosmical  veil  wbicL 
extinguishes  the  smaller  magnitudes,  cuts  off  the  nebulous  light  of  distant 
masses,  and  closes  our  view  in  impenetrable  darkness ;  while  at  another 
we  are  compelled  by  the  clearest  evidence  telescopes  can  afford  to  believe 
that  star-strown  vistas  lie  ojxn,  exhausting  their  powers  and  stretching 
out  beyond  their  utmost  reach,  as  is  proved  by  that  very  phaenomenoii 
which  the  existence  of  such  a  veil  would  render  impossible,  viz.  infinito 
increase  of  number  and  diminution  of  magnitude,  terminating  in  compi.  i. 
irresolvable  nebulosity.     Such  is,  in  effect,  the  spectacle  afforded  by  a  very 
large  portion  of  the  Milky  Way  in  that  interesting  region  near  its  point 
of  bifurcation  in  Scorpio  (arts.  789,  702,)  where,  through  the  iiollrvis 
and  deep  recesses  of  its  complicaied  structure  we  behold  what  lias  all  lie 
appearance  of  a  wide  and  indefinitely  prolonged  area  strewed  over  wiili 
discontinuous  masses  and  clouds  of  stars  which  the  telescope  at  length 
refuses  to  analyse.'     Whatever  other  conclusions  we  may  draw,  this  isii-t 
any  how  be  regarded  as  the  direction  of  the  greatest  linear  extens^ion  ot 
the  ground-plan  of  the  galaxy.     And  it.  would  appear  to  foik>w,  also,  a«:. 
not  less  obvious  consequence-,  that  in  those  regions  where  that,  z'^ni 
clearly  resolved  into  stars  well  separated  and  seen  ^ojWted  on  #  U'i4 
ground,  and  where  by  consequence  it  is  certain  if  the  foregoing  view.' 


'  It  would  be  doing  great  injuslice  to  the  illustrious  nsfronower  of  ?uIkova  (who?) 
opinion,  if  we  here  seem  to  controvert,  it  is  with  the  utmost  possible  dei'ereiiCf'  aiiJ 
respect)  not  to  mention  that  at  the  time  of  his  writing  the  remarkable  essay  »\f*^i 
more  than  once  cited,  in  which  the  views  in  question  are  delivered,  he  could  not  \\m 
been  aware  of  ihe  important  facts  alluded  to  in  the  text,  the  work  in  wiui^  Jih«y  "fj 
described  being  then  unpublished. 


nes 
Wdui 
and 
flgtri 


i^ 


DISTANCE   OF   THE   FIXED   STARS. 


455 


telescopes  suffices 
,  however,  to  warn 
id,  and  that  by  an 
certain  views  taken 

celestbl  spaces,  in 
iufeebled  more  th.n 
ht  thus  originating, 
stance  increases  iu 
;.penetrating  powers 
^rt  from  such  obscu- 
I  of  the  objects  of  a 

the  grounds  (partly 
affice  here  to  observe 

equally  so  to  every 
:hat  ut  one  part  of  its 

cosmical  veil  whieli 
)ulou3  ligbt  of  distant 
gg-  while  ut  another 

can  afford  to  believe 
)0wcrs  and  stretching 
aat  very  phenomenon 
uipossible,  viz.  infinite 
rmiuating  in  compl  i 
,acle  afforded  by  a  very 

y  region  near  its  point 
'through  the  iiollcffs 
ehold  what  has  all  tlio 
rea  strewed  over  viM 
le  telescope  at  lecgful 
e  may  draw,  this  ii.n«t 
est  linear  extensif^n  nt 
jar  to  UWw,  also,  u^; 
)ns  where  th»t.  zone 

the  foregoing  vievr?'' 

jnomer  of  Pulkova  (wW 
,osi  possible  delereuw  M 
remarkable  epsay  »W*ai 
hlivered,  he  could  not  havj 
.he  work  m  whwh  they  > 


correct  that  we  look  out  beyond  them  into  space,  the  smallest  visible  stars 
appear  as  such,  not  by  reason  of  excessive  distance,  but  of  a  real  inferiority 
of  size  or  brightness. 

(709.)  When  we  speak  of  the  comparative  remoteness  of  certain 
regions  of  the  starry  heavens  beyond  others,  and  of  our  own  situation  in 
them,  the  question  immediately  arises,  what  is  the  distance  of  the  nearest 
fixed  star  ?  What  is  the  scale  on  which  our  visible  firmament  is  con- 
structed ?  And  what  proportion  do  its  dimensions  bear  to  those  of  our 
own  immediate  system?  To  these  questions  astronomy  has  at  length 
been  enabled  to  afford  an  answer. 

(800.)  The  diameter  of  the  earth  has  served  us  for  the  base  of  a  tri- 
angle, in  the  trvjonomctrical  mriwij  of  our  system  (ai't.  274,)  by  which  to 
calculate  the  distance  of  the  sun ;  but  the  extreme  minuteness  of  the  sun's 
parallax  (art.  357,)  renders  the  calculation  from  this  ''ill-conditioned" 
triangle  (art.  275,)  so  delicate,  that  nothing  but  the  fortunate  combination 
of  favourable  circumstances,  afforded  by  the  transit?  of  Venus  (art.  479,) 
could  render  its  results  even  tolerably  worthy  of  reliance.  But  the  earth's 
diameter  is  too  small  a  base  for  direct  triangulation  to  the  verge  even  of 
our  own  system  (art.  526,)  and  we  are,  therefore  obliged,  to  substitute 
the  annudl  parallax  for  the  diurnal,  or,  which  comes  to  the  same  thing, 
to  ground  our  calculation  on  the  relative  velocities  of  the  earth  and  planets 
in  their  orbits  (art.  486,)  when  we  would  push  our  triangulation  to  that 
extent.  It  might  be  naturally  enough  expected,  that  by  this  enlargement 
of  our  base  to  Vhe  vast  diameter  of  the  earth's  orbit,  the  'j  :x  t  step  in  our 
survey  (art.  2V5,)  would  be  made  at  a  great  advan(age; — that  our  change 
of  station,  from  side  to  side  of  it,  would  produce  a  considerable  and  easily 
nioasurable  amount  of  annual  parallax  in  the  stars,  and  that  by  its  nieans 
ffc  shouW  come  to  a  knowledge  of  their  distance.  Tint,  after  exhausting 
ovory  refiwaaent  of  observation,  astronomers  were,  np  to  a  very  late  period, 
unabl<?  to  come  to  any  positive  and  coincident  conclusion  upon  this  head ; 
and  tiif'  ^.riount  of  sueh  parallax,  even  for  the  nearest  fi.xed  star  examined 
*ith  x\\<\  requisite  attention,  remained  mixed  up  with,  and  cojicealed 
g,  1 1*0.  cwjifB  incidental   to  all   astronomical  determinations.     The 


anion 


natufft  of  tWstte  ern^rs  has  been  explained  in  the  earlier  part  if  this  work, 
sfvd  wf!  need  tvA  remind  elw  reader  of  the  difficulties  which  must  necessa- 
rily atteiad  the  "ttempt  *o  4iwntangle  an  element  not  exceeding  a  few 
tenth?  t4m  mgfJKi,  't  ■>'  iiX'^'t  i  whole  second,  from  the  host  of  uncertain- 
ties o»trffe4  on  tb*  r«'»!n!ts  of  observations  by  them  :  none  of  thom  indi- 
vidually fMrrbflps  of  greater  magnitude,  but  embarrassing  by  their  number 
and  fluctuating  awiount.  Nevertheless,  by  successive  refinements  in 
mixuiMii^  making,  and  by  eonstantly  progressive  approximation  to  the 


■j 


456 


OUTLINES   OF  ASTRONOMY. 


exact  knowledge  of  the  Uranograpliical  corrections,  that  assurance  had 
been  obtained,  even  in  the  earlier  years  of  the  present  century,  viz.  that 
no  star  visible  in  northern  latitudes,  to  which  attention  had  been  directed, 
manifested  an  amount  of  parallax  exceeding  a  single  second  of  arc.  It  is 
worth  while  to  pause  for  a  moment  to  consider  what  conclusions  would 
follow  from  the  admission  of  a  parallax  to  this  amount. 

(801.)  Radius  is  to  the  sine  of  1"  a?  200205  to  1.  In  this  proportion 
then  at  least  must  the  distance  of  the  fixed  stars  from  the  sun  exceed  that 
of  the  sun  from  the  earth.  Again,  the  latter  distance,  as  we  have  already 
fieen  (art.  357,)  exceeds  the  earth's  radius  in  the  proportion  of  280^4  to 
1.  Taking  therefore  the  earth's  radius  for  unity,  a  parallax  of  1"  sup- 
poses a  distance  of  4!U705!)700  or  nearly  five  thou.sand  millions  of  sucii 
units:  and  lastly,  to  descend  to  ordinary  standards,  since  the  earth's  radius 
may  be  taken  at  4000  of  our  miles,  we  find  10788230040000  or  about 
twenty  billions  of  miles  for  our  resulting  distance.  '' 

(802.)  In  such  numbers  the  imagination  is  lost.  The  only  mode  wc 
have  of  conceiving  such  intervals  at  all  is  by  the  time  which  it  would 
require  for  light  to  traverse  them.  Light,  as  we  know  (art.  545,)  travels 
at  the  rate  of  102000  miles  per  second,  traversing  a  semidiameter  of  the 
earth's  orbit  in  8"'  13'-3.  It  would,  therefore,  occupy  200205  times  this 
interval,  or  3  years  and  83  days  to  traverse  the  distance  in  (question.  Now 
as  this  is  an  inferior  limit  which  it  is  already  ascertained  that  even  the 
brighlest  and  therefore  (in  the  absence  of  all  other  indications)  the  dis- 
tance of  those  innumerable  rftars  of  the  smaller  magnitudes  which  the 
telescope  discloses  lo  us  !  What  for  the  dimensions  of  the  galaxy  in 
whose  remoter  regions,  as  we  have  seen,  the  united  lustre  of  myriads 
of  stars  is  perceptible  only  in  powerful  telescopes  as  a  feeble  nebulous 
gleam ! 

(803.)  The  space-penetrafirig  power  of  a  telescope,  or  the  comparative 
diisiance  to  which  a  given  star  would  require  to  be  removed,  in  order  that 
it  may  appear  of  the  same  briglitness  in  the  telescope  as  before  to  the 
naked  eye,  may  be  calculated  from  the  aperture  of  tha  telescope  compared 
with  thai  of  the  pupil  of  the  eye,  and  from  its  retlecting  or  transmitting 
power,  ^.  e.  the  proportion  of  the  incident  light  it  conveys  to  the  observer','* 
eye.  Thus  it  has  bcea  comput<id  that  the  space-penetrating  power  of  such 
a  refl'^ctor  as  that  used  in  the  star-gaugos  above  referred  to  is  expressed 
by  the  number  75.  A  star,  then,  of  the  sixth  magnitude,  removed  to 
75  times  its  distance,  would  still  be  peroiiptiblc  «s  a  star  with  that  instru- 
ment, and  admitting  such  a  star  to  have  100th  part  of  the  light  of  a 
,«t-audard  siar  of  the  first  magnitude,  it  will  follow  that  such  a  f'.jndar! 
star,  if  removed  to  750  times  its  distance,  would  excite  in  iht  eye,  wbcu 


«r»-| 


DISTANCE    OF   THE    FIXED    STARS. 


457 


assurance  liad 
ntury,  viz.  that 
\  been  dircctod, 
id  of  arc.  It  is 
inclusions  would 

1  this  proportion 

;  sun  exceed  that 
we  have  already 

tion  of  289^4  to 

rallax  of  1"  sun- 
millions  of  such 
the  earth's  radius 

)040000  or  about 

[he  only  mode  wc 
ne  which  it  would 
(art.  545,)  travels 
iiuidiameter  of  the 
'200205  times  this 
P  in  question.    Now 
ined  that  even  the 
indications)  the  dis- 
gnitudes  which  the 
s  of  the  galaxy  in 
lustre  of  myriads 
a  feeble  nebulous 

or  the  comparative 
lOved,  in  order  that 
fpe  as  before  to  the 
1  telescope  compared 
Ling  or  transmitting 
Lys  to  the  observer's 
[rating  power  of  such 
lerred  to  is  expressed 
Ignitude,  removed  to 
Itar  with  that  instru- 
L  of  the  liglit  of  a 
that  such  afu-ndard 
cite  in  th«  «ye,  when 


viewed  through  the  gauging  telescope,  the  same  impression  as  a  star  of 
the  sixth  magnitude  docs  to  the  naked  eye.  Among  the  infinite  multitude 
of  such  stars  in  the  remoter  regions  of  the  galaxy,  it  is  but  uiir  to  con- 
clude that  innumerable  individurls  equal  in  intrinsic  brightness  to  those 
which  immediately  surround  us,  must  exist.  The  light  of  such  stars, 
then,  mu.'^t  have  occupied  upwards  of  2000  years  in  travelling  over  the 
distance  which  separates  them  from  our  own  system.  It  follows,  then, 
that  when  weol>scrve  the  places  and  note  the  appearance  of  such  stars,  we 
are  only  reading  their  history  of  two  thousand  years'  anterior  date,  thus 
wonderfully  recorded.  We  cannot  escape  this  coiitlusion,  but  by  adopting 
as  an  alternative  an  intrinsic  inferiority  of  light  in  all  the  smaller  stars 
of  the  galaxy.  Wc  shall  be  better  able  to  estimtite  the  probability  of  this 
alternative  \'hen  we  shall  liav;;  made  acquaintance  with  other  sidereal 
systems,  whose  existence  the  telescope  discloses  to  u«,  and  whose  analogy 
will  satisfy  us  that  the  view  of  the  subject  hero  taken  is  in  perfect  har- 
mony with  the  general  tenor  of  astronomical  facts. 

(804.)  Hitherto  wc  have  spoken  of  a  parallax  of  1"  as  a  mere  limit, 
below  which  that  of  any  star  yet  examined,  assuredly,  or  at  least  very 
probably,  falls,  and  it  is  not  without  a  certain  convenience  to  regard  this 
amount  of  parallax  as  a  sort  of  unit  of  reference,  which,  connected  in  the 
reader's  recollection  with  a  parallactic  unit  of  di;-tance  from  our  system 
of  20  billions  of  miles,  and  with  a  3[  years'  journey  of  light,  may  save 
bira  the  trouble  of  such  calculations,  and  ourselves  the  necessity  of  cover- 
ing our  pages  with  such  enormous  numbers,  when  speaking  of  stars  whose 
parallax  has  actually  been  ascertained  with  some  approach  to  certainty, 
either  by  direct  meridian  observation,  or  by  more  refined  and  delicate 
methods.     These  we  shall  proceed  to  explain,  after  first  pointing  out  the 
theoretical  peculiarities  which  enable  us  to  separate  and  disentangle  its 
effects  from  those  of  the  Uranographical  corrections,  and  from  other  causes 
of  error,  which,  being  periodical  in  their  nature,  add  greatly  to  the  diffi- 
culty of  the  subject.     The  effects  of  precession  and  proper  motion  (see 
art.  852,)  which  are  uniformly  progressive  from  year  to  year,  and  that  of 
rutation,  which  runs  through  its  period  in  nineteen  years,  it  is  obvious 
enough,  separate  thcrr.selves  at  once  by  these  characters  from  that  of  pa- 
rallax ;  and,  being  known  with  very  great  precision,  and  being  certainly 
independent,  as  regards  their  causes,  of  any  individual  peculiarity  in  the 
:tars  affected  by  them,  whatever  small  uncertainty  may  remain  respecting 
tlie  numerical  elements  which  enter  into  their  computation  (or,  in  mathe- 
u^^fj&i  language,  their  co-efficients),  can  give  rise  to  no  embarrassment. 
Wkk  regjird  fcr>  aberration  the  case  is  materially  different.     This  correc- 
tion iiffects  the  place  of  a  star  by  a  fluctuation,  annual  in  its  period,  and 


IK. 


458 


OUTLINES   OF  ASTRONOMY. 


B 


fn  ,■ 


therefore,  so  far  agreeing  with  parallax.  It  is  also  very  similar  in  the 
law  of  its  variation  at  different  seasons  of  the  year,  parallax  having  for 
its  apex  (see  art.  343,  344,)  the  apparent  place  of  the  sun  in  the  ecliptic, 
and  aberration  a  point  in  the  same  great  circle  90°  behind  that  place,  so 
that  in  fact  the  forrauloo  of  calculation  (the  coeflScients  excepted)  are  the 
same  for  both,  substituting  only  tor  the  sun's  longitude  in  the  expression 
for  the  one,  that  longitude  diminished  by  90"  for  the  other.  Moreover,  in 
the  absence  of  absolute  certainty  respecting  the  nature  of  the  propagation 
of  light,  astronomers  have  hitherto  considered  it  necessary  to  assume,  at 
least  as  a  possibility^  that  the  velocity  of  light  may  be  to  some  slight 
amount  dependent  on  individual  peculiarities  in  the  body  emitting  it.' 

(805.)  If  we  suppose  a  line  drawn  from  the  star  to  the  earth  at  all 
seasons  of  the  year,  it  is  evident  that  this  line  will  sweep  over  the  surface 
of  an  exceedingly  acute,  oblique  cone,  having  for  its  axis  the  line  joining 
the  sun  and  star,  and  for  its  base  the  earth's  annual  orbit,  which,  for  the 
present  purpose,  we  may  suppose  circular.  The  vStar  will  therefore  appear 
to  describe  each  year  about  its  mean  place,  regarded  as  fixed,  and  in  virtue 
of  parallax  alone,  a  minute  ellipse,  the  section  of  this  cone  by  the  surface 
of  the  celestial  sphere,  perpendicular  to  the  visual  ray.  But  there  is  also 
another  way  in  which  the  same  fact  may  be  represented.  The  apparent 
orbit  of  the  star  about  its  mean  place  as  a  centre,  will  be  precisely  that 
which  it  would  appear  to  describe,  if  seen  from  the  s'ln,  supposing  it 
really  revolved  about  that  place  in  a  circle  exactly  equal  to  the  earth's 
annual  orbit,  in  a  plane  parallel  to  the  ecliptic.  This  is  evident  from  the 
equality  and  parallelifera  of  the  lines  and  directions  concerned.  Now  the 
eifect  of  aberration  (disregarding  the  slight  variation  of  the  earth's  ve- 
locity in  diflFerent  parts  of  its  orbit)  is  precisely  similar  in  law,  and  differs 
only  in  amount,  and  in  its  bearing  reference  to  a  direction  90°  different 
in  longitude.  Suppose,  iu  order  to  fix  our  ideas,  the  maximum  of  parallax 
to  be  1"  and  that  of  aberration  20-5",  and  let  A  B,  ab,  be  two  circles 
imagined  to  be  described  separately,  as  al-ove,  by  the  star  about  its  mean  place 
S,  in  virtue  of  these  two  causes  respec' '  vely,  S  T  being  a  line  parallel  to  that 
of  the  line  of  equinoxes.  Then,  if  in  virtue  of  parallax  alone,  the  star 
would  be  found  at  a,  in  the  smaller  orbit,  it  would,  in  virtue  of  aberration 
alone,  be  found  at  A,  in  the  larger,  the  angle  a  S  A  being  a  right  angle. 
Drawing  then  A  C  equal  and  parallel  to  S  a,  and  joining  S  C,  it  will  in 


y  In  the  actual  state  of  astronomy  and  photology  this  necessity  can  hardly  be  cons 
dercd  as  still  existing,  an''  it  is  desirable,  therefore,  thnt  the  practice  of  nstronomers 
of  introducing  an  unkno  vn  correction  for  the  constant  of  aberration  into  their  "  equa- 
tions of  condition"  for  the  determination  of  pnrailax,  should  be  disused,  since  it  actu- 
ally tends  to  introduce  error  into  the  tinal  result. 


PARALLAX  OF  THE  FIXED  STARS. 


459 


similar  in  the 
Uax  having  for 
in  the  ecliptic, 
i  that  place,  so 
icepted)  are  the 
a  the  expression 
ir.    Moreover,  in 
the  propagation 
iry  to  assume,  at 
3  to  some  slight 
'  emitting  it.' 
the  earth  at  all 
)  over  the  surfoce 
s  the  line  joining 
)it,  which,  for  the 
1  therefore  appear 
xed,  and  in  virtue 
jne  by  the  surface 
But  there  is  also 
d.     The  apparent 
^  be  precisely  that 
s'ln,  supposing  it 
ual  to  the  earth's 
3  evident  from  the 
icerned.     Now  the 
of  the  earth's  ve- 
in law,  and  differs 
ction  90°  different 
iximum  of  parallax 
a  b,  be  two  circles 
bout  its  mean  place 
line  parallel  to  that 
lax  alone,  the  star 
virtue  of  aberration 
)eing  a  right  angle, 
ling  S  C,  it  will  in 

y  can  hardly  be  cons 
ractice  of  astronomers 
ition  into  their  "  equa- 
I  disused,  since  it  actu- 


virtue  of  both  simultaneously  be  found  in  C,  i.  e.  in  the  circumference  of 
a  circle  whose  radius  is  S  C,  and  at  a  point  in  that  circle  in  advance  of  A, 
the  aberrational  place,  by  the  angle  A  S  C.  Now,  since  S  A  :  A  C  : : 
20-5  : 1,  we  find  for  the  angle  A  S  C  2"  47'  35",  and  for  the  length  of 

Fig.  109. 


the  radius  S  C  of  the  circle  representing  the  compound  motion  20''-524. 
The  difference  (0"-024)  between  this  and  S  C,  the  radius  of  the  aberra- 
tion circle,  is  quite  imperceptible,  and  even  supposing  a  quantity  so  mi- 
nute to  bo  capable  of  detection  by  a  prolonged  series  of  observations,  it 
would  remain  a  question  whether  it  were  produced  by  parallax  or  by  a 
specific  difference  of  aberration  from  the  general  average  20"*5  in  the  star 
itself.  It  is  therefore  to  the  difference  of  2°  48'  between  the  angular 
situation  of  the  displaced  star  in  this  hypothetical  orbit,  i.  e.  in  the 
arguments  (as  they  are  called)  of  the  joint  correction  (P  S  C)  and  that  of 
aberration  alone  (y  S  A),  that  we  have  to  look  for  the  resolution  of  the 
problem  of  parallax.  The  reader  may  easily  figure  to  himself  the  deli- 
cacy of  an  inquiry  which  turns  wholly  (even  when  stripped  of  all  its  other 
difficulties)  on  ihc  precise  determination  of  a  quantity  of  this  nature,  and 
of  such  very  moderate  magnitude. 

(806.)  But  these  other  difficulties  themselves  are  of  no  trifling  order. 
All  astroooraicai  instruments  are  affected  by  differences  of  temperature. 
Not  only  do  the  materials  of  which  they  are  composed  expand  and  con- 
tract,  but  the  Masonry  and  solid  pifrs  on  which  they  are  erected,  nay  even 
the  very  soil  o«  which  these  ar«'  founded,  participate  in  the  general  change 
from  snmnvr  warmth  to  winter  cold.  Hence  arise  slow  oscillatory  move- 
ments of  exceedingly  minute  amount,  which  levels  and  plumb-lines  afford 


::| 


460 


OUTLINES   OF  ASTRONOMY. 


r»»T  vo 


'■taim 


■^ 


but  very  inadequate  means  of  detecting,  and  which  beint/  also  annual  in 
their  period  (after  rejecting  whatever  is  merely  casual  and  momentary) 
mix  themselves  intimately  with  the  matter  of  our  inquiry.  Refraction 
too,  besides  its  casual  variations  from  night  to  night,  which  a  long  series 
of  observations  would  eliminate,  depends  for  its  theoretical  expression  on 
the  constitution  of  the  strata  of  our  atmosphere,  and  the  law  of  tho  dis- 
tribution of  heat  and  moisture  at  different  elevations,  which  cannot  be 
unaffected  by  difference  of  season.  No  wonder  then  that  mere  raoridional 
observations  should,  almost  up  to  the  present  time,  have  proved  insufficient, 
except  in  one  very  remarkable  instance,  to  afford  unquestionable  evidence, 
and  satisfactory  quantitative  measureuient  of  the  parallel  of  any  fixed 
star. 

(807.)  The  instance  referred  to  is  that  of  a  Cvontauri,  one  of  tho  brightest 
and  for  many  other  reasons,  one  of  the  most  remarkable  of  the  southern 
stars.  From  a  series  of  observations  of  this  star,  made  at  the  Koyal 
Observatory  of  the  Cape  of  Good  Hope  in  the  years  1832  and  1S33,  by 
Professor  Ilenderson,  with  the  mural  circle  of  that  establishment,  a  paral- 
lax to  the  amount  of  an  entire  second  was  concluded  on  his  reduction  of 
the  observations  in  question  after  his  return  to  England.  Subsequent 
observations  by  Mr.  IMaclear,  partly  with  the  same,  and  partly  with  a  now 
and  far  more  efficiently  constructed  instrument  of  the  same  description 
made  in  the  years  1839  and  1840,  have  fully  confirmed  the  reality  of  the 
parallax  indicated  by  Professor  Henderson's  observations,  though  with  a 
slight  diminution  in  its  concluded  amount,  which  comes  out  equal  to 
0".9128  or  about  -JSths  of  a  second;  hri<jht  stars  in  its  immediate  neigh- 
hourhood  heing  unaffected  hy  a  similar  periodical  displacement,  and  thus 
affording  satis/actor)/  proof  that  the  displacement  indicated  in  the  case 
of  the  star  in  qiiestion  is  not  m.erehj  a  result  of  annual  variations  of 
temperature.  As  it  is  impivsible  at  present  to  answer  for  so  minute  a 
quantity  as  that  by  which  this  result  differs  from  an  exact  second,  we  may 
consider  the  distance  of  this  star  as  approximately  expressed  by  the  paral- 
lactic unit  of  distance  referred  to  in  art.  ^04, 

(808.)  A  short  time  previous  to  the  publication'  of  this  important 
result,  the  detection  of  a  sensible  and  measurable  amount  of  parallax  in  the 
star  N^  (il  Cygni  of  Flamsteed's  catalogue  of  stars  was  announced  by  the 
celebrated  astronomer  of  Kcinigsberg,  the  late  M.  Bessel.'^  This  is  a  small 
Mm!  inconspicuous  star,  hardly  exceeding  the  ^ixth  magnitude,  but  which 
had  bcou  poiuteil  out  for  especial  observation  by  the  remarkable  circum- 

'  rrofessor  llciulcrson's  paper  was  read  before  the  Astronomical  Society  of  London, 
Jan.  3,  iS39.     It  bo*ts  date  Dec.  24,  1838. 
"Astronomische  X*chrichten,  Nos.  365,  366.    Dec.  13,  1838. 


4<- 


PARALLAX  OF  THE  FIXED  STARS. 


461 


H 


iho  annual  in 
I  momentary) 
^.     Refraction 
h  a  long  scries 
expression  on 
law  of  tlio  dis- 
licb  cannot  bo 
Here  meridional 
ved  insufficient, 
jnablc  evidence, 
t)l  of  any  fixed 

!  of  tbc  brigbtest 
of  tbe  soutiicrn 
le  at  tbc  Koyal 
32  and  1833,  by 
isbnient,  a  paral- 

bis  reduction  of 
,nd.  Subsequent 
)artly  witli  a  new 

same  description 
tbe  reality  of  tbc 
us,  thougb  witb  a 

les  out  equal  to 
\immediate  neigh- 

cement,  and  thus 
\cated  in  the  case 

,al  variations  of 
for  so  minute  a 
|ct  second,  we  may 

sssed  by  tbe  paral- 

I  of  tbis  important 

,  of  parallax  in  tbe 

announced  by  tbe 

1.2    Tbis  is  a  small 

Jrnitudc.  but  wbich 

jmarkablc  circum- 

lal  Society  of  London, 


stance  of  its  being  affected  by  tijiroj)^-  motion  (see  art.  852)  i.  c.  a  regular 
and  continually  progressive  annual  displacement  among  tbe  surrounding 
stars  to  tbe  extent  of  more  tban  5"  per  annum,  a  quantity  so  very  much 
exceeding  tbo  average  of  similar  minute  annual  displacements  wbieb  many 
otber  stars  exhibit,  as  to  lead  to  a  suspicion  of  its  being  actually  nearer  to 
our  system.  It  is  not  a  little  remarkable  that  a  similar  presumption  of 
proximity  exists  also  in  the  case  of  a  Centauri,  whose  unusually  largo 
proper  motion  of  nearly  4"  per  annum  is  stated  by  Professor  Henderson 
to  have  been  the  motive  which  induced  him  to  subject  his  oi^sorvatious  of 
that  star  to  that  severe  discussion  which  led  to  the  detection  of  its  parallax. 
M.  Bessel's  observations  of  61  Cygni  were  commenced  in  August  1837, 
immediately  on  the  establishment  at  the  Klinigsberg  observatory  of  a 
magnificent  heliometer,  the  workmanship  of  the  celebrated  optician  Frauu- 
hofer,  of  Munich,  an  instrument  especially  fitted  for  the  system  of  obser- 
vation adopted ;  which  being  totally  different  from  that  of  direct  meri- 
dional observation,  more  refined  in  its  conception,  and  susceptible  of  far 
greater  accuracy  in  its  practical  application,  we  must  now  explain. 

(809.)  Parallax,  proper  motion,  and  specific  aberration  (denoting  by 
the  latter  phrase  that  part  of  the  «^  ration  of  a  star's  light  which  may 
be  supposed  to  arise  from  its  individunl  peculiarities,  and  which  we  have 
every  reason  to  believe  at  all  events  un  exceedingly  miuute  fraction  of  the 
whole,)  are  tbo  only  uranographical  corrections  which  do  not  necessarily 
affect  alike  the  apparent  places  of  two  stars  situated  in,  or  veri/  nearly  in, 
the  same  visual  line.  Supposing  then  two  stars  at  an  immense  distance, 
the  one  behind  the  other,  but  otherwise  so  situated  as  to  appear  very 
nearly  along  the  same  visual  line,  they  will  constitute  what  is  called  a  star 
optically  double,  to  distinguish  it  from  a  star  physically  double,  of  which 
more  hereafter.  Aberration  (that  which  is  common  to  all  stars),  preces- 
sion, nutation,  nay,  even  refraction,  and  instrumental  causes  of  ap)parent 
displacement,  will  affect  them  alike,  or  so  very  nearly  alike  (if  the  minute 
difference  of  their  apparent  places  be  taken  into  account)  as  to  admit  of 
the  difference  being  neglected,  or  very  accurately  allowed  for,  by  an  easy 
calculation.  If  then,  instead  of  attempting  to  determine  by  observation 
the  place  of  tbe  nearer  of  two  very  unequal  stars  (which  will  probably  be 
the  larger)  by  direct  observation  of  its  right  ascension  and  polar  distance, 
we  content  ourselves  with  referring  its  place  to  that  of  its  remoter  and 
smaller  companion  by  differential  observation,  i.  e.  by  measuring  only  its 
difference  of  situation  from  the  latter,  we  are  at  once  relieved  of  the 
necessity  of  making  these  corrections,  and  from  all  uncertainty  as  to  their 
influence  on  the  result.  And  for  the  very  same  reason,  errors  of  adjust- 
ment (art,  136),  of  graduation,  and  a  host  of  instrumental  errors,  which 


■■m  ,.f 
'Iff 


ivA^V 


,j.Sii 


462 


OUTLINES   OF    ASTRONOMY. 


wonM  for  this  delu  ,ito  purpose  fatally  affect  the  ahsuiute  dctcnuiniitlon  of 
either  star's  place,  arc  harmless  when  only  the  differ'- 'ifo  of  their  places, 
each  equally  affected  by  such  causes,  is  required  to  be  known. 

(810.)  Throwing  aside  therefore  the  consideration  of  all  these  errors 
and  corrections,  and  disregarding  for  the  present  the  minute  effect  of 


Fig.  110. 


MIL"" 


tb', 


'KW» 


spccifie  alnrvirjj'.n  and  the  uniformly  progressive  effect  of  proper  motion, 
let  us  tivif'e  ihv  effect  of  the  differences  of  the  parallaxes  of  two  stars  thus 
juxtaposed,  or  their  apparent  relative  distance  and  position  at  various 
reasons  of  rh;i  year.  Now  the  parallax  being  inversely  as  the  distance, 
the  dimensions  of  the  small  ellipses  apparently  described  (art.  805)  by 
each  star  on  the  concave  surface  of  the  heavens  by  parallactic  displacement 
will  differ, — the  nearer  star  describing  the  larger  ellipse.  Jiut  both  ^tiirs 
lying  very  nearly  in  the  same  direction  from  the  sun,  these  ellipses  will  be 
riiniilar  and  similarly  situated.  Suppose  S  and  s  to  be  the  positions  of  the 
two  stars  as  seen  from  the  sun,  and  let  A  B  C  D,  «  &  c  <l,  be  their  paral- 
lactic ellipses ;  then,  since  they  will  be  at  all  times  similarly  situated  in 
these  ellipses,  when  the  one  star  is  seen  at  A,  the  other  will  be  seen  at  a. 
When  the  earth  has  made  a  quarter  of  a  revolution  in  its  orbit,  their 
apparent  places  will  be  Bi;  when  another  quarter,  C  c;  and  when 
another,  D  d.  If,  then,  we  measure  carefully,  with  micrometers  adapted 
for  the  purpose,  their  apparent  situation  with  respect  to  each  other,  at 
different  times  of  the  year,  we  should  perceive  a  periodical  change,  both 
in  the  direction  of  the  line  joining  them,  and  in  the  distance  between 
their  centres.  For  the  lines  A  a  and  C  c  cannot  be  parallel,  nor  the  lines 
B  b  and  D  d  equal,  unless  the  ellipses  be  of  equal  dimensions,  i.  e.  unless 
the  two  stars  have  the  same  parallax,  or  are  equidistant  from  the  earth. 
(811.)  Now,  micrometers,  properly  mounted,  enable  us  to  measure  very 


PARALLAX   OF   THE   FIXED   STARS. 


468 


mimition  of 
their  places, 

tlicso  errors 
ate  effect  of 


exactly  both  tho  distance  between  two  objects  which  can  be  seen  together 
in  the  same  field  of  a  telescope,  and  tho  position  of  the  lino  joining  them 
with  respect  to  the  horizon,  or  tho  meridian,  or  any  other  determiiiato 
direction  in  tho  heavens.  The  double  imago  micrometer,  and  especially 
the  hcl'ometer  (art.  200,  *201)  is  peculiarly  adapted  for  this  purpose.  Tho 
images  of  tho  two  stars  formed  side  by  cidc,  or  in  tho  same  lino  prolonged, 
however  momentarily  displaced  by  temporary  '-^fraction  or  instrumental 
tremor,  move  tof/ethei;  preserving  their  rel;*^  ituation,  the  judgment 
of  which  is  no  way  disturbed  by  such  ir  'nents.     Tho  helio- 

meter  also,  taking  in  a  greater  range  thai;  oromcters,  enables 

us  to  compare  one  largo  star  with  more  thai  ,,  cont  small  one,  and 

to  select  such  of  tho  latter  among  many  near  it,  as  shall  bo  most  favour- 
ably situated  for  the  detection  of  any  motion  in  the  large  one,  not  partici- 
pated in  by  its  neighbours. 

(812.)  The  star  examined  by  IJcssel  has  two  such  neighbours,  both  very 
minute,  and  therefore  probably  very  distant,  most  favourably  situated,  tho 
one  (.s)  at  a  distance  of  T  42",  the  other  (.s')  at  11'  46"  from  the  Inrgo 
star,  and  so  situated,  that  their  directions  from  that  star  make  nearly  a 
right  angle  with  each  other.      The  effect  of  parallax  therefore  would 
necessarily  cause  the  two  distances  S  s  and  S  .s'  to  vary  so  as  to  attain 
tbcir  maximum  and  minimum  values  alternately  at  three-monthly  inter- 
vals, and  this  is  what  was  actually  observed  to  take  place,  the  one  distance 
being  always  on  tho  increase  or  decrease  when  the  oUicr  was  stationary 
(the  uniform  effect  of  proper  motion  being  understood  of  course  to  bo 
always  duly  accounted  for).     This  alternation,  though  so  small  in  amount 
as  to  indicate,  as  a  final  result,  a  parallax,  or  rather  a  difference  of  paral- 
laxes between  tho  large  and  small  stars  of  hardly  more  than  one  third  of 
a  second,  was  maintained  with  sucli  regularity  as  to  leave  no  room  for 
reasonable  doubt  as  to  its  cause,  and  having  been  confirmed  by  tho  further 
continuance  of  these  observations,  and  quite  recently  by  the  exact  coinci- 
dence between  the  result  thus  obtained,  and  that  deduced  by  31.  Peters 
from  observations  of  the  same  star  at  the  observatory  of  Pulkova',  is  con- 
sidered on  all  hands  as  fully  established.     The  parallax  of  this  star  finally 
resulting  from  Bessel's  observation  is  0"'348,  so  that  its  distance  from  our 
system  is  very  nearly  three  parallactic  units.  (Art.  804.) 

(813.)  The  bright  star  a  Lyroe  has  also  near  it,  at  only  43"  distance 
(and  therefore  within  the  reach  of  the  parallel  wire  or  ordinary  double 
image  micrometer)  a  very  minute  star,  which  has  been  subjected  since 
1835  to  a  severe  and  assiduous  scrutiny  by  M.  Struve,  on  the  same  prin- 
ciple of  differential  observation.     He  has  thus  established  the  existence 


It* 


'  With  the  great  vertical  circle  by  Ertel. 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


^/. 


1.0 


I.I 


11.25 


■»  Ui2   12.2 

HA 


Sdences 
Corporation 


r<\- 


<^ 


13  WnST  MAIN  STRUT 

WIUTIR.N.Y.  14SM 

(71«)t7a^S03 


4^ 


) 


&z 


■^M| 


464  OUTLINES  OF  ASTKONOMY. 

of  a  measurable  amount  of  parallax  in  the  large  star,  less  indeed  than 
that  of  61  Cygni  (being  only  about  J  of  a  second),  but  yet  sufficient 
(such  was  the  delicacy  of  his  measurements)  to  justify  this  excellent 
observer  in  announcing  the  result  as  at  least  highly  probable,  on  the 
strength  of  only  five  nights'  observation,  in  1835  and  1836.  This  pro- 
bability, the  continuation  of  the  measures  to  the  end  of  1838  and  the 
corroborative,  though  not  in  this  case  precisely  coincident,  result  of  Mr. 
Peters's  investigations  have  converted  into  a  certainty.  M.  Struve  has 
the  merit  of  being  the  first  to  bring  into  practical  application  this  method 
of  observation,  which,  though  proposed  for  the  purpose,  and  its  great  ad- 
vantages pointed  out  by  Sir  William  Herschel  so  early  as  1781',  remained 
long  unproductive  of  any  result,  owing  partly  to  the  imperfection  of 
micrometers  for  the  measurement  of  distance,  and  partly  to  a  reason 
which  we  shall  presently  have  occasion  to  refer  to. 

(814.)  If  the  component  individuals  S,  s  (^Jig.  art.  810,)  bo  (as  is  often 
the  case)  very  close  to  each  other,  the  parallactic  variation  of  their  angle 
of  position,  or  the  extreme  angle  included  between  the  lines  A  a,  Cc, 
may  be  very  considerable,  even  for  a  small  amoun'^i  of  difference  of  paral- 
laxes between  the  large  and  small  stars.  For  instance  in  the  case  of  two 
adjacent  stars  15"  asunder,  and  otherwise  favourably  situated  for  observa- 
tion, an  annual  fluctuation  to  and  fro  in  the  apparent  direction  of  their 
line  of  junction  to  the  extent  of  half  a  degree  (a  quantity  which  could 
not  escape  notice  in  the  means  of  numerous  and  careful  measurements) 
would  correspond  to  a  difference  of  parallax  of  only  g  of  a  second.  A 
difterence  of  1"  between  two  stars  apparently  situated  at  5"  distance 
might  cause  an  oscillation  in  that  line  to  the  extent  of  no  less  than  11°, 
and  if  nearer  one  proportionally  still  greater.  This  mode  of  observation 
has  not  yet  been  put  in  practice,  but  seems  to  offer  great  advantages." 

(815.)  The  following  is  a  list  of  stars  to  which  parallax  has  been  up 

to  the  present  time  more  or  less  probably  assigned : 

a  Centauri 0'913  (Henderson.) 

61  Cygni 0-348  (Bessel.) 

a  Lyfffl 0-261  (Struve.) 

"  Sirius 0-230  (Henderson.) 

,-     1830  Groombridge* 0-226  (Peters.) 

IJrssB  Majoris 0-133    ditto. 

:-'i   "     ir  ;     Arcturus  0-127    ditto. 

Polaris  0-067    ditto. 

Capella  0-046    ditto. 

■  It  has  been  referred  even  to  Galileo.  But  the  general  explanation  of  Parallax  in 
the  Systema  Cosmicum,  Dial.  iii.  p.  271  (Leyden  edit.  1699)  to  which  the  reference 
applies,  does  not  touch  any  of  the  peculiar  features  of  the  case,  or  meet  any  of  its 
difficulties. 

^  See  Phil.  Trans.  1826.  p.  266,  et  seq.  and  1827,  for  a  list  of  stars  well  adapted  for 

such  observation,  with  the  times  of  the  year  most  favourable. — The  list  in  Phil.  Trans. 

1826,  is  incorrect. 

*  Groombridge's  catalogue  of  circumpolar  stars. 


PARALLAX  OF  THE  FIXED  STARS. 


465 


iss  indeed  than 
it  yet  sufficient 
^  this  excellent 
robable,  on  the 
836.    Thispro- 
,f  1838  and  the 
Qt,  result  of  Mr. 
M.  Struve  has 
ition  this  method 
,  and  its  great  ad- 
3 1781',  remained 
)  imperfection  of 
artly  to  a  reiwon 

LO,)  be  (as  is  often 
tion  of  their  angle 
the  lines  A  a,  C  c, 
difference  of  paral- 
i  in  the  case  of  two 
ituated  for  observa- 
t  direction  of  their 
lantity  whicb  could 
jful  measurements) 

1  of  a  second.  A 
^ted  at  5"  distance 
jf  no  less  than  11°, 

lode  of  observation 
^at  advantages." 
[arallax  has  been  up 

1 0-913  (Henderson.) 
1  0-348  (Bessel.) 
0-261  (Struve.) 
O-2'30  (Henderson.; 
0-226  (Peters.) 
0*133    ditto. 
0-127    ditto. 
0-067    ditto. 
I  0-046    ditto. 
Iplanation  of  Parallax  in 

I)  to  which  the  reference 
lase,  or  meet  any  of  its 

If  stars  well  adapted  for 
■iThe  list  in  Phil.  Trans. 


Although  the  extreme  minuteness  of  the  last  four  of  these  results  de* 
prives  them  of  much  numerical  reliance,  it  is  at  least  certain  that  the 
parallaxes  by  no  means  follow  the  order  of  magnitudes,  and  this  is  farther 
shown  by  the  fact  that  u  Cygni,  one  of  M.  Peters's  stars,  shows  absolutely 
no  indications  of  any  measurable  parallax  whatever. 

(816.)  From  the  distance  of  the  stars  we  are  naturally  led  to  the  con- 
sideration of  their  real  magnitudes.     But  here  a  difficulty  arises,  which, 
so  far  as  we  can  judge  of  what  optical  instruments  are  capable  of  effi^ct- 
ing,  must  always  remain  insuperable.     Telescopes  afford  us  only  negative 
information  as  to  the  apparent  angular  diameter  of  any  star.     The  round, 
well-defined,  planetary  discs  which  good  telescopes  show  when  turned  upon 
any  of  tho  brighter  stars  are  phaenomena  of  diffraction,  dependent,  though  • 
at  present  somewhat  enigmatically,  on  the  mutual  interference  of  tho  rays 
of  light.     They  are  consequently,  so  far  as  this  inquiry  is  concerned, 
mere  optical  illusions,  and  have  therefore  been  termed  spiirious  diace. 
The  proof  of  this  is  that  telescopes  of  different  apertures  and  magnifying 
powers,  when  applied  for  the  purpose  of  measuring  their  angular  diame- 
ters, give  different  results,  the  greater  aperture  (even  with  the  same  mag- 
nifying power)  giving  the  smaller  disc.     Thai  the  true  disc  of  even  a 
large  and  bright  star  can  have  but  a  very  minute  angular  measure,  ap- 
pears from  the  fact  that  in  the  occultation  of  such  a  star  by  the  moon,  its 
extinction  is  ahsoltitely  instantaneons,  not  the  smallest  trace  of  gradual 
diminution  of  light  being  perceptible.     The   apparent  or  spurious  disc 
also  remains  'perfectly  round  and  of  its  full  size  up  to  the  instant  of  dis- 
appearance, which  could  not  be  the  case  were  it  a  real  object.     If  our  sun 
were  removed  to  the  distance  expressed  by  our  parallactic  unit  (art.  804), 
its  apparent  diameter  of  32'  3"  would  bo  reduced  to  only  0"-0093,  or  less 
than  the  hundredth  of  a  second,  a  quantity  which  we  have  not  the  smallest 
reason  to  hope  any  practical  improvement  in  telescopes  will  ever  show  as 
an  object  having  distinguishable  form. 

(817.)  There  remains  therefore  only  the  indication  which  the  quantity 
I  of  light  they  send  to  us  may  afford.     But  here  again  another  difficulty 
besets  us.     The  light  of  the  sun  is  so  immensely  superior  in  intensity  to 
[that  of  any  star,  that  it  is  impracticable  to  obtain  any  direct  comparison 
I  between  them.     But  by  using  the  moon  as  an  intermediate  term  of  com- 
parison it  may  be  done,  not  indeed  with  much  precision,  but  sufficiently 
well  to  satisfy  in  some  degree  our  curiosity  on  the  subject.     Now  a  Cen- 
jtauri  has  been  directly  compared  with  the  moon  by  the  method  explained 
jin  Art.  783.     By  a  mean  of  eleven  such  comparisons  made  in  various 
[states  of  the  moon,  duly  reduced  and  making  the  proper  allowance  on 
Iphotometric  principles  for  the  moon's  light  lost  by  transmission  through 
30 


If 


466 


OUTLINES   OF  ASTRONOMY. 


the  lens  and  prism,  it  appears  that  the  mean  quantity  of  light  sent  to  the 
earth  by  a  full  moon  exceeds  that  sent  by  a  Ccntauri  in  the  proportion  of 
27408  to  1.  Now  Wollaston,  by  a  method  apparently  unobjectionable, 
found'  the  proportion  of  the  sun's  light  to  that  of  the  full  moon  to  be 
that  of  801072  to  1.  Combining  these  results,  we  find  the  light  sent  us 
by  the  sun  to  be  that  sent  by  a  Ccntauri  as  21,955,000,000;  or  about 
twenty-two  thousand  millions  to  1.  Hence  from  the  parallax  assigned, 
above  to  that  star,  it  is  easy  to  conclude  that  its  intrinsic  splendour,  as 
compared  with  that  of  our  sun  at  equal  distances,  is  2-3247,  that  of  the 
sun  being  unity.' 

(818.)  The  light  of  Sirius  is  four  times  that  of  a  Centauri  and  its  pa- 
rallax only  0"'230  (Art.  230).  This  in  effect  ascribes  to  it  an  intrinsic 
splendour  equal  to  63-02  times  that  of  our  sun.'* 

«  Wollaston,  Phil.  Trans.  1829,  p.  27. 

*  Results  of  Astronomical  Observations  at  the  Cape  of  Good  Hope,  (fc.  Art.  278,  p. 
363.  If  only  the  results  obtained  near  the  quadratures  of  the  moon  (which  is  the  sit- 
uation most  favourable  to  exactness)  be  used,  the  resulting  value  of  the  intrinsic  light 
of  the  star  (the  sun  being  unity)  is  4-1586.  On  the  other  hand,  if  only  those  procured 
near  the  full  moon  (the  worst  time  for  observation)  be  employed,  the  result  is  1-4017. 
Discordances  of  this  kind  will  startle  no  one  conversant  with  Photometry.  That  a 
Centauri  really  emits  more  light  than  our  sun  must,  we  conceive,  be  regarded  as  an 
established  fact.  To  those  who  may  refer  to  the  work  cited  it  is  necessary  to  mention 
that  the  quantity  there  designated  by  M,  expresses,  on  the  scale  there  adopted,  500 
times  the  actual  illuminating  power  of  the  moon  at  the  time  of  observation,  that  oi  the 
mean  full  moon  beuig  unity. 

*  See  the  work  above  cited,  p.  367. — Wollaston  makes  the  light  of  Sirius  one  20,000- 
millionth  of  the  sun's.  Stsinbeil  by  a  very  uncertain  method  found  O  =  (3286500)'X 
ArcturuB. 


,y  J. 


i' 


'V, 


PERIODICAL  STARS. 


467 


light  sent  to  the 
the  proportion  of 
J  unobjectionable, 
5  full  moon  to  be 
d  the  ligbt  sent  us 
,000,000,  or  about 

parallax  assigned, 
rinsio  splendour,  as 
2-3247,  that  of  the 

Centauri  and  its  pa- 
ss to  it  an  intrinsio 


d  Hope.  ij-c.  Art.  278,  p. 
5  moon  (which  is  the  sit- 
ilue  of  the  intrinsic  hght 
,d,  if  only  those  procured 
lyed,  the  result  is  1-4017. 
iih  Photometry.    That  a 
jceive,  be  regarded  as  an 
I  it  is  necessary  to  mention 
p  scale  there  adopted,  500 
of  observation,  that  oi  the 

ieht  of  Sinus  one  20,000- 
d  found  0  =  (3286500?X 


CHAPTER  XVI. 

VARIABLE  AND  PERIODICAL  STARS. — LIST  OP  THOSE  ALREADY  KNOWN. 

—  IRREGULARITIES  IN   THEIR  PERIODS  AND  LUSTRE  WHEN  BRIGHT- 
EST.—  IRREGULAR  AND  TEMPORARY  STARS. —  ANCIENT  CHINESE  RE- 
CORDS OF   SEVERAL.  —  MISSING   STARS.  —  DOUBLE   STARS.  —  THEIR' 
CLASSIFICATION. —  SPECIMENS  OF  EACH  CLASS. — BINARY   SYSTEMS. 

—  REVOLUTION  ROUND  EACH  OTHER.  —  DESCRIBE  ELLIPTIC  ORBITS 
UNDER  THE  NEWTONIAN  LAW  OF  GRAVITY. —  ELEMENTS  OF  ORBITS 
OP  SEVERAL. —  ACTUAL  DIMENSIONS  OP  THEIR  ORBITS. —  COLOURED 
DOUBLE  STARS. — PHiENOMENON  OF  COMPLEMENTARY  COLOURS. — 
SANGUINE  STARS. — PROPER  MOTION  OF  THE  STARS. — PARTLY  AC- 
COUNTED FOR  BY  A  REAL  MOTION  OF  THE  SUN.  —  SITUATION  OF 
THE  SOLAR  APEX. — AGREEMENT  OP  SOUTHERN  AND  NORTHERN 
STARS  IN  GIVING  THE  SAME  RESULT. — PRINCIPLES  ON  WHICH  THE 
INVESTIGATION  OF  THE  SOLAR  MOTION  DEPENDS. — ABSOLUTE  VE- 
LOCITY OF  THE   sun's    MCriON.  — supposed    REVOLUTION    OP  THE 

.  WHOLE  SIDEREAL  SYSTEM  ROUND  A  COMMON  CENTRE. —  SYSTEMA- 
TIC PARALLAX  AND  ABERRATION. — EFFECT  OF  THE  MOTION  OF 
LIGHT  IN  ALTERING  THE  APPARENT  PERIOD  OF  A  BINARY  STAR. 

(819.)  Now,  for  what  purpose  are  we  to  suppose  such  magnificent  bodies 
scattered  through 'the  abyss  of  space?  Surely  not  to  illuminate  our 
nights,  which  an  additional  moon  of  the  thousandth  part  of  the  size  of 
our  own  would  do  much  better,  nor  to  sparkle  as  a  pageant  void  of  mean- 
ing and  reality,  and  bewilder  us  among  vain  conjectures.  Useful,  it  is 
true,  they  are  to  man  as  points  of  exact  and  permanent  reference ;  but  he 
must  have  studied  astronomy  to  little  purpose,  who  can  suppose  man  to  bo 
the  only  object  of  his  Creator's  care,  or  who  does  not  see  in  the  vast  and 
I  wonderful  apparatus  around  us  provision  for  other  races  of  animated 
beings.  The  planets,  as  we  have  seen,  derive  their  light  from  the  sun ; 
[but  that  cannot  be  the  case  with  the  stars.  These  doubtless,  then,  are 
I  themselves  suns,  and  may,  perhaps,  each  in  its  sphere,  be  the  presiding 
I  centre  round  which  other  planets,  or  bodies  of  which  we  can  form  no  con- 
Iception  from  sstky  analogy  offered  by  our  own  system,  may  be  circulating. 


a. 


■i 


<m 

m 


i..r  I 


« 


li  1 


468 


OUTLINES   OF  ASTKONOMY. 


m 

,   ■■  C2I 

1 

;@s: 

^n 

i 

•$^i 

i ' 

sacai 

1 

!>•»■ 

H 

^**".-*krt 

H 

^■*«»'-:3 

1 

*..,g 


(820.)  Analogies,  however,  more  than  conjectural,  are  not  wanting  to 
indicate  a  correspondence  between  the  dynamical  laws  which  prevail  in  the 
remote  regions  of  the  stars  and  those  which  govern  the  motions  of  our  own 
sj'stem.  Wherever  we  can  trace  the  law  of  periodicity  —  the  regular  re- 
currence of  the  same  phsenomeua  in  the  same  times  —  wc  are  strongly 
impressed  with  the  idea  of  rotatory  or  orbitual  motion.  Among  the  stars 
are  several  which,  though  no  way  distinguishable  from  others  by  any  appa- 
rent change  of  place,  nor  by  any  difference  of  appearance  in  telescopes, 
yet  undergo  a  more  or  less  regular  periodical  increase  and  diminution  of 
lustre,  involving  in  one  or  two  cases  a  complete  extinction  and  revival. 
These  are  called  periodical  stars.  The  longest  known  and  one  of  the  most 
remarkable  is  the  star  Omicron,  in  the  constellation  Cetus  (sometimes 
called  Mira  Ceti),  which  was  first  noticed  as  variable  by  Fabricius  in  1596. 
It  appears  about  twelve  times  in  eleven  years,  or  more  exactly  in  a  period 
of  SSI*  15"  7°  J  remains  at  its  greatest  brightness  about  a  fortnight,  being 
then  on  some  occasions  equal  to  a  large  star  of  the  second  magnitude ; 
decreases  during  about  three  months,  till  it  becomes  completely  invisible 
to  the  naked  eye,  in  which  state  it  remains  about  five  months :  and  con- 
tinues increasing  during  the  remainder  of  its  period.  Such  is  the  general 
course  of  its  phases.  It  does  not  always  however  return  to  the  same 
degree  of  brightness,  nor  increase  and  diminish  by  the  same  gradations, 
neither  are  the  successive  intervals  of  its  maxima  equal.  From  the  recent 
observations  and  inquiries  into  its  history  by  M.  Argelander,  the  mean 
period  above  assigned  would  appear  to  be  subject  to  a  cyclical  fluctua-, 
tion  embracing  eighty-eight  such  periods,  and  having  the  eflFect  of 
gradually  lengthening  and  shortening  alternately  those  intervals  to  the 
extent  of  twenty-five  days  one  way  and  the  other.'  The  irregularities  in 
the  degree  of  brightness  attained  at  the  maximum  are  probably  also  peri- 
odical. Ilevelius  relates*  that  during  the  four  years  between  October 
1672  and  December  1 676  it  did  not  appear  at  all.  It  was  unusuall)- 
bright  on  October  5,  1839  (the  epoch  of  its  maximum  for  that  year  ac- 
cording to  M.  Argelander 's  observations)  when  it  exceeded  o  Ceti  and 
equalled  p  AurigaQ  in  lustre. 

(821.)  Another  very  remarkable  periodical  star  is  that  called  Algol,  or 
ji  Persei.  It  is  usually  visible  as  a  star  of  the  second  magnitude,  and 
such  it  continues  for  the  space  of  2*  13^",  when  it  suddenly  begins  to  di- 
minish in  splendour,  and  in  about  8  J  hours  is  reduced  to  the  fourth  mag- 
nitude, at  which  it  continues  about  15"'.  It  then  begins  again  to  increase, 
and  in  3}  hours  more  is  restored  to  its  usual  brightness,  going  through  all 
its  changes  in  2*  20"  48»  58»*5.    This  remarkable  law  of  variation  cer- 

'  Actronom.  Nachr.  No.  624.  *  Lalande's  Astronomy,  Art.  794. 


PERIODICAL   STARS. 


469 


5  not  wanting  to 

ch  prevail  in  tbc 

)tions  of  our  own 

-the  regular  rc- 

•  wc  are  strongly 
Among  the  stars 

hers  by  any  appa- 

aco  in  telescopes, 

md  diminution  of 

Btion  and  revival. 

nd  one  of  the  most 
Cetus  (sometimes 

Fabricius  in  1596. 
exactly  in  a  period 

it  a  fortnight,  being 

second  magnitude; 

completely  invisible 

5  months:  and  con- 
Such  is  the  general 
return  to  the  same 

,he  same  gradations, 

al.     From  the  recent 
rgelander,  the  mean 

to  a  cyclical  fluctua-. 

Ling  the   effect  of 
liose  intervals  to  tk 
The  irregularities  in 
re  probably  also  peri- 
Us  between  October 
II.    It  was  unusually 
lum  for  that  year  ac 
exceeded  a  Ceti  and 

a  that  called  Algol,  or 

Icond  magnitude,  and 

Isuddenly  begins  to  di- 

led  to  the  fourth  mag- 

tgins  again  to  increase, 

less,  going  through  all 
law  of  variation  cer- 

Ltronomy,  Art.  794. 


tainly  appears  strongly  to  suggest  the  revolution  round  it  of  some  opaque 
body,  which,  when  iuterpo.scd  between  us  and  Algol,  cuts  off  a  large  por- 
tion of  its  light ;  and  this  is  accordingly  the  view  taken  of  the  matter  by 
Goodricke,  to  whom  we  owe  the  discovery  of  this  remarkable  fact,'  in  the 
year  1782 ;  since  which  time  the  same  phaenomena  have  continued  to  be 
observed,  but  with  this  remarkable  additional  point  of  interest,  viz.  that 
the  more  recent  observations,  as  compared  with  the  earlier  ones,  indicate 
a  diminution  in  the  periodic  time.  The  latest  observations  of  Argelander, 
Heis,  and  Schmidt,  even  go  to  prove  that  this  diminution  is  not  uniformly 
progressive,  but  is  actually  proceeding  with  accelerated  rapidity,  which 
however  will  probably  not  continue,  but,  like  other  cyclical  combinations 
in  astronomy,  will  by  degrees  relax,  and  then  be  changed  into  an  increase, 
according  to  laws  of  periodicity  which,  as  well  as  their  causes,  remain  to 
be  discovered.  The  first  minimum  of  this  star  in  the  year  1844  occurred 
on  Jan,  3,  at  4'  14»  Greenwich  mean  time.*  '  .      ,•' 

(822.)  The  star  S  in  the  constellation  Gepheus  is  also  subject  to  peri- 
odical variations,  which,  from  the  epoch  of  its  first  observation  by  Good- 
ricke in  1784  to  the  present  time,  have  been  continued  with  perfect  regu- 
larity. Its  period  from  minimum  to  minimum  is  5*  8"  47"  39'-5,  the 
first  or  epochal  minimum  for  1849  falling  on  Jan.  2,  3"  13"  37"  M.  T.  at 
Greenwich.  The  extent  of  its  variation  is  from  the  fifth  to  between  the 
third  and  fourth  magnitudes.  Its  increase  is  more  rapid  than  its  diminu- 
tion, the  interval  between  the  minimum  and  maximum  of  its  light  being 
only  l*  14'',  while  that  from  the  maximum  to  the  minimum  is  3''  lO"". 

(823.)  The  periodical  star  f3  Lyrse,  discovered  by  Goodricke  also  in 
1784,  has  a  period  which  has  been  usually  stated  at  from  6*  G*"  to  6*  11*, 
and  there  is  no  doubt  that  in  about  this  interval  of  time  its  light  under- 
goes a  remarkable  diminution  and  recovery.  The  more  accurate  observa- 
tions of  M.  Argelander  however  have  led  him  to  conclude^  the  true  period 
to  be  12*  21"  53"  10%  and  that  in  t'us  period  a  double  maximum  and 
minimum  takes  place,  the  two  maxima  being  nearly  equal  and  both  about 

'  The  same  discovery  appears  to  have  been  made  nearly  about  the  same  time  by 
Palitzch,  a  farmer  of  Prolitz,  near  Dresden, — a  peasant  by  station,  an  astronomer  by 
nature, — who,  from  his  familiar  acquaintance  with  the  aspect  of  the  heavens,  had  been 
led  to  notice  among  so  many  thousand  stars  this  one  as  distinguished  from  the  rest  by  its 
variation,  and  had  ascertained  its  period.  The  same  Palitzch  was  also  the  first  to  re- 
discover the  predicted  comet  of  Halley  in  1759,  which  he  saw  nearly  a  month  before 
any  of  the  astronomers,  who,  armed  with  their  telescopes,  were  anxiously  watching 
its  return.    These  anecdotes  carry  us  back  to  the  era  of  the  Chaldean  shepherds. 

» Ast.  Nach.  No.  472. 

'  Astron.  Nachr.  No.  264.  See  also  the  valuable  papers  by  this  excellent  astron- 
1  omer  in  A.  N.  Nos.  417,  455,  &c. 


11 


I  : 


'I  ! 


470 


OUTLINES  OF  ASTRONOMT. 


•Sea' 


tot  -rw  •' 


the  3*4  magnitude,  but  the  minima  considerably  unequal,  viz.  4-8  and 
4 -dm.  In  addition  to  this  curious  subdivision  of  the  whole  interval  of 
change  into  two  semi-periods,  we  are  presented  in  the  case  of  this  star 
with  another  instance  of  slow  alteration  of  period,  which  has  all  the  ap- 
pearance of  being  itself  periodical.  From  the  epoch  of  its  discovery  m 
1784  to  the  year  1840  the  period  was  continually  lengthening,  but  more 
and  more  slowly,  till  at  the  last-mentioned  epoch  it  ceased  to  increase,  and 
has  since  been  slowly  on  the  decrease.  As  an  epoch  for  the  least  or  ab- 
solute minimum  of  this  star,  M.  Argelander's  calculations  enable  us  to 
assign  1846  January  8*  0"  9"  53»  G.  M.  T. 

(824.)  Another  periodical  star  whose  changes  have  been  carefully  ob- 
served is  tj  Aquilse  or  Antinoi,  first  pointed  out  by  Pigott  in  1784  (a  year 
fertile  in  such  discoveries)  as  belonging  to  that  class.  Its  period  is  7''  i^ 
18"  58%  the  first  minimum  for  1849  occurring  on  Jan.  2,  at  19»  22-  55' 
G.  M.  T.  It  occupies  fifty-seven  hours  in  its  increase  from  5m  to  4'3m, 
and  115  hours  in  its  decrease^ 

(825.)  These  are  all  the  variable  stars  which  have  been  observed  with 
sufficient  care  and  for  a  sufficient  length  of  time  to  enable  us  to  speak 
with  precision  as  to  their  periods,  epochs,  and  phases  of  brightness.  But 
the  number  of  those  whose  period  is  approximately  or  roughly  known  is 
considerable,  and  of  those  whose  change  is  certain,  though  its  period  and 
limits  are  as  yet  unknown,  still  more  so.  The  following  table  includes 
the  principal  among  them,  though  each  year  adds  to  their  number : — 


star. 


jS  Persei  (Algol) 

ATauri 

Cephei 

q  Aquilffi 

*  Cancri  R.  A.  (1800)  = 

8"  32»-5  N.  P.  D.  70<»  16' 

f  Geminorum 

^LyriB 

allerculis  

59  B.  Scuti  R.  A.  180]  = 

IS"  37™;  N.  P.  D.  =  95°  67' .... 

s  AurigSB 

0  Ceti  (Mira) * 

*  Scrpentis  R.  A.  1828  = 

15"  40'»  45' 5  P.  D.  74°  20'  30" 

xCygni 

u  HydrsB  (B.  A.  C.  4501.) 

*  Cephei  (B.  A.  C.  7582.) 

34  Cygni  (B.  A.  C.  6990.) , 

»  Leonis  (B.  A.  C.  3345.) , 

xSagittarii 

t/>  Leonis 


Period. 


Change  of  Mag. 


d.    dec. 
2-8673 

4± 

6-3664 

7-1763 

9-016 
10-2 
12-9119 
63  db 

71-200 
260  ± 
331-63 

S35± 

396-875 

494  i 
6  or  6  years 
18  years  ± 
Many  years 
Ditto 
Ditto 


firom 

2 

4 

3-4 

3-4 

7-8 
4-3 
3-4 
3 

5 
3 
2 

7? 

6 

4 

3 

6 

6 

3 

6 


to 
4 

5-4 
5 
4*5 

10 
4-5 
4-6 
4 

0 
4 
0 

0 
11 
10 

6 

0 

0 

6 

0 


DlsooTered  by 


Goodrioke,  1782. 
Baxendell,  1848. 
Ooodricke,  1784. 
Pigott,  1784. 

Hind,  1848. 
Schmidt,.  1847. 
Goodricke,  1784. 
Horschel,  1796. 

Pigott,  1796. 
Heis,  1846. 
Fabrioius,  1696. 

Harding,  1826. 
Kirch,  1687. 
Maraldi,  1704. 
Herschel,  1782. 
Janson,  1600. 
Koch,  1782. 
Halley,  1676. 
Hontaaari,  1667. 


VARIABLE  AND   PERIODICAL   STARS. 


m 


lual,  via.  4-8  and 
whole  interval  of 
3  case  of  this  star 
oh  has  all  the  ap- 
of  its  discovery  m 
jthening,  but  more 
ted  to  increase,  and 
•or  the  least  or  ab- 
itions  enable  us  to 

e  been  carefully  ob- 
jott  in  1784  (a  year 
Its  period  is  7'  4" 
a.  2,  at  IQ'' 22-55' 
36  from  6m  to  4-3m, 

5  been  observed  with 

enable  us  to  speali 

of  br'^htness.    But 

r  or  roughly  known  18 

though  its  period  and 

owing  table  includes 

their  number  :— 


» 


0 
6 


6 


1  Qoodrioke,  1782. 
Baxendelli  1848. 
Goodricke,  1784. 
Pigott,  1784. 

I  Hind,  1848. 
I  8ohinidt,,1847. 

Goodricke,  1784. 

Horschel,  1796. 

Pigott,  1795. 
Hei8,1846. 
Fabrioius,  15»o. 

I  Harding,  1826. 
Kirch,  1687. 
Maraldi,  1704. 
Herschel,  1782. 
Janson,  1600. 
Koch,  1782. 
Halley,1676. 
1  Montaaarii  loO«. 


Star. 


>>Cygni 

«  Virginia  R.  A.  (1840)  => 

12"  3™5  N.  P.  D.  82°  8' 

'»  CoronoD  Bor.  (B.  A.  C.  6230).... 

7  Arietis  (B.  A.  C.  681.) 

q ArgAs 

a  Orionis  

a  Ur889  Majoris 

tl  UrssB  Mnjoris 

^UrssB  Minoris 

a  Cassiopeiffi 

a  Ilydrse 

♦  R.  A.  (1847)  =  22*  68"  67-9  N. 
P.  D.  =  80o  17' 30" 

»  R.  A.  (1848)  =  7*  33™  65-2  N. 
P.  D.  =  66°  11' 56" 

*  R.  A.  (1848)  =  7"  40"!  10-3  N. 
P.  D.  =»  66°  53'  29". 

Near  *'r.  A.  22*  21m  O'-kyisi's.) 
N.  P.  D.  100°  42'  40" 

«  R.  A.  (1848)  14*  44"'  39»-6  N.  P. 
D.  101°  45' 26" 

i  UrsBD  Mnjoris 


Poriod. 


d.    dec. 
Many  years 

145  days 

10}  months 

5  years? 

Irregular 

Ditto 

Some  years 

Ditto 

2  or  3  years  ? 

226  days  ? 

29  or  30  days! 

Unknown 

Ditto 

Ditto 

Ditto 

Ditto 
Many  years 


Change  of  Slag. 


from 
4-6 

6-r 

0 

0 

1 

1 

1-2 

1-2 

2 

2 

23 

8? 


7-8 

8 
2? 


to 
5-6 

0 

0 

8 

4 

1-2 

2 

2 

2-3 

2-3 

3 

0 

0 

0 

0 

9-10 
2-3 


DlacoTored  by 


Herschel,  Jr.,  1842? 

Harding,  1814. 
Pigott,  1795. 
Piazzi,  1798. 
Burohell,  1827. 
Herschel,  jr.,  1836. 
Ditto,  1846. 
Ditto,  1846. 
Struve,  1838. 
Herschel,  jr.,  1838. 
Ditto,  1837. 

Hind,  1848. 

Ditto,  1848. 

Ditto,  1848. 

RUmker. 

Schumacher. 
JAatter  of  general 
remark. 


N.  B.  In  the  above  list  the  letters  B.  A.  C.  indicate  the  catalogue  of  the  British  Asso- 
ciation, B.  the  catalogue  of  Bode.  Numbers  before  the  name  of  the  constellation  (oa 
34  Cygni)  denote  Flamsteed's  stars.  Since  this  table  was  drawn  up,  four  additional 
stars,  variable  from  the  8th  or  9th  magnitude  to  0,  have  been  communicated  to  ua  by 
Mr.  Hind,  whose  places  are  as  follows:  (1.)  R.  A.  1*  SS""  24';  N.  P.  D.  81°  9'  39"; 
(•2.)  4*  SO™  42',  82°  6'  36"  (1846) ;  (3.)  8*  43»  8.,  86°  11'  (1800) ;  (4.)  22*  12"  9',  82° 
59'  24"  (1800.)  Mr.  Hind  remarks  that  about  several  variable  stars  some  degree  of 
haziness  is  perceptible  at  their  minimum.  Have  they  clouds  revolving  round  them  as 
planetary  or  cometary  attendants?  He  also  draws  attention  to  the  fact  that  the  red 
colour  predominates  among  variable  stars  generally.  The  double  star,  Nn.  2718  of 
Struve's  Catalogue,  R.  A.  20*  34",  P.  D.  77°  54',  is  stated  by  the  author  to  v-  rriable. 
Captain  Smyth  (Celestial  Cycle,  i.  274)  mentions  also  3  Leonis  and  18  Le  Miis  as 
variable,  the  former  from  G"  toO,  P=78  days,  the  latter  from*5"  to  10",  P  =  311"*  23*, 
but  without  citing  any  authority.  Piazzi  sets  down  96  and  97  Virginia  and  38  Herculis 
as  variable  stars.  [The  blood-red  star,  4*  51"  50-9',  102°  2'  4"  (1850),  discovered  by 
Mr.  Hind,  is  stated  by  Schmidt  (Ast.  Nachr.  760)  to  have  been  seen  by  him  6"  in  Jan. 
1850,  and  to  have  totally  disappeared  in  Dec.  1850  and  Jan.  1851.] 

(826.)  Irregularities  similar  to  those  which  have  been  noticed  in  the 
case  of  o  Ceti,  in  respect  of  the  maxima  and  minima  of  brightness  attained 
in  successive  periods,  have  been  also  observed  in  several  others  of  the  stars 
in  the  foregoing  list,  x  Cygni,  for  example,  is  stated  by  Cassini  to  have 
been  scarcely  visible  throughout  the  years  1699,  1700,  1701,  at  those 
times  when  it  was  expected  to  be  most  conspicuous.  No.  59  Scuti  is 
sometimes  visible  to  the  naked  eye  at  its  minimum,  and  sometimes  not  so, 
and  its  maximum  is  also  very  irregular.    Pigott's  variable  star  in  Corona 


r-' 


ii 


lli.; 


472 


OUTLINES   OF   ASTRONOMY. 


It-  -^  '-,^ 
Elf  13 

Mil  THi-lJ^ 


is  stated  by  M.  Argelandcr  to  vary  for  tho  most  part  so  little  that  the 
unaided  eyo  can  hardly  decide  on  its  maxima  and  minima,  while  yot  after 
the  lupso  of  whole  ycara  of  these  slight  fluctuations,  they  suddenly  become 
BO  great  that  the  star  completely  vanishes.  The  variations  of  a  Orionis, 
which  were  most  striking  and  unequivocal  in  the  years  1836— 1H44>, 
within  the  years  since  elapsed  became  much  less  conspicuous.  They 
seem  now  (Jan.  1849)  to  have  recommenced. 

(827.)  These  irregularities  prepare  us  for  other  phionomena  of  stellar 
variation,  which  have  hitherto  been  reduced  to  no  law  of  periodicity,  and 
must  be  looked  upon,  in  relation  to  our  ignorance  and  inexperience,  as 
altogether  casual;  or,  if  periodic,  of  periods  too  long  to  have  occurred 
more  than  once  within  the  limits  of  recorded  observation.  The  phosno- 
mena  we  allude  to  are  those  of  Tem^wrary  Stars,  which  have  appeared, 
from  time  to  time,  in  diflferent  parts  of  the  heavens,  blazing  forth  with 
extraordinary  lustre ;  and  after  remaining  awhile  apparently  immoveable, 
have  died  away,  and  left  no  trace.  Such  is  the  star  which,  suddenly  ap- 
pearing some  time  about  the  year  125  b.  c,  and  which  was  visible  in  the 
day-time,  is  said  to  have  attracted  the  attention  of  Hipparchus,  and  led 
him  to  draw  up  a  catalogue  of  stars,  the  earliest  on  record.  Such,  too, 
was  the  star  which  appeared,  A.  d.  380,  near  a  Aquilse,  remaining  for 
three  weeks  as  bright  as  Venus,  and  disappearing  entirely.  In  the  years 
945, 1264,  and  1572,  brilliant  stars  appeared  in  the  region  of  the  heavens 
between  Cepheus  and  Cassiopeia;  and,  from  the  imperfect  account  wc 
have  of  the  places  of  the  two  earlier,  as  compared  with  that  of  the  Inst, 
which  was  well  determined,  as  well  as  from  the  tolerably  near  coincidence 
of  the  intervals  of  their  appearance,  we  may  suspect  them,  with  Oood- 
ricke,  to  bo  one  and  the  same  star,  with  a  period  of  312  or  perhaps  of 
156  years.  The  appearance  of  the  star  of  1572  was  bo  sudden,  that 
Tycho  Brahe,  a  celQl)rated  Danish  astronomer,  returning  one  evening  (the 
11th  of  November)  from  his  laboratory  to  his  dwelling-house,  was  sur- 
prised to  find  a  group  of  country  people  gazing  at  a  star,  which  he  was 
sure  did  not  exist  half  an  hour  before.  This  was  the  star  in  questioD. 
It  was  then  as  bright  as  Sirius,  and  continued  to  increase  till  it  surpassed 
Jupiter  when  brightest,  and  was  visible  at  mid-day.  It  began  to  diminish 
in  December  of  the  same  year,  and  in  March,  1574,  had  entirely  disap- 
peared. So,  also,  on  the  10th  of  October,  1604,  a  star  of  this  kind,  and 
not  less  brilliant,  bnrst  forth  in  the  constellation  of  Serpentarius,  which 
continued  visible  till  October,  1605. 

(828.)  Similar  phsenomena,  though  of  a  less  splendid  character,  have 
taken  place  more  recently,  as  in  the  case  of  the  star  of  the  third  magni- 
tude discovered  in  1670,  by  Anthelm,  in  the  head  of  the  Swan ;  which, 


■>l 


IRREGULAR  AND  TEMPORARY  STARS. 


478 


J  little  that  the 
I,  while  yet  after 
suddenly  become 
m  of  a  Ononis, 
irs  1836—1840, 
lapicuous.     They 

inomena  of  stellar 
>f  periodicity,  and 
d  inexperionco,  as 
to  have  occurred 
;ion.     The  phaino- 
ich  have  appeared, 
blazing  forth  with 
irently  immoveable, 
which,  suddenly  ap- 
h  was  visible  in  the 
lipparchus,  and  led 
record.     Such,  too, 
^uilse,  remaining  for 
tirely.    In  the  years 
egion  of  the  heavens 
aperfect  account  we 
rith  that  of  the  last, 
bly  near  coincidence 
•t  them,  with  Good- 
:  312  or  perhaps  of 
vras  so  sudden,  that 
ing  one  evening  (the 
Uing-house,  was  sur- 
a  star,  which  he  was 
the  star  in  question, 
rease  till  it  surpassed 
It  began  to  diminish 
4,  had  entirely  disap- 
jtar  of  this  kind,  and 
Serpentarius,  which 

^ndid  character,  have 
Ir  of  the  third  magni- 
])f  the  Swan;  which, 


after  becoming  completely  invisible,  re-nppcared,  and,  after  undergoing 
one  or  two  singular  fluctuations  of  light,  during  two  years,  at  last  died 
away  entirely,  and  has  not  since  been  seen. 

(829.)  On  the  night  of  the  28th  of  April,  1848,  Mr.  Hind  observed  a 
star  of  the  fifth  magnitude  or  5-4  (very  conspicuous  to  the  naked  eye)  in 
a  part  of  the  constellation  Ophiuehus  (ll.A.  IG''  51"'  l'-5.  N.P.D.  102" 
39'  14"),  where,  from  perfect  fumiliurity  with  that  region,  he  was  certain 
that  up  to  the  fifth  of  that  month  no  star  so  bright  as  9-10  m.  previously 
existed.  Neither  has  any  record  been  discovered  of  a  star  being  there 
observed  at  any  previous  time.  From  the  time  of  its  discovery  it  con- 
tinued to  diminish)  without  any  alteration  of  place,  and  before  the 
advance  of  the  season  rendered  further  observation  impracticable,  was  . 
nearly  extinct.  Its  colour  was  ruddy,  and  was  thought  by  many 
observers  to  undergo  remarkable  changes,  an  effect  probably  of  its  low 
situation. 

(880.)  The  alterations  of  brightness  in  the  southern  star  tj  Arg{!t9,  which 
have  been  recorded,  are  very  singular  and  surprising.    In  the  time  of  Halley 
(1677)  it  appeared  as  a  star  of  the  fourth  magnitude.     Lacaille,  in  1751, 
observed  it  of  the  second.    In  the  interval  from  1811  to  1815,  it  was  again 
of  the  fourth ',  and  again  from  1822  to  1826  of  the  second.     On  the  1st 
of  February,  1827,  it  was  noticed  by  Mr.  Burchell  to  have  increased  to 
the  first  magnitude,  and  to  equal  a  Crueis.     Thence  again  it  receded  to 
the  second ;  and  so  continued  until  the  end  of  1837.     All  at  once  in  the 
beginning  of  1888  it  suddenly  increased  in  lustre  so  as  to  surpass  all  the 
stars  of  the  first  magnitude  except  Sirius,  Canopus,  and  a  Centauri,  which 
last  star  it  nearly  equalled.     Thence  it  again  diminished,  but  this  time 
not  below  the  first  magnitude  until  April,  1843,  when  it  had  again 
JDoreascd  so  as  to  surpass  Canopus,  and  nearly  equal  Sirius  in  splendour. 
"A  strange  field  of  speculation,"  it  has  been  remarked,  "is  opened  by 
this  phaDnomenon.     The  temporary  stars  heretofore  recorded  have  all 
become  totally  extinct.    Variable  scars,  so  far  as  they  have  been  carefully 
attended  to,  have  exhibited  periodical  alternations,  in  some  degree  at 
least  regular,  of  splendour  and  comparative  obscurity.     But  here  we  have 
a  star  fitfully  variable  to  an  astonishing  extent,  and  whose  fluctuations  are 
spread  over  centuries,  apparently  in  no  settled  period,  and  with  no  regu- 
larity of  progression.     What  origin  can  we  ascribe  to  these  sudden  flashes 
and  relapses?     What  conclusions  are  we  to  draw  as  to  the  comfort  or 
I  kbitability  of  a  system  depending  for  its  supply  of  light  and  heat  on  so 
I  uncertain  a  source  ?"     Speculations  of  this  kind  can  hardly  be  termed 
visionary,  when  we  consider  that,  from  what  has  before  been  said,  we  are 
compelled  to  admit  a  community  of  nature  between  the  fixed  stars  and  our 


I' 


m 
* 


-'i 


474 


OUTLINES  OF  ASTRONOMY. 


^■*  -I.  ^ 


•». 


own  sun ;  and  when  wo  reflect  that  geology  testifies  to  the  fact  of  exten- 
sive changes  having  taken  place  at  epochs  of  the  most  remote  antiquity  in 
the  climate  and  temperature  of  our  globe ;  changes  difficult  to  reconcile 
with  the  operation  of  secondary  causes,  such  as  a  dificrent  distribution  of 
sea  and  land,  but  which  would  find  an  easy  and  natural  explanation  in  a 
slow  variation  of  the  supply  of  light  and  hebt  afforded  primarily  by  the  sun 
itself. 

(881.)  The  Chinese  annals  of  Ma-touan-lin/  in  which  buind  officiaUij 
recorded,  though  rudely,  remarkable  astronomical  phaenomena,  supply  a 
long  list  of  "  strange  stars,"  among  which,  though  the  greater  part  urc 
evidently  comets,  some  may  be  recognized  as  belonging  in  all  probability 
to  the  class  of  Temporary  Stars  as  above  characterized.  Such  is  that 
which  is  recorded  to  have  appeared  in  A.  D.  178,  between  a  and  fi  Hen- 
tauri,  which  (no  doubt,  scintillating  from  its  low  situation)  exhibited 
(« the  five  colours,"  and  remained  visible  from  December  in  that  year  till 
July  in  the  next.  And  another  which  these  annals  assign  to  a.  d.  1011, 
and  which  would  seem  to  be  identical  with  a  star  elsewhere  referred  to 
A.  D.  1012,  "  which  was  of  extraordinary  brilliancy,  and  remained  visible 
in  the  southern  part  of  the  heavens  during  three  months,"'  a  situation 
agreeing  with  the  Chinese  record,  which  places  it  low  in  Sagittarius. 
Among  several  less  unequivocal  is  one  referred  to  b.  c.  184,  in  Scorpio, 
which  may  possibly  have  been  Hipparchus's  star.  None  of  the  stars  of 
A.  D.  889,  945,  1264,  and  1572,  however,  are  noticed  in  these  records. 
It  is  worthy  of  especial  notice,  that  all  the  stars  of  this  kind  on  record, 
of  which  the  places  are  distinctly  indicated,  have  occurred,  without  excfp' 
tioTif  in  or  close  upon  the  borders  of  the  Milky  Way,  and  that  only  within 
tho  following  semicircle,  the  preceding  having  offered  no  example  of  the 
kind. 

(882.)  On  a  cartful  re-examination  of  the  heavens,  and  a  comparison 
of  catalogues,  many  stars  are  now  found  to  be  missing ;  and  although 
there  is  no  doubt  that  these  losses  have  arisen  in  the  great  majority  of 
instances  from  mistaken  entries,  and  in  some  from  planets  having  been 
mistaken  for  stars,  yet  in  some  it  is  equally  certain  that  there  is  no  mis- 
take in  the  observation  or  entry,  and  that  the  star  has  really  been  observed, 
and  as  really  has  disappeared  from  the  heavens.  The  whole  subject  of 
variable  stars  is  a  branch  of  practical  astronomy  which  has  been  too  little 
followed  up,  and  it  is  precisely  that  in  which  amateurs  of  the  science,  and  j 

'  Tranelated  by  M.  Edward  Biot,  Connoissance  des  Temps,  1846. 

*  Hind,  Notices  of  the  Astronomical  Society,  viii.  156,  citing  Hepidannus.  He  placet  I 
the  Chinese  star  of  173  b.c.  between  a  and  fi  Canit  Mitwrit,  but  M.  Biot  distinctly  says  | 
a,  &  pied  oriental  du  Centaure. 


DOUBLE  STARS. 


476 


he  fact  of  extcn. 
mote  antiquity  in 
Bcult  to  reconcile 
nt  distribution  of 
i  explanation  in  a 
imarily  by  the  Bun 

ch  btund  oficialhi 
jonomena,  supply  a 
10  greater  part  iirc 
g  in  all  probability 
aod.  Sucb  is  that 
tween  a  and  »3  (Wi- 
situation)  exhibikd 
ibcr  in  that  year  till 
ssign  to  A.  D.  1011, 
Isewhere  referred  to 
ttnd  remained  visible 
months,'"  a  situation 
,  low  in  Sagittarius, 
i.  c.  184,  in  Scorpio, 
None  of  the  stars  of 
•ed  in  these  records. 
;  this  kind  on  record, 
•urred,  without  excep- 
and  that  only -within 

jd  no  example  of  the 

Ins,  and  a  comparison 
Issing;  and  although 
[he  great  majority  of 
planets  having  been 
1  that  there  is  no  mis- 
,  really  been  observed, 
,Tho  whole  subject  of 
[ich  has  been  too  little 
irs  of  the  science,  and 


[)9,  1846. 
_  Hepidannus. 
fcutM.Biot  distinctly  says 


He  places 


especially  voyagers  at  sea,  provided  with  only  good  eyes,  or  moderate  in- 
strumenls,  might  employ  their  time  to  excellent  advantage.  It  holds  out 
a  sure  promise  of  rich  discovery,  and  is  one  in  wbicli  astronomers  in 
established  observatories  are  almost  of  necessity  precluded  from  taking  a 
part,  by  the  nature  of  the  observations  required.  Catalogues  of  the  com- 
parative brightness  of  the  stars  in  each  constellation  have  been  constructed 
by  Sir  Wm.  Herschel,  with  the  express  object  of  funlitating  those  re- 
searches,  and  the  reader  will  find  them,  and  a  full  account  of  his  method 
of  comparison,  in  the  Phil.  Trans.  1706,  and  subsequent  years. 

(888.)  We  come  now  to  a  class  of  phaenomona  of  quite  a  different 
character,  and  which  give  us  a  real  and  positive  insight  into  the  nature 
of  at  least  some  among  the  stars,  and  enable  us  unhesitatingly  to  declare . 
them  subject  to  the  same  dynamical  laws,  and  obedient  to  the  same  power 
of  gravitation  which  governs  our  own  system.     Many  of  the  stars,  when 
examined  with  telescopes,  are  found  to  be  double,  i.  e.  to  consist  of  two 
(in  some  cases  three  or  more)  individuals  placed  near  together.  This  might 
be  attributed  to  accidental  proximity,  did  it  occur  only  in  a  few  instances ; 
but  the  frequency  of  this  companionship,  the  extreme  closeness,  and,  in 
many  cases,  the  near  equality  of  the  stars  so  conjoined,  would  alone  lead 
to  a  strong  suspicion  of  a  more  near  and  intimate  relation  than  mere 
casual  juxtaposition.     The  bright  star,  Castor,  for  example,  when  much 
magnified,  is  found  to  consist  of  two  stars  of  nearly  the  third  magnitude, 
within  5"  of  each  other.     Stars  of  this  magnitude,  however,  are  not  so 
common  in  the  heavens  as  to  render  it  otherwise  than  excessively  impro- 
bable that,  if  scattered  at  random,  they  would  fall  so  near.     But  this  im- 
probability becomes  immensely  increased  by  a  consideration  of  the  fact,  that 
this  is  only  one  out  of  a  great  many  similar  instances.    Mitchell,  in  1 767, 
applying  the  rules  for  the  calculation  of  probabilities  to  the  case  of  the 
six  brightest  stars  in  the  group  called  the  Pleiades,  found  the  odds  to  be 
500000  to  1  against  their  proximity  being  the  mere  result  of  a  random 
scattering  of  1500  stars  (which  he  supposed  to  be  the  total  number  of 
stars  of  that  magnitude  in  the  celestial  sphere')  over  the   heavens. 
Speculating  further  on  this,  as  an  indication  of  physical  connexion  rather 
than  fortuitous  assemblage,  he  was  led  to  surmise  the  possibility,  (since 
converted  into  a  certainty,  but  at  that  time,  antecedent  to  any  observation) 
of  the  existence  of  compound  stars  revolving  about  one  another,  or  rather 
about  their  common  centre  of  gravity.     M.  Struve,  pursuing  the  same 
train  of  thought  as  applied  specially  to  the  cases  of  double  and  triple 

■  This  number  is  considerably  too  small,  and  in  consequence,  MitcheU's  odds  in 
this  case  materially  overrated.  But  enough  will  remain,  if  this  be  rectitied,  fully  to 
bear  out  his  argument.    Phil.  Trans,  vol.  57. 


t 
I 


476 


OUTLINES   OF  ASTRONOMY. 


•SCSI 


» 


combinations  of  stars,  and  grounding  his  computations  on  a  more  perfect 
enumeration  of  the  stars  visible  down  to  the  7th  magnitude,  in  the  part 
of  the  heavens  visible  at  Dorpat,  calculates  that  the  odds  are  9570  to  1 
against  any  two  stars,  from  the  1st  to  the  7th  magnitude,  inclusive,  out 
of  the  whole  possible  number  of  binary  combinations  then  visible,  falling, 
(if  fortuitously  scattered)  •  ithin  4"  of  each  other.  Now,  the  number 
of  instances  of  such  binary  combinations  actually  observed  at  the  dato 
of  this  calculation  was  already  91,  and  many  more  have  since  been 
added  to  the  list.  Again,  be  calculates  that  the  odds  against  any 
suvh  stars  fortuitously  scattered,  falling  within  32"  of  a  third,  so  as  to 
constitute  a  triple  star,  is  not  less  than  173524  to  1.  Now,  four  such 
combinations  occur  in  the  heavens;  viz.  e  Orionis,  a  Ononis,  11  Monoce- 
rotis,  and  ^  Cancri.  The  conclusion  of  a  physical  connexion  of  some  kind 
or  other  is  therefore  unavoidable.  ■:  "- 

(834.)  Presumptive  evidence  of  another  kind  is  furnished  by  the  fol- 
lowing coasideration.  Both  a  Centauri  and  61  Cygni  are  "  Do&ble  Stars." 
Bbth  consist  of  two  individuals,  nearly  equal,  and  separated  from  each 
other  by  an  interval  of  about  a  quarter  of  a  minute.  In  the  case  of  61 
Cygni,  the  stars  exceeding  the  7th  magnitude,  there  is  already  a  priuid 
facie  probability  of  9578  to  1  against  their  apparent  proximity.  Tiic 
two  stars  of  a  Centauri  are  both  at  least  of  the  2d  magnitude,  of  which 
altogether  not  more  than  about  50  or  60  exist  in  the  whole  heavens. 
But,  waiving  this  consideration,  both  these  stars,  as  we  have  already  seen, 
have  a  proper  motion,  so  considerable  that,  supposing  the  constituent  in- 
dividuals unconnected,  one  would  speedily  leave  the  other  behind.  Yet, 
at  the  earliest  dates  at  which  they  were  respectively  observed,  these  stars 
were  not  perceived  to  be  double,  and  it  is  only  to  the  employment  of  tele- 
scopes magnifying  at  least  8  or  10  times,  that  we  owe  the  knowledge  we 
now  possess  of  their  being  so.  With  such  a  telescope,  Lacaille,  in  1751, 
was  barely  able  to  perceive  the  separation  of  the  two  constituents  of  a  Cen- 
tauri, whereas,  had  one  of  them  only  been  affected  with  the  observed 
proper  motion,  they  should  then  have  been  6'  asunder.  In  these  cases, 
then,  some  physical  connexion  may  be  regarded  as  proved  by  this  fact 
alone. 

(835.)  Sir  William  Herschel  has  enumerated  upwards  of  500  double 
stars,  of  which"  the  individuals  are  less  than  32"  asunder.  M.  Struve, 
prosecuting  the  inquiry  with  instruments  more  conveniently  mounted  for 
the  purpose,  and  wrought  to  an  astonishing  pitch  of  optical  perfection, 
has  added  more  than  five  times  that  number.  And  other  observers  have 
extended  still  further  the  catalogue  of  "  Double  Stars,"  without  exhaust- 
ing the  fertility  of  the  heavens.    Among  these  are  a  great  many,  in 


DOUBLE   STARS. 


477 


on  a  more  perfect 
tude,  in  tbo  part 
ids  are  9570  to  1 
ado,  inclusive,  out 
len  visible,  falling, 
Now,  the  number 
jerved  at  the  dato 
I  have  eince  been 
odda  against  any 
,f  a  third,  so  as  to 
I.     No\7,  four  such 
)rioni8, 11  Monoce- 
aexion  of  some  kind 

■urnished  by  the  fol- 
are  "  Doiible  Stars." 
separated  from  each 
In  the  case  of  61 
e  is  already  a  prima 
ent  proximity.     The 
magnitude,  of  vrhich 
.  the  vehole  heavens. 
Le  have  already  seen, 
,g  the  constituent  in- 
other  behind.     Yet, 
observed,  these  stars 
e  employment  of  tele- 
te  the  knovfledge  \fe 
[pe,  Lacaille,  in  1751, 
I  constituents  of  o  Cen- 
|ed  with  the  observed 
ader.     In  these  cases, 
ts  proved  by  this  fact 

Ipwards  of  500  double 
lasunder.  M.  Struve, 
Iveniently  mounted  for 
of  optical  perfection, 
other  observers  have 
T8,"  without  exhaust- 
pe  a  great  many,  in ' 


which  the  distance  between  the  component  indiviJuals  does  not  exceed  a 
single  second.  They  are  divided  into  classes  by  M.  Struve  (the  first  living 
authority  in  this  department  of  Astronomy)  according  to  the  proximity 
of  their  component  individui^ls.     The  first  class  comprises  those  only  in 
which  the  distance  does  not  exceed  1" ;  the  second  those  in  which  it  ex- 
ceed* 1",  but  falls  short  of  2";  the  3d  class  extends  from  2"  to  4"  dis» 
tance;  the  4th  from  4"  to  8";  the  5lh  from  8"  to  12";  the  6th  from  12" 
to  16" ;  the  7th  from  lb"  to  24" ;  the  8th  from  24"  to  32  .     Each  class 
he  again  subdivides  into  two  sub-classes  of  whish  the  one  under  the  ap- 
pellation of  conspicuous  double  stars  (duplices  lucidae)  comprehends  those 
in  which  both  individual i^  exceed  the  8}  magnitude,  that  is  to  say,  are 
separateli/  bright  enough  to  be  easily  seen  in  any  moderately  good  tele- 
scope.    All  others,  in  which  one  or  both  the  constituents  are  below  this 
limit  of  easy  visibility,  are  collected  into  another  sub-class,  which  he 
terms  residuary  {^Duplices  reliquse).     This  arrangement  is  so  far  conve- 
nient, that  after  a  little  practice  in  the  use  of  telescopes  as  applied  to 
such  objects,  it  is  easy  to  judge  what  optical  power  will  probably  suffice 
to  resolve  a  star  of  any  proposed  class  and  either  sub-class,  or  would  at 
least  be  so  if  the  second  or  residuary  sub-class  were  further  sub-divided 
by  placing  in  a  third  sub-class  "  delicate"  double  stars,  or  those  in  which 
the  companion  star  is  so  very  minute  as  to  requi/e  a  high  degree  of  optical 
power  to  perceive  it,  of  which  instances  will  presently  be  given. 

(836.)  The  following  may  be  taken  as  specimens  of  each  class.  They 
are  all  taken  from  among  the  lucid,  or  conspicuous  stars,  and  to  such  of 
our  readers  as  may  be  in  possession  of  telescopes,  and  may  be  disposed  to 
try  them  on  such  objects,  will  afford  him  a  ready  test  of  their  degree  of 
efficiency.       "' 

,       >'  Class  L,  r  to  1".  '      ' 


y  CoronsB  Bor. 
yCenlnuri. 
y  Lupi. 
c  Arictis. 
(,  Uerculis. 


y  Circini. 
0  Cvgni. 
c  ChamsBleontis. 


a  Piscium. 
^  HydriB. 
y  Ceti. 
y  Leonis. 
y  Corone  Aus. 


»>  Coronae. 
q  Elerculis. 
A  Cassiopeiae. 
A  Ophiuchi. 
ir  Lupi. 


7  Ophiuchi. 
0  Draconis. 
0  UrscB  IVInjoris. 
X  Aquilee. 
<o  Leonis. 


Class  II.,  1"  to  2". 


(  Bootis. 

I  Cassiopeiffi. 

'  2  Cancri. 


^  Ursffi  Majoris. 
ir  Aquilse. 
ff  Coronas  Bor. 


Class  III.,  2"  to  4". 

y  Virginia.  {  Aquarii. 

i  Serpentis.  \  Orionis. 

t  Bootis.  (  Leonis. 

t  Draconis.  i  Trianguli, 

c  HydrsB.  k  Leporis. 


Atlas  Pleiadum. 
4  Aqunrii. 
42  ComiB. 
52  Arieti.s. 
66  Piscium. 


2  Camelopardi. 
32  Orionia. 
52  Orionis. 


fi  Draconis. 
jt  Canis. 
fi  Herculis. 
a  CasBJopeiiG. 
44  Bootis. 


II* 

II' 
II 


■11' 


478 


OUTLINES  OF  ASTRONOMY. 


H  Eridani. 
70  Ophiuchi. 
12  Eridani. 
32  Eridani. 
95  Herculis. 


Class  IV.,  4"  to  8". 

a  Crucis.  8  Phoenicia.  i  Cephei. 

a  Herculis.  « Cephei.  ir  Booiis. 

a  Geminorum.  X  Ononis.  p  Capricorni. 

i  Geminorum.  ia  Cygni.  v  Argus. 

i  Coronae  Bor.  ( Bootis.  w  Aurigs. 

Class  v.,  8"  to  12". 

j3  Orionis.  {  AntlioB. 

y  Arietis.  i  Cassiopeise. 

Y  Delphini.  0  Eridani. 

Class  VI.,  12"  to  16". 

a  Centauru  y  Volantis. 

0  Cephei.  n  Lnpi. 
/3  ScorpiL  {  Urs«d  Major. 

Class  VII.,  16"  to  24". 

a  Canum  Yen.  0  Serpentis. 

c  Norms.  k  Corons  Aus. 

i  Piscium.  X  Tauri. 

Class  VIII.,  24"  to  32". 

S  Herculis.  «  Herculis. 

If  Lyra.  *  Cephei. 

1  Cancri.  >!/  Draconis. 

(837.)  Among  the  most  remarkable  triple,  quadruple,  or  multiple  stars 
(for  such  also  occur)  may  be  enumerated, 
a  Andromedae.  fl  Orionis.  fScorpii. 


1  Orionis. 
f  Eridani. 

2  Canum  Yen. 


K  Bootis. 
8  Monocerotis. 
61  Cygni. 


24  Comae. 
41  Draconis. 
61  Ophiuchi. 


X  Cygni. 
23  Ononis. 


e  Lyrae. 
^  Cancri. 


/I  Lupi. 
/I  Bootis. 


11  Monocerotis. 

12  Lyncis. 


^>n2> 


Of  these  a  Andromedae,  ft.  Bootis,  and  ft  Lupi,  appear  in  telescopes,  even 
of  considerable  optical  power,  only  as  ordinary  double  stars  j  and  it  is  only 
when  excellent  instruments  are  used  that  their  smaller  companions  are 
subdivided  and  found  to  be  in  fact,  extremely  close  double  stars.  $  Lyrse 
offers  the  remarkable  combination  of  a  double-double  star.     Viewed  with 


Fi^  111. 


a  telescope  of  low  power  it  appears  as  a  coarse  and  easily  divided  double 
star,  but  on  increasing  the  magnifying  power,  each  individual  is  perceived 


It 


OF  BINART  STARS. 


479 


H  Eridani. 
70  Ophiuchi. 
12  Eridani. 
32  Eridani. 
95  Heroulis. 


onis. 
iani. 
mm  Ven. 


JOtlS. 

[onocerottB. 
lygni. 


3oinee. 

Draconifc 

3phittclu> 


Cygm. 
Ononis. 


pie,  or  multiple  stars 

Scorpii. 
Monocerotis. 

Lyncis. 

ir  in  telescopes,  even 

stars;  and  it  is  only 

lUer  companions  are 

louble  stars.    «  Lyr» 

star.    Viewed  with 


a  2  Cancri. 

a  Polaris. 

K  Circini. 

a  2  Capricorni. 

0  Aquarii. 

K  Geminorum. 

a  Indi. 

Y  HydrsB. 

/I  Persei. 

0  LyrtB. 

Ursae  Majoris. 

7  Bootis. 

leasUy  divided  double 
idividual  is  perceived 


to  be  beautifully  an*^.  vlosely  double,  the  one  pair  being  about  2}",  the 
other  about  8"  asunder.  Each  of  the  stars  ^  Cancri,  I  Scorpii,  11  Mono- 
cerotis, and  12  Lyncis  consists  of  a  principal  star,  closely  double,  and  a 
smaller  and  more  distant  attendant,  while  0  Orionis  presents  the  phae- 
nomenon  of  four  brilliant  principal  stars,  of  the  respective  4th,  6th,  7th, 
and  8th  magnitudes,  forming  a  trapezium,  the  longest  diagonal  of  which 
is  21".4,  and  accompanied  by  two  excessively  minute  and  very  close  com- 
panions (as  in  the  annexed  figure),  to  perceive  both  which  is  one  of  the 
severest  tests  which  can  be  applied  to  a  telescope. 

(838.)  Of  the  "delicate"  sub-class  of  double  stars,  or  those  consisting 
of  very  large  and  conspicuous  principal  stars,  accompanied  by  very  minute 
companions,  the  following  specimens  may  suffice : 

^  Virginis. 

X  Eridani. 
16  Aurigse. 
94  Ceti. 

(83P.)  To  the  amateur  of  Astronomy  the  double  stars  offer  a  subject 
of  very  pleasing  interest,  as  tests  of  the  performance  of  his  telescopes, 
and  by  reason  of  the  finely  contrasted  colours  which  many  of  them  ex- 
hibit, of  which  more  hereafter.     But  it  is  the  high  degree  of  physical 
interest  which  attaches  to  them,  which  assigns  them  a  conspicuous  place 
in  modem  Astronomy,  and  justifies  the  minute  attention  and  unwearied 
diligence  bestowed  on  the  measurement  of  their  angles  of  position  and 
distances,  and  the  continual  enlargement  of  our  catalogues  of  them  by 
the  discovery  of  new  ones.     It  was,  as  we  have  seen,  under  an  impression 
that  such  combinations,  if  diligently  observed,  might  afibrd  a  measure 
of  parallax  through  the  periodical  variations  it  might  be  expected  to  pro- 
duce in  the  relative  situation  of  the  small  attendant  star,  that  Sir  W. 
Herschcl  was  induced  (between  the  years  1779  and  1784)  to  form  the 
first  extensive  catalogues  of  them,  under  the  scrutiny  of  higher  magni- 
fying powers  than  had  ever  previously  been  applied  to  such  purposes.     In 
the  pursuit  of  this  object,  the  end  to  which  it  was  instituted  as  a  means 
was  necessarily  laid  aside  for  a  time,  until  the  accumulation  of  more 
abundant  materials  should  have  afforded  a  choice  of  stars  favourably  cir- 
cumstanced for  systematic  observation.    Epochal  measures  however,  of 
each  star,  were  secured,  and,  on  resuming  the  subject,  his  attention  was 
altogether  diverted  from  the  original  object  of  the  inquiry  by  phsenomena 
of  a  very  unexpected  character,  which  at  once  engrossed  his  whole  atten- 
tion.   Instead  of  finding,  as  he  expected",  that  annual  fluctuation  to  and 
fro  of  one  star  of  a  double  star  with  respect  to  the  other, — that  alternate 
annual  increase  and  decrease  of  their  distance  and  angle  of  position,  which 
tlip  parallnx  of  the  earth's  annual  motion  would  produce, — be  observed, 


yf 


i 


480 


OUTLINES   OF  ASTRONOMY. 


> 


«:?: 


in  many  instances,  a  regular  progressive  change ;  in  some  cases  bearing 
chiefly  on  their  distance,  —  in  others  on  their  position,  and  advancing 
steadily  in  one  direction,  so  as  clearly  to  indicate  either  a  real  motion  of 
the  stars  themselves,  or  a  general  rectilinear  motion  of  the  sun  and  whole 
solar  system,  producing  a  parallax  of  a  higher  order  than  would  arise  from 
the  earth's  orbitual  motion,  and  which  might  be  called  systismatic 
parallax. 

(840.)  Supposing  the  two  stars,  and  also  the  sun,  in  motion  independ- 
ently of  each  other,  it  is  clear  that  for  the  interval  of  several  years,  these 
motions  must  be  regarded  as  rectilinear  and  uniform.  Hence,  a  very 
slight  acquaintance  with  geometry  will  sufBce  to  show  that  the  apparent 
motion  of  one  star  of  a  double  star,  referred  to  the  other  as  a  centre,  and 
mapped  down,  as  it  were,  on  a  plane  in  which  that  other  shall  be  taken 
for  a  fixed  or  zero  point,  can  be  no  other  than  a  right  line.  This,  at 
least,  must  be  the  case  if  the  stars  be  independent  of  each  other ;  but  it 
will  be  otherwise  if  they  have  a  physical  connexion,  such  as,  for  instance, 
real  proximity  and  mutual  gravitation  would  establish.  In  that  case,  they 
would  describe  orbits  round  each  other,  and  round  their  common  centre 
of  gravity  j  and  therefore  the  apparent  path  of  either,  referred  to  the  other 
as  fixed,  instead  of  being  a  portion  of  a  straight  line,  would  be  bent  into 
a  curve  concave  towards  that  other.  The  observed  motions,  however,  were 
so  slow,  that  many  years'  observation  was  required  to  ascertain  this  point; 
and  it  was  not,  therefore,  until  the  year  1803,  twenty-five  years  from  the 
commencement  of  the  inquiry,  that  any  thing  like  a  positive  conclusion 
could  be  come  to  respecting  the  rectilinear  or  orbitual  character  of  the 
observed  changes  of  position. 

(841.)  In  that,  and  the  subsequent  year,  it  was  distinctly  announced 
by  him,  in  two  papers,  which  will  be  found  in  the  Transactions  of  the 
Royal  Society  for  those  years',  that  there  exist  sidereal  systems,  composed 
of  two  stars  revolving  about  each  other  in  regular  orbits,  and  constituting 
what  may  be  termed  binary  stars,  to  distinguish  them  from  double  stars 
generally  so  called,  in  which  these  physically  connected  stars  are  con- 
founded, perhaps,  with  others  only  optically  double,  or  casually  juxta- 
posed in  the  heavens  at  different  distances  from  the  eye ;  whereas  the  in- 
dividuals of  a  binary  star  are,  of  course,  equidistant  from  the  eye,  or,  at 
least,  cannot  differ  more  in  distance  than  the  semi-diameter  of  the  orbit 
they  describe  about  each  other,  which  is  quite  insignificant  compared  with 
the  immense  distance  between  }:hem  and  the  earth.  Between  fifty  and 
sixty  instances  of  changes,  to  a  greater  or  less  amount,  in  the  angles  of 

*  The  announcement  was  in  fact  made  in  1802,  but  unaccompanied  by  the  observa- 
tions establishing  the  fact. 


OF  BINARY  8TARS. 


481 


ae  cases  bearing 
1,  and  advancing 
a  real  motion  of 
ae  sun  and  whole 
'would  arise  from 
called   systematic 

motion  independ- 
everal  years,  these 
1.     Hence,  a  very 
that  the  apparent 
er  as  a  centre,  and 
ther  shall  be  taken 
ght  line.    This,  at 
each  other ;  but  it 
ich  as,  for  instance, 
In  that  case,  they 
leir  common  centre 
referred  to  the  other 
^  would  be  bent  into 
tions,  however,  ^yere 
ascertain  this  point; 

■five  years  from  the 
positive  conclusiou 

lal  character  of  the 

I  distinctly  announced 

Transactions  of  the 
il  systems,  composed 
,its,  and  constituting 
jm  from  double  stars 

lected  stars  are  con- 
[e,  or  casually  juxta- 

eye ;  whereas  the  in- 
t  from  the  eye,  or,  at 
(diameter  of  the  orbit 
lificant  compared  with 
Between  fifty  and 

)unt,  in  the  angles  of 

pmpanied  by  the  observa- 


position  of  double  stars,  are  adduced  in  the  menioirs  above  mentioned ; 
many  of  which  are  too  decided,  and  too  regularly  progressive,  to  allow  of 
their  nature  being  misconceived.  In  particular,  among  the  more  con- 
spicuous stars, — Castor,  y  Virginis,  I  Ursae,  70  Ophiuchi,  a  and  tj  Coronee, 
I  Bootis,  fj  Cassiopeiae,  y  Leonis,  ^  Herculis,  8  Cygni,  fi  Bootis,  <  4  and  < 
5  Lyrae,  %  Ophiuchi,  fi  Draconis,  and  ^  Aquarii,  are  enumerated  as  among 
the  most  remarkable  instances  of  the  observed  ipotion ;  and  to  some  of 
them  even  periodic  times  of  revolution  are  assigned;  approximative  only, 
of  course,  and  rather  to  be  regarded  as  rough  guesses  than  as  results  of 
any  exact  calculation,  for  which  the  data  were  at  the  time  quite  inade- 
quate. For  instance,  the  revolution  of  Castor  is  set  down  at  334  years, 
that  of  y  Virginis  at  708,  and  that  of  y  Leonis  at  1200  years. 

(842.)  Subsequent  observation  has  fully  confirmed  these  results.  Of 
all  the  stars  above  named,  there  is  not  one  which  is  not  found  to  be  fully 
entitled  to  be  regarded  as  binary ;  and,  in  fact,  this  list  comprises  nearly 
all  the  most  considerable  objects  of  that  description  which  have  yet  been 
detected,  though  (as  attention  has  been  closely  drawn  to  the  subject,  and 
observations  have  multiplied)  it  has,  of  late,  received  large  accessions. 
Upwards  of  a  hundred  double  stars,  certainly  known  to  possess  this  cha- 
racter, were  enumerated  by  M.  Madler  in  1841,'  and  more  are  emerging 
into  notice  with  every  fresh  mass  of  observations  which  come  before  the 
public.  They  require  excellent  telescopes  for  their  effective  observation, 
being  for  the  most  part  so  close  as  to  necessitate  the  use  of  very  high 
magnifiers  (such  as  would  be  considered  extremely  powerful  microscopes 
if  employed  to  examine  objects  within  our  reach),  to  perceive  an  interval 
between  the  individuals  which  compose  them.  '  • 

(843.)  It  may  easily  be  supposed,  that  phsenomena  of  this  kind  would 
not  pass  without  attempts  to  connect  them  with  dynamical  theories.  From 
their  first  discovery,  they  were  naturally  refeiTcd  to  the  agency  of  some 
power,  like  that  of  gravitation,  connecting  the  stars  thus  demonstrated  to 
be  in  a  state  of  circulation  about  each  other;  and  the  extension  of  the 
Newtonian  law  of  gravitation  to  these  remote  systems  was  a  step  so  ob- 
vious, and  so  well  warranted  by  our  experience  of  its  all-suflScient  agency 
in  our  own,  as  to  have  been  expressly  or  tacitly  made  by  every  one  who 
has  given  the  subject  any  share  of  his  attention.  We  owe,  however,  the 
first  distinct  system  of  calculation,  by  which  the  elliptic  elements  of  the 
orbit  of  a  binary  star  could  be  deduced  from  observations  of  its  angle  of 
position  and  distance  at  different  epochs,  to  M.  Savary,  who  showed^  that 
the  motions  of  one  of  the  most  remarkable  among  them  (S  Ursae)  were 

'  Dorpat  Observations,  vol.  ix.  1640  and  1S41.  •  Connoiss.  des  Temps,  1830. 

31 


}; 


482 


OUTLINES   OP  ASTBONOMY. 


?& 


explicable,  within  the  limits  allowable  for  error  of  observation,  on  the 
supposition  of  an  elliptic  orbit  described  in  the  short  period  of  58^  years. 
A  different  process  of  computation  conducted  Professor  Encke'  to  an 
elliptic  orbit  for  70  Ophiucbi,  described  in  a  period  of  seventy-four  years. 
M.  Mddler  has  especially  signalized  himself  in  this  line  of  inquiry  (see 
note).  Several  orbits  have  also  been  calculated  by  Mr.  Hiud  and  Cap- 
tain Smyth,  and  the  author  of  these  pages  has  himself  attempted  to  con- 
tribute his  mite  to  these  interesting  investigations.  The  following  may 
be  stated  as  the  chief  results  which  have  been  hitherto  obtained  in  this 
branch  of  astronomy : —  ,  i- 

*  Berlin  Ephem.  1832. 

The  elements  Nos.  1,  2,  3,  4  c,  5,  6  c,  7,  11  b,  12  a,  are  extracted  from  M.  Miid- 
ler's  synoptic  view  of  the  history  of  double  stars  in  vol.  ix.  of  the  Dorpat  Observations: 
4  a,  from  the  Connoiss.  des  Temps,  1830:  4  b,  6  b,  and  11  a,  from  vol.  v.  Trans. 
AstroD.  Soc.  Lond. :  6  a,  from  Berlin  Ephemeris,  1832 :  No.  8,  from  Trans.  Astron. 
Soc.  vol.  vi. :  No.  9,  11  c,  12  b,  and  13  from  Notices  of  the  Astronomical  Society, 
vol.  vii.  p.  22,  and  viii.  p.  159,  and  No.  10  from  the  author's  "  Results  of  Astronomical 
Observations,  &c.  at  the  Cape  of  Good  Hope,"  p.  297.  The  £  prefixed  to  No.  7, 
denotes  the  number  of  the  star  in  M.  Struve's  Dorpat  Catalogue  (Catalogue  Novus 
Stellarum  Duplicium,  &c.  Dorpat,  1827),  M^hich  contains  the  places  for  1826  of  3113 
of  these  objects. 

The  "  position  of  the  node"  in  col.  4,  expresses  the  angle  of  position  (see  Art.  204) 
of  the  line  of  intersection  of  the  plane  of  the  orbit,  with  the  plane  of  the  heavens  on 
which  it  is  seen  projected.  The  "  inclination"  in  col.  6  is  the  inclination  of  these  two 
planes  to  one  another.  Col.  5  shows  the  angle  actually  included  in  tlte  plane  of  the 
orbit,  between  the  line  of  nodes  (defined  as  above)  and  the  line  of  apsides.  The  ele- 
ments assigned  in  this  table  to  w  Leonis,  (  Bootis,  and  Castor  must  be  considered  as 
very  doubtful,  and  the  same  may  perhaps  be  said  of  those  ascribed  to  m  2  Bootis,  which 
rest  on  too  small  an  arc  of  the  orbit,  and  that  too  imperfectly  observed,  to  afford  a 
secure  basis  of  calculation.  .  , 


;r;  .-=.'.:■; 


HV.' 


aCI' 


ORBITS   OF  BINARY  STARS. 


488 


)8ervation,  on  the 
jriod  of  58  i  years, 
jsor  Encke'  to  an 
seventy-four  years, 
ine  of  inquiry  (see 
Ir.  Hind  and  Cap- 
f  attempted  to  con- 
The  following  may 
rto  obtained  in  this 


ttracted  from  M.  Mad- 
leDorpat  Observations: 
I  a,  from  vol.  v.  Trans. 

8,  from  Trans.  Astron. 
3  Astronomical  Society, 

Results  of  Astronomical 
he  S  prefixed  to  No.  7, 
logue  (Catalogus  Novus 
,e  places  for  1826  of  3112 

of  position  (see  Art.  204) 
plane  of  the  heavens  on 
9  inclination  of  these  two 
luded  m  the  plane  of  tht 
ine  of  apsides.  The  ele- 
or  must  be  considered  as 
pribedto»i2Booti8,which 
ctly  observed,  to  afford  a 


\ 


w'<' 


•j.'f 


a 
I 


I 
1 

I 


u»      i-i  Tfi      Ks  •^  CO  c«      m  di      e^  90      lO  i-i  w  w  "s  "s 'it 
o 


e^      m  04  ^  >o  94  e^  ^  >A  »«  x)  04  ^  »«  CO  e^  c<3  e«i  i-i  04  >o 

o 

pH«ei-i'.4iooo>Aiamo4t«.oe>9eoJb>»-<e'4a»coi-iH< 
H*  -H  o»  CO  »o  «p  «e  o  o»  o 


ee«e«ocococo»4aoe^'Tii'^eo 

040404 


I  04  CO 


<ococoe4i;>04erHe404mc4aa'^eoes>a^^eoiHjc>.M 
.. -       «s  lA  to 


04i-l0404'^i«i«?HF-l 


e>« 


04        04 


o>'^rH>4h>oo>A>cto»-ee>Aa»<4<maoco)-<ioiH^eo^ 
CO  04      a>  a>  e>  s>  CO '<4i  CO  04  iH  K»  04      x»  04  rn  04  04  ih  ao  co 


^o«eooeaoco»-ooao^>>040>aeooooe>H 
iA«eco'.^toio-.4icoet>co>o»>«e>oo404>at««orHee4 
'^t>'^«Df>coi^cootocoa>?oaa>aot.*Qaftu»eeoo 

'*COe<5i-Ht-..-ieO'^COWTfiTH090»-i«0>^0»e4'*'0'^ 
•>*COO4T^«'»(<T>«p-«|t'^'^.*>«W<J3b-*-e4«t-0pO»'^ 

oooooooooooooooeoeooeee 


m 


"3  Zt.      •«  «  « 


.a 


*9      tl   ^ 


a  a  n  .3  «  •-  ~  -w  P.  Bi5  5  i?  S  ■«  o  -S  5 


^c'E"^ 


2  §  2  SbftS  S'S.«; 
lH04eO'^'<i'^"i''0«0«©W*^aOO>Oi-5iH.H0404CO'^>0 


O  ■- 

eoPqo^-o'^'^iS'^faW 


►•' 


f 


f'l:! 


si 


484 


OUTLINES  OF  ASTRONOMT. 


3m » 

255:3' 


4 


-<; 


St., 


(844.)  Of  the  stars  in  tbo  above  list,  that  which  has  been  most  assidu- 
ously watched,  and  has  oiFercd  phsenotnenon  of  the  greatest  interest,  is 
y  Virginis.  It  is  a  star  of  the  vulgar  8rd  magnitude  (3.08  s  Photom. 
3'494),  and  its  component  individuals  are  very  nearly  equal,  and  as  it 
would  seem  in  some  slight  degree  variable,  since,  according  to  the  obser- 
vations of  M.  Struve,  the  one  is  alternately  a  little  greater  and  a  little 
less  than  the  other,  and  occasionally  exactly  equal  to  it.  It  has  been 
known  to  consist  of  two  stars  since  the  beginning  of  the  eighteenth  cen- 
tury ;  the  distance  being  then  between  six  and  seven  seconds,  so  that  any 
tolerably  good  telescope  would  resolve  it.  When  observed  by  Herschel 
in  1780,  it  was  5"-66,  and  continued  to  decrease  gradually  and  regularly 
till  at  length,  in  1836,  the  two  stars  had  approached  so  closely  as  to  appear 
perfectly  round  and  single  under  the  highest  magnifying  power  which 
could  be  applied  to  most  excellent  instruments  —  the  great  refractor  at 
Pulkowa  alone,  with  a  magnifying  power  of  1000,  continuing  to  indicate, 
by  the  wedge-shaped  form  of  the  disc  of  the  star  its  composite  nature. 
By  estimating  the  ratio  of  its  length  to  its  breadth  and  measuring  the 
former,  M.  Struve  concludes  that,  at  this  epoch  (1836-41),  the  distance 
of  the  two  stars,  centre  from  centre,  might  be  stated  at  0"-22.  From  that 
time  the  star  again  opened,  and  at  present  (1849)  the  individuals  arc  more 
than  2"  asunder.  This  very  remarkable  diminution  and  subsequent  in- 
crease of  distance  has  been  accompanied  by  a  corresponding  and  equally 
remarkable  increase  and  subsequent  diminution  of  relative  angular  motion. 
Thus,  in  the  year  1783  the  apparent  angular  motion  hardly  amounted  to 
half  a  degree  per  annum,  while  in  1830  it  had  increased  to  5*^,  in  1834 
to  20°,  in  1835  to  40°,  and  about  the  middle  of  1836  to  upwards  of  70' 
per  annum,  or  at  the  rate  of  a  degree  in  five  days.  This  is  in  entire  con- 
fcrmity  with  the  principles  of  dynamics,  which  establish  a  necessary  con- 
nexion between  the  angular  velocity  and  the  distance,  as  well  in  the 
apparent  as  in  the  real  orbit  of  one  body  revolving  about  another  under 
the  influence  of  mutual  attraction ;  the  former  varying  inversely  as  the 
square  of  the  latter,  whatever  be  the  curve  described  and  whatever  the 
law  of  the  attractive  force.  It  fortunately  happens  that  Bradley,  in  1718, 
had  noticed  and  recorded  in  the  margin  of  one  of  his  observation  books, 
the  apparent  direction  of  the  line  of  junction  of  the  two  stars,  as  seen  on 
the  meridian  in  his  transit  telescope,  viz.,  parallel  te  the  line  joining  two 
conspicuous  stars  a  and  S  of  the  same  constellation,  as  seen  by  the  naked 
eye.  This  note,  rescued  from  oblivion  by  the  late  Professor  Rigaud,  has 
proved  of  singular  service  in  the  verification  of  the  elements  above 
assigned  to  the  orbit,  which  represent  the  whole  series  of  recorded  obser- 
vations that  date  up  to  the  end  of  1846  (comprising  an  angular  movement 


ORBITS   OF   BINARY   STARS. 


485 


been  most  assidu- 
reatest  interest,  is 
(3.08  =  Photom. 
y  equal,  and  as  it 
•ding  to  the  obser- 
reater  and  a  little 
3  it.    It  has  been 
he  eighteenth  cen- 
cconds,  so  that  any 
served  by  Herschel 
lUuUy  and  regularly^ 
closely  as  to  appear 
ifying  power  which 
e  great  refractor  at 
ntinuing  to  indicate, 
t3  composite  nature, 
and  measuring  the 
;36-41),  the  distance 
it0"-22.    From  that 
!  individuals  arc  more 
and  subsequent  in- 
ponding  and  equally 
ative  angular  motion. 
I  hardly  amounted  to 
eased  to  5°,  in  1834 
;6  to  upwards  of  70" 
This  is  in  entire  con- 
)lish  a  necessary  con- 
mce,  as  well  in  the 
about  onother  under 
^ing  inversely  as  the 
|)ed°and  whatever  the 
[hat  Bradley,  in  1718, 
lis  observation  books, 
two  stars,  as  seen  on 
.  the  line  joining  two 
as  seen  by  the  naked 
'rofessor  Rigaud,  has 
the  elements  above 
ies  of  recorded  obser- 
an  angular  movement 


of  nearly  nine-tenths  of  a  complete  circuit),  both  in  angle  and  distance, 
with  a  degree  of  exactness  fully  equal  to  that  of  observation  itself.  No 
doubt  can,  therefore,  remain  as  to  the  prevalence  in  this  remote  system  of 
the  Newtonian  law  of  gravitation. 

(845.)  The  observations  of  f  Ursae  Majoris  are  equally  well  repre- 
sented by  M.  Madler's  elements  (4  c  of  our  table,)  thus  fully  justifying 
the  assumption  of  the  Newtonian  law  as  that  which  regulates  the  motions 
of  their  binary  systems.  And  even  should  it  be  the  case,  as  M.  Madlcr 
appears  to  consider,  that  in  one  instance  at  least  (that  of  p  Ophiuchi,) 
deviations  from  elliptic  motion,  too  considerable  to  arise  from  mere  error 
of  observation,  exist  (a  position  we  are  by  no  means  prepared  to  grant,)' 
we  should  rather  be  disposed  to  look  for  the  cause  of  such  deviations  in 
perturbations  arising  (as  Bcssel  has  suggested)  from  the  large  or  central 
star  itself  being  actually  a  close  and  hitherto  unrecognized  double  star 
than  in  any  defect  of  generality  in  the  Newtonian  law. 

(846.)  If  the  great  length  of  the  periods  of  some  of  these  bodies  be 
remarkable,  the  shortness  of  those  of  others  is  hardly  less  so.     ^  Herculis 
bus  already  completed  two  revolutions  since  the  epoch  of  its  first  discovery, 
exhibiting  in  its  course  the  extraordinary  spectacle  of  a  sidereal  occulta- 
tion,  the  small  star  having  twice  been  completely  hidden  behind  the  largo 
one.    I?  Coronae,  f  Cancri,  and  S  Ursae  have  each  performed  more  than 
one  entire  circuit,  and  70  Ophiuchi  and  y  Virginis  have  accomplished  by 
far  the  larger  portion  of  one  in  angular  motion.     If  any  doubt,  therefore, 
could  remain  as  to  the  reality  of  their  orbitual  motions,  or  any  idea  of 
explaining  them  by  mere  parallactic  changes,  or  by  any  other  hypothesis 
than  the  agency  of  centripetal  force,  these  facts  must  suffice  for  their  com- 
plete dissipation.     We  have  the  same  evidence,  indeed,  of  their  rotations 
about  each  other,  that  we  have  of  those  of  Uranus  and  Neptune  about  the 
sun ;  and  the  correspondence  between  their  calculated  and  observed  places 
in  such  very  elongated  ellipses,  must  be  admitted  to  carry  with  it  proof  of 
the  prevalence  of  the'  Newtonian  law  of  gravity  in  their  systems,  of  the 
very  same  nature  and  cogency  as  that  of  the  calculated  and  observed  places 
of  comets  round  the  central  body  of  our  own. 
(847.)  But  it  is  not  with  the  revolutions  of  bodies  of  a  planetary  or 

'  p  Ophiuchi  belongs  to  the  class  of  very  unequal  double  stars,  the  mogniiiidesof  the 
I  individuals  being  4  and  7.    Such  stars  present  difficulties  in  the  exact  meiisiirement  of 
their  angles  of  position  which  even  yet  continue  to  embarrass  the  <>l)>t  i  ver,  though, 
uwing  to  later  improvements  in  the  art  of  executing  such  measurements,  their  influ- 
ence is  confined  within  much  narrower  limits  than  in  the  earlier  history  of  the  subject. 
I  In  simply  placing  a  fine  single  wire  parallel  to  the  line  of  junction  of  two  such  stars  it 
I  is  easily  possible  to  commit  an  error  of  3°  or  4°.    By  placing  them  between  two  parallel 
thick  wires  such  errors  are  in  great  measure  obviated. 


486 


OUTLINES  OF  ASTRONOMY. 


C*^i 


cometary  nature  round  a  nolar  centre  that  we  are  now  concerned ;  it  is 
with  that  of  sun  round  sun  —  each,  perhaps,  at  least  in  some  binary  sys- 
tems whore  the  individuals  are  very  remote  and  their  period  of  revolution 
very  long,  accompanied  with  its  train  of  planets  and  tJieir  satellites,  closely 
shrouded  from  our  view  by  the  splendour  of  their  respective  suns,  and 
crowded  into  a  space  bearing  hardly  a  greater  proportion  to  the  enormous 
interval  which  separates  them,  than  the  distances  of  the  satellites  of  our 
planets  from  their  primaries  bear  to  their  distances  from  the  sun  itself. 
A  less  distinctly  characterized  subordination  would  be  incompatible  with 
the  stability  of  their  systems,  and  with  the  planetary  nature  of  their  orbits- 
Unless  closely  nestled  under  the  protecting  wing  of  their  immediate  supe- 
rior, the  sweep  of  their  other  sun  in  its  perihelion  passage  round  their 
own  might  carry  them  off,  or  whirl  them  into  orbits  utterly  incompatible 
with  the  conditions  necessary  for  the  existence  of  their  inhabitants.  It 
must  bo  confessed,  that  we  have  here  a  strangely  wide  and  novel  field 
for  speculative  excursions,  and  one  which  it  is  not  easy  to  avoid  luxu- 
riating in. 

(848.)  The  discovery  of  the  parallaxes  of  a  Centauri  and  61  Cygni, 
both  which  are  above  enumerated  among  the  "  conspicuous"  double  stars 
of  the  6th  class  (a  distinction  fully  merited  in  the  case  of  the  former  by 
the  brilliancy  of  both  its  constituents),  enables  us  to  speak  with  an  ap- 
proach to  certainty  as  to  the  absolute  dimensions  of  both  their  orbits,  and 
thence  to  form  a  probable  opinion  as  to  the  general  scale  on  which  these 
astonishing  systems  are  constructed.  The  distance  of  the  two  stars  of  61 
Cygni  subtends  at  the  earth  an  angle  which,  since  the  earliest  micro- 
metrical  measures  in  1781,  has  varied  hardly  half  a  second  from  a  mean 
value  15"'5.  On  the  other  hand,  the  angle  of  position  has  altered  since 
the  same  epoch  by  nearly  50°,  so  that  it  would  appear  probable  that  tbe 
true  form  of  the  orbit  is  not  far  from  circular,  its  situation  at  right  angles 
to  the  visual  line,  and  its  periodic  time  probably  not  short  of  500  years, 
Now,  as  the  ascertained  parallax  of  this  star  is  0'^348,  which  is,  there- 
fore, the  angle  the  radius  of  the  earth's  orbit  would  subtend  if  equally 
remote,  it  follows  that  the  mean  distance  between  the  stars  is  to  that 
radius,  as  15"-5  :  0"-348,  or  as  44-54  : 1.  The  orbit  described  by  these 
two  stars  about  each  other  undoubtedly,  therefore,  greatly  exceeds  la 
dimensions  that  described  by  Neptune  about  the  sun.  Moreover,  suppo- 
sing the  period  to  be  five  centuries  (and  the  distance  being  actually  on  tbe 
increase,  it  can  hardly  be  less)  the  general  propositions  laid  down  by 
Newton',  taken  in  conjunction  with  Kepler's  third  law,  enable  us  to  calcu- 
late the  sum  of  the  masses  of  the  two  stars,  which,  on  these  data  we  find 

•  Principia,  I.  i.    Prop.  57,  58.  59.  ,,  „,„.„.  , 


COLOURED   DOUBLE   STARS. 


487 


jt  concerned ;  it  is 
n  some  binary  sys- 
eriod  of  revolution 
tr  satellites,  closely 
ispective  suns,  and 
on  to  the  enormous 
;he  satellites  of  our 
rom  the  sun  itself. 
B  incompatible  with 
ature  of  their  orbits- 
leir  immediate  supe- 
passage  round  their 
utterly  incompatible 
leir  inhabitants.    It 
(ride  and  novel  field 
easy  to  avoid  luxu- 

tauri  and  61  Cygni, 
picuous"  double  stars 
sase  of  the  former  by 
to  speak  with  an  ap- 
both  their  orbits,  and 
I  scale  on  which  these 
af  the  two  stars  of  61 
;e  the  earliest  micro- 
,  second  from  a  mean 
ition  has  altered  since 
ear  probable  that  tbc 
tuation  at  right  angles 
ot  short  of  500  years, 
'^348,  which  is,  there- 
xld  subtend  if  equally 
D  the  stars  is  to  that 
bit  described  by  these 
:e,  greatly  exceeds  in 
an.    Moreover,  suppo- 
e  being  actually  on  the 
lositions  laid  down  by 
law,  enable  us  to  calcu- 
I,  on  these  data  we  find 


to  be  0*858,  tho  mass  of  our  sun  being  1.     The  sun,  therefore,  is  neither 
vastly  greater  nor  vastly  less  than  the  stars  composing  61  Cygni. 

(849.)  The  data  in  the  case  of  a  Centauri  are  more  uncertain.  Since 
the  year  1822,  tho  distance  has  been  steadily  and  pretty  rapidly  decreasing 
at  the  rate  of  about  half  a  second  per  annum,  and  that  with  very  little 
change  in  the  angle  of  position.  Hence,  it  follows  evidently  that  tho 
plane  of  its  orbit  passes  nearly  through  tho  earth,  and  (the  distance  about 
the  middle  of  1834  having  been  17V')  it  is  very  probable  that  either  an 
occultation,  like  that  observed  in  ^  Hcrculis,  on  a  close  appulse  of  the 
two  stars,  will  take  place  about  the  year  1867.  As  the  observations  wo 
possess  afford  no  sufficient  grounds  for  a  satisfactory  calculation  of  elliptic 
dements'  we  must  be  content  to  assume  what,  at  all  events,  they  fully 
justify,  viz.,  that  the  major  semiazis  must  exceed  12",  and  is  very  pro- 
bably considerably  greater.  Now  this  with  a  parallax  of  0"'913  would 
give  for  the  real  value  of  the  semiaxis  13-15  radii  of  the  earth's  orbit,  as 
a  minimum.  The  real  dimensions  of  their  ellipse,  therefore,  cannot  be  so 
small  as  the  orbit  of  Saturn ;  in  all  probability  exceeds  that  of  Uranus ; 
and  may  possibly  be  much  greater  than  either. 

(850.)  The  parallel  between  these  two  double  stars  is  a  remarkable  one. 
Owing  no  doubt  to  their  comparative  proximity  to  our  system,  their  appa- 
rent proper  motions  are  both  unusually  great,  and  for  the  same  reason 
probably  rather  than  owing  to  unusually  largo  dimensions,  their  orbits 
appear  to  us  under  what,  for  binary  double  stars,  we  must  call  unusually 
large  angles.  Each  consists,  moreover,  of  stars,  not  very  unequal  in 
brightness,  and  in  each  both  tho  stars  are  of  a  high  yellow  approaching 
to  orange  colour,  the  smaller  individual,  in  each  case,  being  also  of  a 
deoper  tint.  Whatever  the  diversity,  therefore,  which  may  obtain  among 
other  sidereal  objects,  these  would  appear  to  belong  to  the  same  family  or 
genus." 

(851.)  Many  of  the  double  stars  exhibit  the  curious  and  beautiful 
phsenomenon  of  contrasted  or  complementary  colours.'    In  such  instances, 

'  Elements  have  been  recently  computed  by  Captain  Jacob,  for  which  see  the  table, 
p.  483. 

'  Similar  combinations  are  very  numerous.  Many  remarkable  instances  occur  among 
the  double  stars  catalogued  by  the  author  in  the  2nd,  3rd,  4th,  6th  and  9th  volumes  of 
Trans.  Roy.  Ast.  Soc.  and  in  the  volume  of  Southern  observations  already  cited.  See 
Nob.  121,  376, 1066,  1907,  2030,  2146,  2244,  2772,  3853,  3395,  3998,  4000,  4065,  4196, 
4210,  4616,  4649,  4765,  5003,  5012,  of  these  catalogues.  The  fine  binary  star,  B.  A.  C. 
No.  4923,  has  its  constituents  15"  apart,  the  one  6m.  yellow,  the  other,  7ffl.  orange. 

»  " other  suns,  perhaps. 

With  their  attendant  moons,  thou  wilt  descry,  .»''    - '  '    > 

Communicating  male  and  female  light, 


488 


OUTLINES  OF  ASTRONOMY. 


tbo  larger  star  is  usually  of  a  ruddy  or  orange  liuo,  whilo  tbo  smaller  one 
appears  blue  or  green,  probably  in  virtuo  of  that  general  law  of  optica, 
which  provides,  that  when  the  retina  is  under  the  influence  of  pxr'tement 
by  any  bright,  coloured  light;  feebler  lights,  which  scon  alone  ii  ild  pro- 
duce no  sensation  but  of  whiteness,  shall  for  the  time  appear  coloured  with 
tbo  tint  complementary  to  that  of  tbo  brighter.  Thus  a  yellow  colour 
predominating  in  the  light  of  the  brighter  star,  that  of  the  less  bright  one 
in  the  same  field  of  view  will  appear  blue ;  while,  if  the  tint  of  the 
brighter  star  verge  to  crimson,  that  of  the  other  will  exhibit  a  tendency  to 
green — or  even  appear  as  a  vivid  green,  under  favourable  circumstances. 
The  former  contrast  is  beautifully  exhibited  by  »  Cancri — the  latter  by  y 
Androroedffl',  both  fine  double  stars.  If,  however,  the  coloured  star  K 
much  the  less  bright  of  the  two,  it  will  not  materially  affect  thi.  ot^  : 
Thus,  for  instance,  tj  Cassiopcise  exhibits  the  beautiful  oombin;itioii  ol  u 
large  white  star,  and  a  small  one  of  a  rich  ruddy  purple.  It  is  by  no 
means,  however,  intended  to  say,  that  in  all  such  cases  one  of  the  colours 
is  a  mere  e£fect  of  contrast,  and  it  may  bo  easier  suggested  in  words,  than 
conceived  in  imagination,  what  variety  of  illumination  tico  mns  —  n  red 
and  a  green,  or  a  yellow  and  a  blue  one — must  afford  a  planet  circulating 
about  either ;  and  what  charming  contrasts  and  "  grateful  vicissitudes," 
—  a  red  and  a  green  day,  for  instance,  alternating  with  a  white  one  and 
with  darkness, — might  arise  rrom  the  presence  or  absence  of  one  or  other, 
or  both,  above  the  hori/ou.  Insulated  stars  of  a  red  colour,  almost  as 
deep,  as  that  of  blood,^  occur  in  many  parts  of  the  heavens,  but  no  green 
or  blue  star  (of  any  decided  hue)  has,  we  believe,  ever  been  noticed  un- 
associated  with  a  companion  brighter  than  itself.  Many  of  the  red  stars 
are  variable.  =  i       /  ,•  ' 

'     '      '         (Which  two  great  86X68  animate  the  world,) 

Stored  in  each  orb,  perhaps,  with  some  that  live." 

Paradise  Loat,  viii.  148. 
'  The  8mall  star  of  y  Andromedee  is  cIo8e  double.    Bot^  its  ir.dividii.als  are  green : » 
similar  combination,  with  even  irore  decided  colours,  is  prtieenu  d  bv  the  double  star, 
h.  881. 

'  The  following  are  the  R.  ascensions  and  N.  P.  disiuiicts  lor  1630,  of  some  of  the 
most  remarkable  of  these  sanguine  or  ruby  stars : — 


il.A. 

N.  P. D.  \ 

R.A. 

N.P.D. 

R.A. 

N.  P.  D. 

h.  m.  8. 

0  t         ft 

h.  m.  8. 

0  /         II 

h.  m.  8. 

o  ;  II 

4  4  -S-d 

61  46  21 

9  48  31 

130  47  12 

20  7  8 

111  50  11 

4  51  31 

.  )2  2  ^- 

10  52  10 

107  24  40 

21  37  18 

31  59  47 

5  j;8  *: 

i.lu  32  1  J 

12  37  31 

148  45  47 

21  37  20 

52  54  47 

■J  27  66 

152  2  42 

16  29  44 

122  2  0 

C'i  these  No.  5  (in  order  of  right  ascension)  is  in  the  same  field  of  view  with  a  Hydre, 
and  No.  9  with  ^  Crucis.    No.  2  (in  the  same  order)  is  variable. 


PROPBR    MOTl.)Na   OF   THB   8TAU3. 


489 


)  the  smaUcr  one 
al  law  of  optica, 
ico  of  pxo"  teinent 
alono  vi    »W  P'"- 
)ear  coloured  with 
J  a  yellow  colour 
he  less  bright  one 
f  the  tint  of  the 
jibit  a  tendency  to 
ble  circumstances. 

i the  latter  by  y 

e  coloured  star  \>^ 
ly  aifect  th..  otV  . 
d  combiniitiou  oi  a 
irple.    It  is  by  no 
,  one  »f  the  colours 
58ted  in  words,  than 
n  tico  jmns  — !vred 
,  a  planet  circulating 
•ateful  vicissitudes," 

ith  a  white  one  and 
,nce  of  one  or  other, 
id  colour,  almost  as 
javens,  but  no  green 
|er  been  noticed  un- 

iny  of  the  red  stars 


llive." 

|t«e  Lost,  viii.  148. 
lir.dividualB  are  green  :(* 
hud  by  the  double  star, 

lor  lti30,  of  Bome  of  the 


R.A. 

.  m.  8. 

7  8 

37  18 

37  20 


N.  P.  D. 

o  '  I' 

111  50  11 
31  59  47 
52  54  47 


^52.)  Another  very  intcn  stin/r  sultjcff  of  inquiry,  in  the  physical 
history  of  the  Btars,  is  their  prupci    nii>tion.     It  woa  first  noticed  by 
HuUcy,  that  three  principal  Hfiirs,  Sirius,      '•^turus,  and  Aldebnruu,  arc 
placed  by  Ptolemy,  on  the  strongih  (»f  observations  nifldc  by  Hipparohus, 
130  years  B.C.,  in  latitudes  respectively  '20',  22',  and  8.S'  mon^  wrthrrly 
than  he  actually  found  them  in  1717.'     Making  due  allowance  for  tlio 
diminution  of  obliquity  of  the  coliptic  in  the  interval  (1847  years)  they 
oupht  to  have  stood,  if  really  fixed,  respectively  10',  14',  and  0'  noro 
nnth'.rlif.     As  the  circumstances  of  the  statement  exclude  the  supposi- 
iioa  of  I  nor  of  transcription  in  the  MSS.,  we  are  necessitated  ti.  admit  a 
uouthward  motion  in  latitude  in  these  stars  to  the  very  considerable  extent, 
■  pectively,  of  87',  42',  and  83',  and  this  is  corroborated  by  an  obwrva- 
tiou  of  Aldebaran  at  Athens,  in  the  year  a.  d.  509,  which  star,  on  the 
lith  of  March  in  that  year,  was  seen  immediately  after  its  eiut^rgenoe 
from  ocoultation  by  the  moon,  in  such  a  position  as  it  could  not  h.ivo  had 
if  tho  occultation  were  not  nearly  central.     Now,  from  the  knowk  ige  we 
have  of  the  lunar  motions,  this  could  not  havo  been  tho  case  had  Alde- 
baran at  that  time  so  much  southern  latitude  as  at  present.     A  jprio  -t,  it 
might  be  expected  that  apparent  motions  of  some  kind  or  other  sli  mid 
be  detected  among  so  great  a  multitude  of  individuals  scattered  through 
space,  and  with  nothing  to  keep  them  fixed.     Their  mutual  attractions 
even,  however  inconceivably  enfeebled  by  distance,  and  counteracted  by 
opposing  attractions  from  opposite  quarters,  must  in  the  lapse  of  counfek' 
less  ages  produce  some  movements — some  change  of  internal  arrangement 
— resulting  from  the  difference  of  the  opposing  actions.     And  it  is  a  fact, 
that  such  apparent  motions  are  really  proved  to  e;(ist  by  the  exact  obser- 
vations of  modern  astronomy.     Thus,  as  we  have  seen,  the  two  stars  of 
61  Oygni  have  remained  constantly  at  the  same,  or  very  nearly  the  same, 
distance,  of  15",  for  at  least  fifty  years  past,  although  they  have  shifted 
their  local  situation  in  the  heavens,  in  this  interval  of  time,  through  no 
less  than  4'  23",  the  annual  proper  motion  of  each  star  being  5"-3 ;  by 
wiiich  quantity  (exceeding  a  third  of  their  interval)  this  system  is  every 
year  carried  bodily  along  in  some  unknown  path,  by  a  motion  which,  for 
many  centuries,  must  be  regarded  as  uniform  and  rectilinear.     Among 
stars  not  double,  and  no  way  differing  from  the  rest  in  any  other  obvious 
particular,  •  Indi'  and  ft  Cassiopeiae  are  to  be  remarked  as  having  the 
greatest  proper  motions  of  any  yet  ascertained,  amounting  respectively  to 
7" '74  and  3"'74  of  annual  displacement.     And  a  great  many  others  have 


•■I 


»d  of  view  with  a  Hydra, 
[le. 


»  Phil.  Trans.  171T,  vol.  xxx.  fo.  736. 
*  D'Arrett.  Aitr.  Nacbr.,  No.  618. 


■>  ?<-- 


490 


OUTLINES   OF  ASTRONOMY. 


KJM*' 


•«l«t^ 


been  observed  to  be  thus  constantly  carried  away  from  their  places  by 
smaller,  but  not  less  unequivocal  motions.* 

(853.)  Motions  which  require  whole  centuries  to  accumulate  before 
they  produce  changes  of  arrangement,  such  as  the  naked  eye  can  detect, 
though  quite  sufficient  to  destroy  that  idea  of  mathematical  fixity  which 
precludes  speculation,  are  yet  too  trifling,  as  far  as  practical  applications 
go,  to  induce  a  change  of  language,  and  lead  us  to  speak  of  the  stars  in 
common  parlance  as  otherwise  than  fixed.  Small  as  they  are,  however, 
astronomers,  once  assured  of  their  reality,  have  not  been  wanting  in  at- 
tempts to  explain  and  reduce  them  to  general  laws.  No  one,  who  reflects 
with  due  attention  on  the  subject,  will  be  inclined  to  deny  the  high  proba- 
bility, nay  certainty,  that  the  sun  as  well  as  the  stars  must  have  a  proper 
motion  in  some  direction ;  and  the  inevitable  consequence  of  such  a  mo- 
tion, if  unparti' ipated  by  the  rest,  must  be  a  slow  average  apparent  ten- 
dency of  all  the  stars  to  the  vanishing  point  of  lines  parallel  to  that 
direction,  and  to  the  region  which  he  is  leaving,  however  greatly  indi- 
vidual stars  might  difier  from  such  average  by  reason  of  their  own  pecu- 
liar proper  motion.  This  is  the  necessary  effect  of  perspective  j  and  it  is 
certain  that  it  must  be  detected  by  observation,  if  we  knew  accurately  the 
apparent  proper  motions  of  all  the  stars,  and  if  wo  were  sure  that  they 
were  independent,  i.  e.  that  the  whole  firmament,  or  at  least  all  that  part 
which  we  see  in  our  own  neighbourhood,  were  not  drifting  along  together, 
by  a  general  set  as  it  were,  in  one  direction,  the  result  of  unknown  pro- 
cesses and  slow  internal  changes  going  on  in  the  sidereal  stratum  to 
which  our  system  belongs,  as  we  see  motes  sailing  in  a  current  of  air, 
and  keeping  nearly  the  same  relative  situation  with  respect  to  one  another. 

(854.)  It  was  on  this  assumption,  tacitly  made  indeed,  but  necessarily 
implied  in  every  step  of  his  reasoning,  that  Sir  William  Herschel,  ia 
1783,  on  a  consideration  of  the  apparent  proper  motions  of  such  stars  as 
could  at  that  period  be  considered  as  tolerably  (though  still  imperfectly) 
ascertained,  arrived  at  the  conclusion  that  a  relative  motion  of  the  sun, 
among  the  fixed  stars  in  the  direction  of  a  point  or  parallactic  apex,  situ- 
ated near  Jt  Herculis,  that  is  to  say,  in  R.  A.  17"  22»=260°  34',  N.  P.  D. 
63°  43'  (1790),  would  account  for  the  chief  observed  apparent  motions, 
leaving,  however,  some  still  outstanding  and  not  explicable  by  this  cause  j 
and  in  the  same  year  Prevost,  taking  nearly  the  same  view  of  the  subject, 
arrived  at  a  conclusion  as  to  the  solar  apex  (or  point  of  the  sphere  towards 
which  the  sun  relatively  advances),  agreeing  nearly  in  polar  distance  with 


'  The  reader  may  consult  "  a  list  of  314  stars  having,  or  supposed  to  have,  a  proper 
motion  of  not  less  than  about  Qf''5  of  a  great  circle"  {fer  annum)  by  the  late  F.  Boily, 
Esq.    Tran$.  A$t.  Soc,  v.  p.  158.  > 


MOTION  OF  THE  SUN  IN  SPACE. 


491 


their  places  by 

ccumulate  before 
id  eye  can  detect, 
tical  fixity  which 
jtical  applications 
ak  of  the  stars  in 
ihey  are,  however, 
en  wanting  in  at- 
0  one,  who  reflects 
ny  the  high  proba- 
lust  have  a  proper 
ace  of  such  a  mo- 
:rage  apparent  ton- 
es parallel  to  that 
wever  greatly  indi- 
of  their  own  pecu- 
rspective ;  and  it  is 
knew  accurately  the 
were  sure  that  they 
at  least  all  that  part 
rting  along  together, 
lit  of  unknown  pro- 
sidereal  stratum  to 
in  a  current  of  air, 
speot  to  one  another, 
leed,  but  necessarily 
^illiam  Herschel,  iu 
Ions  of  such  stars  as 
igh  still  imperfectly) 
I  motion  of  the  sun, 
jarallactic  apex,  situ- 
1=260"  34,  N.  P.  D. 
id  apparent  motions, 
licable  by  this  cause; 
view  of  the  subject, 
jf  the  sphere  towards 
a  polar  distance  with 

Ipposed  to  have,  a  proper 
lum)  by  the  late  F.  Baily, 


the  foregoing,  but  differing  from  it  about  27°  in  right  ascension.  Since 
that  time  methods  of  calculation  have  been  improved  and  concinnated, 
our  knowledge  of  the  proper  motions  of  the  stars  has  been  rendered  more 
precise,  and  a  greater  number  of  cases  of  such  motions  have  been  re- 
corded. The  subject  has  been  resumed  by  several  eminent  astronomers 
and  mathematicians :  viz.  1st,  by  M.  Argelander,  who,  from  the  conside- 
ration of  the  proper  motions  of  21  stars  exceeding  1"  per  annum  iu  arc, 
has  placed  the  solar  apex  in  K.  A.  256''  25',  N.  P.  D.  51°  23' ;  from  those 
of  50  stars  between  0"-5  and  1"0,  in  255°  10'  51°  26';  and  from  those 
of  319  stars  having  motions  between  0"-l  and  0"-5  per  annum,  in  261° 
11'  59°  2' :  2ndly,  by  M.  Luhndahl,  whose  calculations,  founded  on  the 
proper  motions  of  147  stars,  give  252°  53',  75°  34' :  and  3rdly,  by  M. 
Otto  Struve,  whose  result  261°  22',  62°  24',  emerges  from  a  very  elabo- 
rate discussion  of  the  proper  motions  of  392  stars.  All  these  places  are 
for  A.  D.  1790. 

(855.)  The  most  probable  mean  of  the  results  obtained  by  these  three 
astronomers,  is  (for  the  same  epoch)  R.  A.  =  259°  9',  N.  P.  D.  55°  23'. 
Their  researches,  however,  extending  only  to  stars  visible  in  European 
observatories,  it  became  a  point  of  high  interest  to  ascertain  how  far  the 
stars  of  the  southern  hemisphere  not  so  visible,  treated  independently  on 
the  same  system  of  procedure,  would  corroborate  or  controvert  their  con- 
clusion. The  observations  of  Lacaille,  at  the  Cape  of  Good  Hope,  in 
1751  and  1752,  compared  with  those  of  Mr.  Johnson  at  St.  Helena,  in 
1829-33,  and  of  Henderson  at  the  Cape  in  1830  and  1831,  have  afforded 
the  means  of  deciding  this  question.  The  task  has  very  recently  been 
executed  in  a  masterly  manner  by  Mr.  Galloway,  in  a  paper  published  iu 
the  Philosophical  Transactions  for  1847  (to  which  we  may  also  refer  the 
reader  for  a  more  particular  account  of  the  history  of  the  subject  than  our 
limits  allow  us  to  give. )  On  comparing  the  records,  Mr.  Galloway  finds 
eighty-one  southern  stars  not  employed  in  the  previous  investigations  above 
referred  to,  whose  proper  motions  in  the  intervals  elapsed  appear  consider- 
able enough  to  assure  us  that  they  have  not  originated  in  error  of  the 
earlier  observations.  Subjecting  these  to  the  same  process  of  computation 
he  concludes  for  the  place  of  the  solar  apex,  for  1790,  as  follows :  viz. 
R.  A.  260°  1',  N.  P.  D.  55°  37',  a  result  so  nearly  identical  with  that 
afforded  by  the  northern  hemisphere,  as  to  afford  a  full  conviction  of  its 
near  approach  to  truth,  and  what  may  fairly  be  considered  a  demonstration 
of  the  physical  cause  assigned. 

(856.)  Of  the  mathematical  conduct  of  this  inquiry  the  nature  of  this 
work  precludes  our  giving  any  account;  but  as  the  philosophical  principle 
on  which  it  is  ba.sed  has  been  misconceived,  it  is  necessary  to  say  a  few 


IP 


li 


492 


OUTLINES  OF   ASTRONOMY. 


<«ft*" 


rim 


■ft  IE 

.  •BJ'«ii.«» 


words  in  explanation  of  it.  Almost  all  the  greatest  discoveries  in  astron* 
omy  have  resulted  from  the  consideration  of  what  we  have  elsewhere 
termed  residual  PHiENOMENA',  of  a  quantitative  or  numerical  kind, 
that  is  to  say,  of  such  portions  of  the  numerical  or  quantitative  results  of 
observation  as  remain  outstanding  and  unaccounted  for  after  subducting 
and  allowing  for  all  that  would  result  from  the  strict  application  of  known 
principles.  It  was  thus  that  the  grand  discovery  of  the  precession  of  the 
equinoxes  resulted  as  a  residual  phaenoraenon,  from  the  imperfect  explana> 
tion  of  the  return  of  the  seasons  by  the  return  of  the  sun  to  the  same 
apparent  place  among  the  fixed  stars.  Thus,  also,  aberration  and  nutation 
resulted  as  residual  phsenomena  from  that  portion  of  the  changes  of  the 
apparent  places  of  the  fixed  stars  which  was  left  unaccounted  for  by  pre* 
cession.  And  thus  again  the  aj7j)arent  proper  motions  of  the  stars  are 
the  observed  residues  of  their  apparent  movements  outstanding  and  unac- 
counted for  by  strict  calculation  of  the  effects  of  precession,  nutation,  and 
aberration.  The  nearest  approach  which  human  theories  can  make  to 
perfection  is  to  diminish  this  residue,  this  caput  mortuum  of  observation, 
as  it  may  be  considered,  as  much  as  practicable,  and,  if  possible,  to  reduce 
it  to  nothing,  either  by  showing  that  something  has  been  neglected  in  our 
estimation  of  known  causes,  or  by  reasoning  upon  it  as  a  new  fact,  and  on 
the  principle  of  the  inductive  philosophy  ascending  from  the  effect  to  its 
cause  or  causes.  On  the  suggestion  of  any  new  cause  hitherto  unresorted 
to  for  its  explanation,  our  first  object  must  of  course  be  to  decide  whether 
such  a  cause  would  produce  such  a  result  iu  kind :  the  next,  to  assign  to 
it  such  an  intensity  as  shall  account  for  the  greatest  possible  amount  of  the 
residual  matter  in  hand.  The  proper  motion  of  the  sun  being  suggested 
as  such  a  cause,  we  have  two  things  disposable — its  direction  and  velocity, 
both  which  it  is  evident,  if  they  ever  became  known  to  us  at  all,  can  only 
be  so  by  the  consideration  of  the  very  phaenomena  in  question.  Our 
object,  of  course,  is  to  account,  if  possible,  for  the  whole  of  the  observed 
proper  motions  by  the  proper  assumption  of  these  elements.  If  this  be 
impracticable,  what  remains  unaccounted  for  is  a  residue  of  a  more  recon- 
dite kind,  but  which,  so  long  as  it  is  unaccounted  for,  we  must  regard  as 
purely  casual,  seeing  that,  for  anything  we  can  perceive  to  the  contrary, 
it  might  with  equal  probability  be  one  way  as  the  other.  The  theory  of 
chances,  therefore,  necessitates  (as  it  does  in  all  such  cases)  the  application 
of  a  general  mathematical  process,  known  as  "  the  method  of  least  squares," 
which  leads,  as  a  matter  of  strict  geometrical  conclusion,  to  the  values  of 
the  elements  sought,  which,  under  all  tJie  circumstanceSf  are  the  most 
probable. 

'  Discourse  on  the  Study  of  Natural  Philosophy.    Cab.  Qyehpadia,  No  14. 


PROPER  MOTION   OF  THE   SUN. 


493 


)verips  in  astron- 
I  have  elsewhere 
numerical  kind, 
titative  results  of 
after  subducting 
jlication  of  known 
5  precession  of  the 
imperfect  explana- 
sun  to  the  same 
•ation  and  nutation 
he  changes  of  the 
ounted  for  by  pre- 
18  of  the  stars  are 
standing  and  unac- 
ssion,  nutation,  and 
eories  can  make  to 
mm  of  observation, 
f  possible,  to  reduce 
een  neglected  in  our 
a  a  new  fact,  and  on 
from  the  effect  to  its 
5  hitherto  unresorted 
be  to  decide  whether 
lie  next,  to  assign  to 
fssible  amount  of  the 
sun  being  suggested 
irection  and  velocity, 
;o  us  at  all,  can  only 
in  question.     Our 
,Ze  of  the  observed 
lements.     If  this  be 
iue  of  a  more  recon- 
,  we  must  regard  as 
sive  to  the  contrary, 
her.     The  theory  of 
cases)  the  application 
W  of  least  squares," 
lion,  to  the  values  of 
fiances,  are  the  most 

Jyclopciia,  No  14. 


(857.)  This  is  the  process  resorted  to  by  all  the  geometers  we  have 
enumerated  in  the  foregoing  articles  (arts.  854,  855).     It  gives  not  only 
the  direction  in  space,  but  also  the  velocity  of  the  solar  motion,  estimated 
on  a  scale  conformable  to  that  in  which  the  velocity  of  the  sidereal  motions 
to  be  explained  are  given;  i.  e.  in  seconds  of  arc  as  subtended  at  the 
average  distance  of  the  stars  concerned,  by  its  annual  motion  in  space. 
But  here  a  consideration  occurs  which  tends  mateiiully  to  complicate  the 
problem,  and  to  introduce  into  its  solution  an  element  depending  on  sup- 
positions more  or  less  arbitrary.     The  distance  of  the  stars  being,  except 
in  two  or  three  instances,  unknown,  we  are  compelled  either  to  restrict  our 
inquiry  to  these,  which  are  too  few  to  ground  any  result  on,  or  to  make 
some  supposition  as  to  the  relative  distances  of  the  several  stars  employed. 
In  this  we  have  nothing  but  general  probability  to  guide  us,  and  two 
courses  only  present  themselves,  either,  1st,  To  class  the  distances  of  the 
stars  according  to  their  magnitudes,  or  apparent  brightnesses,  and   to 
institute  separate  and  independent  calculations  for  each  class,  including 
stars  assumed  to  be  equidistant,  or  nearly  so :  or,  2dly,  To  class  them 
according  to  the  observed  amount  of  their  apparent  proper  motions,  on 
the  presumption  that  those  which  appear  to  move  fastest  are  really  nearest 
to  us.     The  former  is  the  course  pursued  by  M.  Otto  Struve,  the  latter 
by  M.  Argelander.     With  regard  to  this  latter  principle  of  classification, 
however,  two  considerations  interfere  with  its  applicability,  viz.  1st  that 
we  see  the  real  motion  of  the  stars  foreshortened  by  the  effect  of  perspec- 
tive; and  2dly,  that  that  portion  of  the  total  appai'ent  proper  motion 
which  arises  from  the  real  motion  of  the  sun  depends,  not  simply  on  the 
absolute  distance  of  the  star  from  the  sun,  but  also  on  its  angular  apparent 
distance  from  the  solar  apex,  being,  cseterts  piribtis,  as  the  sine  of  that 
angle.     To  execute  such  a  classification  correctly,  therefore,  we  ought  to 
know  both  these  particulars  for  each  star.     The  first  is  evidently  out  of 
our  reach.     We  are  therefore,  for  that  very  reason,  compelled  to  regard  it 
as  casual,  and  to  assume  that  on  the  average  of  a  great  number  of  stars  it 
would  be  uninfluential  on  the  result.     But  the  second  cannot  be  so  sum- 
marily disposed  of.     By  the  aid  of  an  approximate  knowledge  of  the  solar 
apex,  it  is  true,  approximate  values  may  be  found  of  the  simply  apparent 
portions  of  the  proper  motions,  supposing  all  the  stars  equidistant,  and 
these  being  subducted  from  the  total  observed  motions,  the  residues  might 
afford  ground  for  the  classification  in  question.'    This,  however,  would  be 

'  M.  Argelander's  classes,  however,  are  constructed  without  reference  to  this  con 
sideration,  on  tho  sole  basis  of  the  total  apparent  amount  proper  motion,  and  are,  there- 
fore, pro  tanlo,  questionable.    It  is  the  more  satisfactory  then  to  find  so  considerable 
an  agreement  among  his  partial  results  as  actually  obtains.     ' 


I 


'i-:l  1 1 
:  1 


494 


OUTLINES  OF  ASTRONOMY. 


F 


a  long,  and  to  a  certain  extent  precarious  system  of  procedure.  On  the 
other  hand,  the  classification  by  apparent  brightness  is  open  to  no  such 
difficulties,  since  wc  are  fully  justified  in  assuming  that,  on  a  general 
average,  the  brighter  stars  are  the  nearer,  and  that  the  exceptions  to  this 
rule  are  casual  in  that  sense  of  the  word  which  it  always  bears  in  such 
inquiries,  expressing  solely  our  ignorance  of  any  ground  for  assuming  a 
bias  one  way  or  other  on  either  side  of  a  determinate  numerical  rule.  In 
Mr.  Galloway's  discussion  of  the  southern  stars  the  consideration  of  dis- 
tance is  waived  altogether,  which  is  equivalent  to  an  admission  of  complete 
ignorance  on  this  point,  as  well  as  respecting  the  real  directions  and 
velocities  of  the  individual  motions. 

(858.)  The  velocity  of  the  solar  motion  which  results  from  M.  Otto 
Struve's  calculations  is  such  as  would  carry  it  over  an  angular  subtense 
of  0"-3392  if  seen  at  right  angles  from  the  average  distance  of  a  star  of 
the  first  magnitude.  If  we  take,  with  M.  Struve,  senior,  the  parallax  of 
such  a  star  as  probably  equal  to  0"'209,'  we  shall  at  once  be  enabled  to 
compare  this  annual  motion  with  the  radius  of  the  earth's  orbit,  the  result 
being  1-623  of  such  units.  The  sun  then  advances  through  space  (rela- 
tively, at  least,  among  the  stars,)  carrying  with  it  the  whole  planetary 
and  cometary  system  with  a  velocity  of  1'623  radii  of  the  earth's  orbit, 
or  154,185,000  miles  po'  anmcm,  or  422,000  miles  (that  is  to  say, 
nearly  its  own  semi-diameter)  per  diem :  in  other  words,  with  a  velocity 
a  very  little  greater  than  one-fourth  of  the  earth's  annual  motion  in  its 
orbit. 

(859.)  Another  generation  of  astronomers,  perhaps  many,  must  pass 
away  before  we  are  in  a  condition  to  decide  from  a  more  precise  and 
extensive  knowledge  of  the  proper  motions  of  the  stars  than  we  at  present 
possess,  how  far  the  direction  and  velocity  above  assigned  to  the  solar 
motion  deviates  from  exactness,  whether  it  continue  uniform,  and  whether 
it  show  any  sign  of  deflection  from  rectilinearity ;  so  as  to  hold  out  a 
prospect  of  one  day  being  enabled  to  trace  out  an  arc  of  the  solar  orbit, 
and  to  indicate  the  direction  in  which  the  preponderant  gravitation  of  the 
sidereal  firmanent  is  urging  the  central  body  of  our  system.  An  analogy 
for  such  deviation  from  uniformity  would  seem  to  present  itself  in  the 
alleged  existence  of  a  similar  deviation  in  the  proper  motions  of  Sirius 
and  Procyon,  both  which  stars  are  considered  to  have  varied  sensibly  in 
this  respect  within  the  limits  of  authentic  and  dependable  observation. 
Such,  indeed,  would  appear  to  be  the  amount  of  evidence  for  this  as  a 
matter  of  fact  as  to  have  given  rise  to  a  speculation  on  the  probable  circu- 
lation of  these  stars  round  opaque  (and  therefore  invisible)  bodies  at  no 
-      f  •  Etudes  d'Astronomie  Stellaire,  p.  107.  .     -  >  ^  • 


SPECULATIONS   ON  A  CENTRAL  SUN. 


495 


edure.     On  tbe 
jpen  to  no  such 
at,  on  a  general 
exceptions  to  this 
ys  bears  in  such 
,d  for  assuming  a 
imerical  rule.    In 
Qsideration  of  dis- 
aission  of  complete 
eal  directions  and 

lults  from  M.  Otto 
m  angular  subtense 
listance  of  a  star  of 
lior,  the  parallax  of 
once  be  enabled  to 
rtb's  orbit,  the  result 
through  space  (rek- 
the  whole  planetary 
of  the  earth's  orbit, 
Ales  (that  is  to  say, 
rordfl,  \?ith  a  velocity 
annual  motion  in  its 

^ps  many,  must  pass 
1  a  more  precise  and 
irs  than  we  at  present 

[assigned  to  the  solar 
(uniform,  and  whether 

1  so  as  to  hold  out  a 
[arc  of  the  solar  orbit, 
Taut  gravitation  of  the 
system.    An  analogy 
\  present  itself  in  the 
[per  motions  of  Sirius 
Vve  varied  sensibly  w 
Spendable  observation. 
Ividence  for  this  as  a 
Ion  the  probable  circu- 
linvisible)  bodies  at  no 

07. 


great  distances  from  them  respectively,  in  the  manner  of  binary  stars : 
[and  it  has  been  recently  shown  by  M.  Peters  (Ast.  Nachr.  748,)  that, 
in  the  case  of  Sirius,  such  a  circulation,  performed  in  a  period  of  50  093 
years  in  an  ellipse  whose  cxcentricity  is  0.7994,  the  perihelion  passage 
taking  place  at  the  epoch  a.  d.  1701-431,  would  reconcile  in  a  remark- 
able manner  the  observed  anomalies,  and  reduce  the  residual  motion  to 
uniformity.")  •■■.■■, 

(860.)  iie  whole  of  tbe  reasoning  upon  which  the  determination  of 
the  solar  motion  in  space  rests,  is  based  upon  the  entire  exclusion  of  any 
law  either  derived  from  observation  or  assumed  in  theory,  affecting  the 
amount  and  direction  of  the  real  motions  both  of  the  sun  and  stars.     It 
supposes  an  absolute  non-recognition,  in  those  motions,  of  any  general 
directive  cause,  such  as,  for  example,  a  common  circulation  of  all  about  a 
common  centre.     Any  such  limitation  introduced  into  the  conditions  of 
the  problem  of  the  solar  motion  would  alter  in  toto  both  its  nature  and 
the  form  of  its  solution.     Suppose,  for  instance,  that,  conformably  to  the 
speculations  of  several  astronomers,  the  whole  system  of  the  Milky  Way, 
including  our  sun,  and  the  stars,  our  more  immediate  neighbours,  which 
constitute  our  sidereal  firmament,  should  have  a  general  movement  of  rota- 
tion in  the  plane  of  the  galactic  circle  (any  other  would  be  exceedingly 
improbable,  indeed  hardly  reconcilable  with  dynamical  principles,)  being 
held  together  in  opposition  to  the  centrifugal  force  thus  generated  by  the 
mutual  gravitation  of  its  constituent  stars.     Except  we  at  the  same  time 
admitted  that  the  scale  on  which  this  movement  proceeds  is  so  enormous 
that  all  the  stars  whose  proper  motions  we  include  in  our  calculations  go 
together  in  a  body,  so  far  as  that  movement  is  concerned  (as  forming  too 
small  an  integrant  portion  of  the  whole  to  differ  sensibly  in  their  relation 
to  its  central  point  j)  we  stand  precluded  from  drawing  any  conclusion 
whatever,  not  only  respecting  the  absolute  motion  of  the  sun,  but  respect- 
ing even  its  relative  movement  among  those  stars,  until  we  have  established 
some  law,  or  at  all  events  framed  some  hypothesis  having  the  provisional 
force  of  a  law,  connecting  the  whole,  or  a  part  of  the  motion  of  each  indi- 
vidual with  its  situation  in  space. 

(861.)  Speculations  of  this  kind  have  not  been  wanting  in  astronomy, 
and  recently  an  attempt  has  been  made  by  M.  Miidler  to  assign  the  local 
centre  in  space,  round  which  the  sun  and  stars  revolve,  which  he  places 
in  the  group  of  the  Pleiades,  a  situation  in  itself  improbable,  lying  as  it 
does  no  less  than  26°  out  of  the  plane  of  the  galactic  circle,  out  of  which 
plane  it  is  almost  inconceivable  that  any  general  circulation  can  take  place. 
In  the  present  defective  state  of  our  knowledge  respecting  the  proper 
motion  of  the  smaller  stars,  especially  in  right  ascension,  (an  element  for 


tl 


t  .1; 

V:  i 


496 


OUTLINES  OF  ASTRONOMY. 


f 


^tfpf 


•»«* 


tha  most  part  far  less  exactly  ascertainable  than  the  polar  distance,  or  at 
least  which  has  been  hitherto  far  less  accurately  ascertained,)  we  cannot 
but  regard  all  attempts  of  the  kind  as  to  a  certain  uxtent  premature, 
though  by  no  means  to  be  discouraged  as  forerunners  of  something  more 
decisive.  The  question,  as  a  matter  of  fact,  whether  a  rotation  of  the 
galaxy  in  its  own  plane  exist  or  not,  might  be  at  once  resolved  by  the 
assiduous  observation,  both  in  H.  A.  and  polar  distance,  of  a  considerable 
number  of  stars  of  the  Milky  Way,  judiciously  selected  for  the  purpose, 
and  including  all  mcu/nitudes,  down  to  the  smallest  distinctly  identifiable, 
and  capable  of  being  observed  with  normal  accuracy :  and  we  would  re- 
commend the  inquiry  to  the  special  attention  of  the  directors  of  permanent 
observatories,  provided  with  adequate  instrumental  means,  in  both  hemi- 
spheres. Thirty  or  forty  years  of  observation,  perseveringly  directed  to 
the  object  in  view,  could  not  fail  to  settle  the  question.' 

(862.)  The  solar  motion  through  space,  if  real  and  not  simply  relative, 
must  give  rise  to  uranographical  corrections  analogous  to  parallax  and 
aberration.  The  solar  or  systematic  parallax  is  no  other  than  that  part 
of  the  proper  motion  of  each  star  which  is  simply  apparent,  arising  from 
the  sun's  motion,  and  until  the  distances  of  the  stars  be  known,  must 
remain  inextricably  mixed  up  with  the  other  or  real  portion.  The  syste- 
matic aberration,  amounting  at  its  maximum  (for  stars  90°  from  the  solar 
apex)  to  about  5",  displaced  all  the  stars  in  great  circles  diverging  from 
that  apex  through  angles  proportional  to  the  sines  of  their  respective  dis- 
tances from  it.  This  displacement,  however,  is  permanent,  and  therefore 
uncognizable  by  any  phaenomenon,  so  long  as  the  solar  motion  remains 
invariable ',  but  should  it,  in  the  course  of  ages,  alter  its  direction  and 
velocity,  both  the  direction  and  amount  of  the  displacement  in  question 
would  alter  with  it.  The  change,  however,  would  become  mixed  up  with 
other  changes  in  the  apparent  proper  motions  of  the  stars,  and  it  would 
seem  hopeless  to  attempt  disentangling  them. 

(863.)  A  singular,  and  at  first  sight  paradoxical  efifect  of  the  progres- 
sive movement  of  light,  combined  with  the  proper  motion  of  the  stars,  is 
that  it  alters  the  apparent  periodic  time  in  which  the  individuals  of  a 
binary  star  circulate  about  each  other.^  To  make  this  apparent,  suppose 
them  to  circulate  round  each  other  'n  a  plane  perpendicular  to  the  visual 

'  An  examination  of  the  proper  motions  of  the  stars  of  the  B.  Assoc.  Catal.  in  the 
portion  of  the  Milky  Way  nearest  either  pole  (where  the  motion  should  be  almost 
wholly  in  R  A)  indicates  no  distinct  syint^.em  of  such  a  rotation.  If  the  question  be 
taken  up  fundamentally,  it  wilt  involve  a  redetermination  from  the  recorded  proper 
motions,  both  of  the  precession  of  the  equinoxes  and  the  change  of  obliquity  of  the 
ecliptic. 

*  Astronomische  Nacbrichten,  No.  520. 


^■i- 


SPECULATIONS  ON  A  CENTRAL  SUN. 


497 


r  distance,  or  at 
ned,)  vre  cannot 
Ltent  premature, 
something  more 
I  rotation  of  the 
5  resolved  by  the 
of  a  considerable 
i  for  the  purpose, 
inctly  identifiable, 
and  we  would  re- 
ctors of  permanent 
ans,  in  both  hemi- 
eringly  directed  to 

aot  simply  relative, 

as  to  parallax  and 

other  than  that  part 

parent,  arising  from 

ITS  be  known,  must 

portion.     The  syste- 

s  90**  from  the  solar 

cles  diverging  from 

their  respective  dis- 

lanent,  and  therefore 

solar  motion  remains 

Lter  its  direction  and 

(lacement  in  question 

ecome  mixed  up  witb 

[e  stars,  and  it  would 

[effect  of  the  progres- 

^jotion  of  the  stars,  is 

the  individuals  of  a 

Lis  apparent,  suppose 

fndicular  to  the  visual 

le  B.  A830C.  Catal.  in  the 
notion  should  be  almost 
Ition.  If  the  question  be 
Irom  the  recorded  propel 
Ihange  of  obliquity  of  the 


ray  in  a  period  of  10,000  days.  Then  if  both  the  sun  and  the  centre  of 
gravity  of  the  binary  system  remained  fixed  in  space,  the  relative  apparent 
situation  of  the  stars  would  be  exactly  restored  to  its  former  state  after 
the  lapse  of  this  interval,  and  if  the  angle  of  position  were  0°  at  first, 
after  10,000  days  it  would  again  bo  so.  But  now  suppose  that  the  centre 
of  gravity  of  the  star  were  in  the  act  of  receding  in  a  direct  line  from 
the  sun,  with  a  velocity  of  one-tenth  part  of  the  radius  of  the  earth's 
orbit  per  diem.  Then  at  the  expiration  of  10,000  days  it  would  be  more 
remote  from  us  by  1000  such  radii,  a  space  which  light  would  require  57 
days  to  traverse.  Although  really,  therefore,  the  stars  would  have  arrived 
at  the  position  0°  at  the  exact  expiration  of  10,000  days,  it  would  requirQ 
57  days  more  for  the  notice  of  that  fact  to  reach  our  system.  In  other 
words,  the  period  would  appear  to  us  to  be  10,057  days,  since  we  could 
only  conclude  the  period  to  be  completed,  when  to  us,  as  observers,  the 
original  angle  of  position  was  again  restored.  A  contrary  motion  would 
produce  a  contrary  effect. 


}    ,, 


r.i'r  ■'.  X.ij'O"    ir^--^^; ■■?■!!•  ■■   -■••-■;^    .■"  :■':-. 
■ci  Ur    »^' i->ji*f '•'■'    :■■'",    "utji'     ':'''•{■:■   ';' 

-i:     •■■.!,'  i-r\  •  ..    ,1'  ■.'''\''\"     '■'■  ,r 

i  "'.i    '    •    ■'-"'.■  ■■  >■  •"■  ''    t    . 


'■i 


fi  "■I'.i 


498 


OUTLINES   OF  ASTRONOMT. 


IP'"*'-  <*« 


CHAPTER  XVII. 
OF    CLUSTERS    OF    STARS    AND    NEBULA. 

OF  CLUSTERING  GROUPS  OF  STARS.  —  GLOBULAR  CLUSTERS.  —  THEIR 
STABILITY  DYNAMICALLY  POSSIBLE.  —  LIST  OP  THE  MOST  REMARK- 
ABLE. —  CLASSIFICATION  OP  NEBULA  AND  CLUSTERS.  —  THEIR 
DISTRIBUTION  OVER  THE  HEAVENS.  —  IRREGULAR  CLUSTERS.  — 
RESOLV ABILITY  OF  NEBULiE.  —  THEORY  OP  THE  FORMATION  OP 
CLUSTERS     BY    NEBULOUS     SUBSIDENCE.  —  OP    ELLIPTIC    NEBULA. 

—  THAT    OP  ANDROMEDA, — ANNULAR  AND    PLANETARY   NEBULiE. 

—  DOUBLE  NEBULiE.  —  NEBULOUS  STARS. — CONNEXION  OP  NEBULAE 
WITH  DOUBLE  STARS.  —  INSULATED  NEBULiE,  OP  FORMS  NOT 
WHOLLY  IRREGULAR.  —  OP  AMORPHOUS  NEBULiB.  —  THEIR  LAW  OP 
DISTRIBUTION  MARKS  THEM  AS  OUTLIERS  OF  THE  GALAXY.— 
NEBULiE,  AND  NEBULOUS  GROUP  OF  ORION. — OF  ARGO.  —  OF  SA- 
GITTARIUS.—  OF  CYGNUS.  —  THE  MAGELLANIC  CLOUDS.  —  SINGULAR 
NEBULA  IN  THE  GREATER  OP  THEM. — THE  ZODIACAL  LIGHT.— 
SHOOTING   STARS. 

(864.)  When  we  cast  our  eyes  over  the  concave  of  the  heavens  iu  a  clear 
night,  we  do  not  fail  to  observe  that  here  and  there  are  groups  of  stars 
which  seem  to  be  compressed  together  in  a  more  condensed  manner  than 
in  the  neighbouring  parts,  forming  bright  patches  and  clusters,  which 
attract  attention,  as  if  they  were  there  brought  together  by  some  general 
cause  other  than  casual  distribution.  There  is  a  group,  called  the  Pleiades, 
in  which  six  or  seven  stars  may  be  noticed,  if  the  eye  be  directed  full 
upon  it ;  and  many  more  if  the  eye  be  turned  carelessly  aside,  while  th 
attention  is  kept  directed '  upon  the  group.  Telescopes  show  fifty  or  sixty 
large  stars  thus  crowded  together  in  a  very  moderate  space,  comparatively 

*  It  is  a  very  remarkable  fact,  that  the  centre  of  the  visual  area  is  far  leci  sensible 
to  feeble  impressions  of  light,  than  the  exterior  portions  of  the  retina.  Few  persons 
are  aware  of  the  extent  to  which  this  comparative  insensibility  extends,  previous  to 
trial.  To  estimate  it,  let  the  reader  look  alternately  full  at  a  star  of  the  fifth  magni- 
tude, and  beside  it ;  or  choose  two  equally  bright,  and  about  3°  or  4°  apart,  and  look 
full  at  one  of  them,  the  probability  is  he  will  see  only  the  other.  The  fact  accounts  for 
the  multitude  of  stars  with  which  we  are  impressed  by  a  general  view  of  the  heavens; 
their  paucity  when  we  come  to  count  them. 


H<'<»'1 


CLUSTERS  OF  STARS  AND   NEBULA. 


499 


LUSTERS.— THEIE 
HE  MOST  BEMARK- 
.XJSTERS.  —  THEIR 
LAR    CLUSTERS.— 
IE    FORMATION    OF 
ELLIPTIC    NEBULiE. 
ANETARY  NEBULiE. 
NEXION  OF  NEBULAE 
E^    OF    FORMS     NOT 
a-.  — THEIR  LAW  OF 
iF    THE    GALAXY. 

OF   ARQO.  — O^   S^- 
JLOUDS.  — SINGULAR 

ZODIACAL  LIGHT. - 

the  heavens  iu  a  clear 
e  are  groups  of  stars 
[ndensed  manner  than 
i  and  clusters,  vWch 
jther  by  some  general 
IP,  called  the  Pleiades, 
(eye  be  directed  full 
lelessli/  aside,  while  tk 
,pe8  show  fifty  or  sixty 

space,  comparatively 

L  area  is  far  lee.  sensible 
f  the  retina.  Few  persons 
Ibility  extends,  previous  to 
I  a  star  of  the  fifth  magm- 
lut  3°  or  4°  apart,  and  looK 
Ifcer  The  fact  accounts  lot 
Inerol  view  of  the  heavens;' 


insulated  from  the  rest  of  the  heavens.  The  constellation  called  Coma 
Berenices  is  another  such  group,  more  diffused,  and  consisting  on  the 
whole  of  larger  stars. 

(865.)  In  the  constellation  Cancer,  there  is  a  somewhat  similar,  but 
less  definite,  luminous  spot,  called  Praesepe,  or  the  bee-hive,  which  a  very 
moderate  telescope,  —  an  ordinary  night-glass  for  instance, — resolves  en- 
tirely into  stars.     In  the  sword-handle  of  Perseus,  also,  is  another  such 
spot,  crowded  with  stars,  which  requires  rather  a  better  telescope  to  resolve 
into  individuals,  separated  from  each  other.     These  are  called  clusters  of 
stars ;  and,  whatever  be  their  nature,  it  is  certain  that  other  laws  of  ag- 
gregation subsist  in  these  spots,  than  those  which  have  determined  the 
scattering  of  stars  over  the  general  surface  of  the  sky.     This  conclusion 
is  still  more  strongly  pressed  upon  us,  when  we  come  to  bring  very 
powerful  telescopes  to  bear  on  these  and  similar  spots.    There  are  a 
great  number  of  objects  which  have  been  mistaken  for  comets,  and,  in 
fact,  have  very  much  the  appearance  of  comets  without  tails :  small  round, 
or  oval  nebulous  specks,  which  telescopes  of  moderate  power  only  show 
as  such.     Messier  has  given,  in  the  Connois.  des  Tempi  for  1784,  a  list 
of  the  places  of  103  objects  of  this  sort ;  which  all  those  who  search  for 
comets  ought  to  be  familiar  with,  to  avoid  being  misled  by  their  similarity 
of  appearance.     That  they  are  not,  however,  comets,  their  fixity  suffi- 
ciently proves )  and  when  we  come  to  examine  them  with  instruments  of 
great  power, — such  as  reflectors  of  eighteen  inches,  two  feet,  or  more  in 
aperture, — ^any  such  idea  is  completely  destroyed.    They  are  then,  for  the 
most  part,  perceived  to  consist  entirely  of  stars  crowded  together  so  as  to 
occupy  almost  a  definite  outline,  and  to  run  up  to  a  blaze  of  light  in  the 
centre,  where  their  condensation  is  usually  the  greatest.     (See  fig.  1, 
pi.  II.,  which  represents  (somewhat  rudely)  the  thirteenth  nebula  of 
Messier's  list  (described  by  him  as  ndbuleuse  sans  Stones'),  as  seen  in  a 
reflector  of  18  inches  aperture  and  20  feet  focal  length.)     Many  of  them, 
indeed,  are  of  an  exactly  round  figure,  and  convey  the  complete  idea  of  a 
globular  space  filled  full  of  stars,  insulated  in  the  heavens,  and  constitut- 
ing in  itself  a  family  or  society  apart  from  the  rest,  and  subject  only  to 
its  own  internal  laws.     It  would  be  a  vain  task  to  attempt  to  count  the 
stars  in  one  of  these  globular  clusters.     They  are  not  to  be  reckoned  by 
hundreds ;  and  on  a  rough  calculation,  grounded  on  the  apparent  intervals 
between  them  at  the  borders,  and  the  angular  diameter  of  the  whole  group, 
it  would  appear  that  many  clusters  of  this  description  must  contain  at 
least  five  thousand  stars,  compacted  and  wedged  together  in  a  round  spaco^ 
whose  angular  diameter  does  not  exceed  eight  or  ten  minutes ;  that  is  to 
say,  in  an  area  not  more  than  a  tenth  part  of  that  covered  by  the  moon. 


il 


]'l 


500 


OUTLINES   OF  ASTRONOMY. 


£2: 

>2: 


*»»■■;  tn 


(866.)  Perhaps  it  may  bo  thought  to  savour  of  the  gigantesque  to  look 
upon  the  individuals  of  such  a  group  as  suns  like  our  own,  and  their  mu- 
tual distances  as  equal  to  those  which  separate  our  sun  from  the  nearest 
fixed  star :  yet,  when  wo  consider  that  their  united  lustre  affects  the  eye 
with  a  less  impression  of  light  than  a  star  of  the  fourth  magnitude,  (for 
the  largest  of  those  clusters  is  barely  visible  to  the  naked  eye,)  the  idea 
we  arc  thus  compelled  to  form  of  their  distance  from  ua  may  prepare  us 
for  almost  any  estimate  of  their  dimensions.  At  all  events,  wo  can 
hardly  look  upon  a  group  thus  insulated,  thus  in  seipm  totusy  teres,  atque 
rotmiduSf  as  not  forming  a  system  of  a  peculiar  and  definite  character. 
Their  round  figure  clearly  indicates  the  existence  of  some  general  bond 
of  union  in  the  nature  of  an  attractive  force ;  and,  in  many  of  them,  there 
is  an  evident  acceleration  in  tho  rate  of  condensation  as  wo  approach  the 
centre,  which  is  not  referable  to  a  merely  uniform  distribution  of  equidis- 
tant stars  through  a  globular  space,  but  marks  an  intrinsic  dtunty  in  their 
state  of  aggregation,  greater  in  the  centre  than  at  the  surface  of  the  mass. 
It  is  difficult  to  form  any  conception  of  the  dynamical  state  of  such  a 
system.  On  the  one  hand,  without  a  rotatory  motion  and  a  centrifugal 
force,  it  is  hardly  possible  not  to  regard  them  as  in  a  state  of  progressive 
collapse.  On  the  other,  granting  such  a  motion  and  such  a  force,  we  find 
it  no  less  difficult  to  reconcile  the  apparent  i^pLericity  of  their  form  with 
a  rotation  of  the  whole  system  round  any  sipgio  axis,  without  which  in- 
ternal collisions  might  at  first  sight  appear  to  be  inevitable.  If  wo  sup- 
pose a  globular  space  filled  with  equal  stars,  uniformly  dispersed  through 
it,  and  very  numerous,  each  of  them  attracting  every  other  with  a  force 
inversely  as  the  square  of  the  distance,  the  resultant  force  by  which  any 
one  of  them  (those  at  the  surface  alone  excepted)  will  be  urged,  in  virtue 
of  their  joint  attractions,  will  be  directed  towards  the  common  centre  of 
the  sphere,  and  will  be  directly  as  the  distance  therefrom.  This  follows 
from  what  Newton  has  proved  of  the  internal  attraction  of  a  homogeneous 
sphere.  (See  also  note  on  Art.  735.)  Now,  under  such  a  law  of  force, 
each  particular  star  would  describe  a  perfect  ellipse  about  the  common 
centre  of  gravity  as  its  centre,  and  that,  in  whatever  plane  and  whatever 
direction  it  might  revolve.  The  condition,  therefore,  of  a  rotation  of  the 
cluster,  as  a  mass,  about  a  single  axis  would  be  unnecessary.  Each 
ellipse,  whatever  might  be  the  proportion  of  its  axis,  or  the  inclination 
of  its  plane  to  the  others,  would  be  invariable  in  every  particular,  and  all 
would  be  described  in  one  common  period,  so  that  at  the  end  of  every 
^liuch  period,  or  annus  magnus  of  the  system,  every  star  of  the  cluster 
(except  the  superficial  ones)  would  be  exactly  re-established  in  its  original 
position,  thence  to  set  out  afresh,  and  run  the  same  unvarying  round  for 


u 


CLASSIFICATION   OP  NEBULA. 


601 


jantesque  to  look 
»n,  and  their  mu- 
from  the  nearest 
re  affects  the  eye 
h  magnitude,  (fov 
ced  eye,)  the  idea 
M  may  prepare  us 
\\  events,  wo  can 

0  totus,  tere»,  atquc 
definite  character. 

some  general  bond 
lany  of  them,  there 
as  wo  approach  the 
tributi"!  of  equidis- 
insio  dtmtl/  in  their 
surface  of  the  mass, 
ical  state  of  such  a 
m  and  a  centrifugal 
a  state  of  progressive 

1  such  a  force,  we  find 
ty  of  their  form  with 

9,  without  which  in- 
svitable.     If  wc  sup- 
Illy  dispersed  through 
ry  other  with  a  force 
t  force  by  which  any 
ill  be  urged,  in  virtue 
the  common  centre  of 
•cfrom.    This  follows 
tion  of  a  homogeneous 
.r  such  a  law  of  force, 
se  about  the  common 
er  plane  and  whatever 
e,  of  a  rotation  of  the 
_^  unnecessary.    Each 
ixis,  or  the  inclination 
L„par/,iWar,andaU 
\t  at  the  end  of  every 
>ry  star  of  the  cluster 
tblished  in  its  original 
unvarying  round  for 


BU  indefinite  succession  of  ages.  Supposing  their  motions,  therefore,  to 
be  so  adjusted  at  any  one  moment  as  that  the  orbits  should  not  intersect 
each  other,  and  so  thut  the  magnitude  of  each  star,  and  the  sphere  of  its 
more  intense  attraction,  should  boar  but  a  small  proportion  to  the  distance 
separating  the  individuiils,  such  a  system,  it  is  obvious,  might  subsist,  and 
realize,  in  great  niensuro,  that  abstract  and  ideal  harmony,  which  Newton, 
in  tho  89th  Proposition  of  the  First  Book  of  tho  Pniicipia,  has  shown 
to  characterize  a  law  of  force  directly  as  the  distance.' 

(867.)  The  following  are  the  places,  for  1830,  of  the  principal  of  these 
remarkable  objects,  as  specimens  of  their  class :  — 


n.  A. 

N.  v.  D.  j 

n.  A. 

N.  V.  D, 

R.  A. 

N.  P.  D. 

h.  m.  H. 

o    / 

h. 

ni.  H. 

o    / 

h. 

m. 

B. 

O     1 

0  16  25 

103   2 

16 

9  56 

87  16 

17 

26 

51 

143  34 

9   8  33 

154  10 

15 

34  56 

127  13 

17 

28 

42 

93   8 

12  47  41 

159  57 

16 

6  55 

112  33 

11 

26 

4 

114   2 

13   4  30 

70  65 

16 

23   2 

102  40 

18 

65 

49 

150  14 

13  16  88 

136  35 

16 

35  37 

53  13 

21 

21 

43 

78  34 

13  34  10 

60  46 

16 

60  24 

119  51 

21 

24 

40 

91  34 

Of  these,  by  far  the  most  conspicuous  and  remarkable  is  «  Centauri  the 
fifth  of  the  list  in  order  of  Right  Ascension.  It  is  visible  to  the  naked 
eye  as  a  dim  round  cometic  object  about  equal  to  a  star  4'5  m.,  though 
probably  if  concentered  in  a  single  point,  the  impression  on  the  eye  would 
be  much  greater.  Viewed  in  a  powerful  telescope  it  appears  as  a  globe 
of  fully  20*  in  diameter,  very  gradually  increasing  in  brightness  to  the 
centre,  and  composed  of  innumerable  stars  of  tho  13th  and  15th  magni- 
tudes (the  former  probably  being  two  or  more  of  the  latter  closely  juxta- 
posed). The  11th  in  order  of  the  list  (R.  A.  16'  35")  is  also  visible  to 
tho  naked  eye  in  very  fine  nights,  between  rj  and  ^  Herculis,  and  is  a 
superb  object  in  a  large  telescope.  Both  were  discovered  by  Halley,  the 
former  in  1677,  and  the  latter  in  1714.        " ' 

(868.)  It  is  to  Sir  William  Herschel  that  we  owe  the  most  complete 
analysis  of  the  great  variety  of  those  objects  which  are  generally  classed 
under  the  common  head  of  Nebulae,  but  which  have  been  separated  by 
him  into  —  Ist.  Clusttrs  of  stars,  in  which  the  stars  are  clearly  distin- 
guishable; and  tiiese,  again,  into  globular  and  irregular  clusters;  2d. 
Resolvable  nebulae,  or  such  as  excite  a  suspicion  that  they  consist  of  stars, 
and  which  any  increase  of  the  optical  power  of  the  telescope  may  be  ex- 
pected to  resolve  into  distinct  stars ;  3d.  Nebula?,  protierly  so  called,  in 
which  there  is  no  appearance  whatever  of  stars ;  which,  again,  have  been 
subdivided  into  subordinate  uses,  according  to  their  brightness  and  size ; 

'  See  also  Quarterly  Review,  No.  94,  p.  540. 


502 


OUTLINES  OF  ASTRONOMT. 


•ana* 


s^ 

*•»•!' 


4th.  Planetary  nebulao ;  5th.  Stellar  nebulas ;  and,  6th.  Nebulou''  stan. 
The  great  power  of  his  telescope  disclosed  the  existence  of  an  immense 
number  of  these  objects  before  unknown,  and  showed  them  to  be  distri- 
buted over  the  heavens,  not  by  any  means  uniformly,  but  with  u  marked 
preference  to  a  certain  district,  extending  over  the  northern  pole  of  the 
galactic  circle,  and  occupying  the  constellations  Leo,  Leo  Minor,  the  body, 
tail,  and  hind  legs  of  Ursa  Major,  Canes  Venatici,  Coma  Berenices,  the 
preceding  leg  of  Bootes,  and  the  head,  wing,  and  sh^  jlders  of  Virgo.  In 
this  region,  occupying  about  one-eighth  of  the  whole  surface  of  the  sphere, 
one-third  of  the  entire  nebulous  contents  of  the  heavens  are  congregated. 
On  the  other  hand,  they  are  very  sparingly  scattered  over  the  constella- 
tions Aries,  Taurus,  the  head  and  shoulders  of  Orion,  Auriga,  Perseus, 
CamclopardaluB,  Draco,  Hercules,  the  northern  part  of  Serpentarius,  the 
tail  of  Serpens,  that  of  Aquila,  and  the  whole  of  Lyra.  The  hours  8, 4, 
5,  and  16,  17,  18,  of  right  ascension  in  the  northern  hemisphere  are  sin- 
gularly poor,  and,  on  the  other  hand,  the  hours  10, 11,  and  12  (but  espe- 
cially 12),  cxtraordinnrily  rich  in  these  objects.  In  the  southern  hemi- 
sphere a  much  greater  uniformity  of  distribution  prevails,  and  with 
exception  of  two  very  remarkable  centres  of  accumulation,  called  the 
Magellanic  clouds  (of  which  more  presently),  there  is  no  very  decided 
tendency  to  their  assemblage  in  any  particular  region. 

(869.)  Clusters  of  stars  are  either  globular,  such  as  we  have  already 
described,  or  of  irregular  figure.  These  latter  are,  generally  speaking, 
less  rich  in  stars,  and  especially  less  condensed  towards  the  centre.  They 
are  also  less  definite  in  outline ;  so  that  it  is  often  not  easy  to  say  where 
they  terminate,  or  whether  they  are  to  be  regarded  otherwise  than  as 
merely  richer  parts  of  the  heavens  than  those  around  them.  Many, 
indeed,  the  greater  proportion  of  them,  are  situated  in  or  close  on  the 
borders  of  the  Milky  Way.  In  some  of  them  the  stars  are  nearly  all  of 
a  size,  in  others  extremely  difierent ;  and  it  is  no  uncommon  thing  to  find 
a  very  red  star  much  brighter  than  the  rest,  occupying  a  conspicuous 
situation  in  them.  Sir  William  Herschel  regards  these  as  globular  clus- 
ters in  a  less  advanced  state  of  condensation,  conceiving  all  such  groups 
as  approaching,  by  their  mutual  attraction,  to  the  globular  figure,  and 
assembling  themselves  together  from  all  the  surrounding  region,  under 
laws  of  which  we  have,  it  is  true,  no  other  proof  than  the  observance  of 
a  gradation  by  which  their  characters  shade  into  one  another,  so  that  it  is 
impossible  to  say  where  one  species  ends  and  the  other  begins.  Among 
the  most  beautiful  objects  of  this  class  is  that  which  surrounds  the  star 
X  Cruois,  set  down  as  a  nebula  by  Lacaille.  It  occupies  an  area  of  about 
one  48th  part  of  a  square  degree,  and  consists  of  about  110  stars  from  the 


-.v_r  .  .';- 


RESOLVABLE  NEBULiB. 


508 


Jfebulou"  stare. 

of  an  immense 

lem  to  be  distri- 

t  vith  a  marked 

lern  pole  of  tbe 

Minor,  the  body, 

a  Berenices,  the 

,T8  of  Virgo.    In 

ice  of  the  ephore, 

» are  congregated. 

ver  the  constella- 

Anriga,  Perseus, 

Serpentarius,  the 

The  hours  3, 4, 

lemisphere  are  sin- 

,  and  12  (but  espe- 

iho  southern  hemi- 

prevails,  and  vith 

ittlation,  called  the 

is  no  very  decided 

as  we  have  already 
generally  speaking, 
J  the  centre.    They 
>t  easy  to  say  where 
otherwise  than  as 
lund  them.     Many, 
in  or  close  on  the 
pirs  are  nearly  all  of 
[ommon  thing  to  find 
pying  a  conspicuous 
lese  as  globular  clus- 
ring  all  such  groups 
globular  figure,  and 
inding  region,  under 
in  the  observance  of 
another,  so  that  it  is 
her  begins.     Among 
b  surrounds  the  star 
ties  an  area  of  about 
it  110  stars  from  the 


7th  magnitude  downwards,  eight  of  tho  more  conspicuous  of  which  aro 
coloured  with  various  shades  of  red,  green,  and  blue,  so  as  to  give  to  the 
whole  the  appearance  of  a  rich  piece  of  jewellery. 

(870.)  Resolvable  nebulae  can,  of  course,  only  be  considered  as  clustcra 
either  too  remote,  jr  consisting  of  stars  intrinsically  too  faint  to  affect  us 
by  their  individual  light,  unless  where  two  or  three  happen  to  be  close 
enough  to  make  a  joint  impression,  and  give  the  idea  of  a  point  brighter 
than  the  rest.     They  are  almost  universally  round  or  oval  —  their  loose 
appendages,  and  irregularities  of  form,  being  as  it  were  extinguished  by 
the  distance,  and  the  only  general  figure  of  the  more  condensed  parts  being 
discernible.     It  is  under  the  appearance  of  objects  of  this  character  that 
all  the  greater  globular  clusters  exhibit  themselves  in  telescopes  of  insuffi- 
cent  optical  power  to  show  them  well ;  and  the  conclusion  is  obvious,  that 
those  which  the  most  powerful  can  barely  render  resolvable,  and  even 
those  which,  with  such  powers  as  are  usually  applied,  show  no  sign  of 
being  composed  of  stars,  would  be  completely  resolved  by  a  further  in- 
crease  of  optical  power.     In  fact,  this  probability  has  almost  been  con- 
verted  into  a  certainty  by  the  magnificent  reflecting  telescope  constructed 
by  Lord  Rosse,  of  six  feet  in  aperture,  which  has  resolved  or  rendered 
resolvable  multitudes  of  nebulse  which  had  resisted  all  inferior  powers. 
The  sublimity  of  the  spectacle  afforded  by  that  instrument  of  some  of  the 
larger  globular  and  other  clusters  enumerated  in  the  list  given  in  Art.  867, 
is  declared  by  all  who  have  witnessed  it  to  be  such  as  no  words  can  express. 
(871.)  Although,  therefore,  nebulae  do  exist,  which  even  in  this  power- 
ful  telescope  appear  as  nebulae,  without  any  sign  of  resolution,  it  may 
very  reasonably  be  doubted  whether  there  be  really  any  essential  physical 
distinction  between  nebulse  and  clusters  of  stars,  at  least  in  the  nature  of 
the  matter  of  which  they  consist,  and  whether  the  distinction  between 
such  nebulse  as  are  easily  resolved,  barely  resolvable  with  excellent  tele- 
scopes, and  altogether  irresolvable  with  the  best,  be  any  thing  else  than 
one  of  degree,  arising  merely  from  the  excessive  minuteness  and  multitude 
of  the  stars,  of  which  the  latter,  as  compared  with  the  former,  consist. 
The  first  impression  which  Halley,  and  other  early  discoverers  of  nebulous 
objects  received  from  their  peculiar  aspect,  so  different  from  the  keen, 
concentrated  light  of  mere  stars,  was  that  of  a  phosphorescent  vapour  (like 
the  matter  of  a  comet's  tail)  or  a  gaseous  and  (so  to  speak)  elementary  form 
of  luminous  sidereal  matter.'    Admitting  the  existence  of  such  a  medium, 
dispersed  in  some  cases  irregularly  through  vast  regions  in  space,  in  others^ 
confined  to  narrower  and  more  definite  limits.  Sir  W.  Herschel  was  led  W 
speculate  on  its  gradual  subsidence  and  condensation  by  the  effect  of  its 
*  Halley,  Phil.  Trans.,  xxix.  p.  390. 


I ; 


!! 


l!l 


f1 


504 


OUTLINES  OP  ASTRONOMY. 


CD 


•*«ir 


own  gravity,  into  more  or  less  regular  spherical  or  spheroidal  forms, 
denser  (as  they  must  in  that  case  be)  towards  the  centre.  Assuming  that 
in  the  progress  of  this  subsidence,  local  centres  of  condensation,  subordi- 
nate to  the  general  tendency,  would  not  be  wanting,  he  conceived  that  in 
this  way  solid  nuclei  might  arise,  whose  local  gravitation  still  further 
condensing,  and  so  absorbing  the  nebulous  matter,  each  in  its  immediate 
neighbourhood,  might  ultimately  become  stars,  and  the  whole  nebulae 
finally  take  on  the  state  of  a  cluster  of  stars.  Among  the  multitude  of 
nebulao  revealed  by  his  telescopes,  every  stage  of  this  process  might  be 
considered  as  displayed  to  our  eyes,  and  in  every  modification  of  form  to 
which  the  general  principle  might  be  conceived  to  apply.  The  more  or 
less  advanced  state  of  a  nebula  towards  its  segregation  into  discrete  stars 
and  of  these  stars  themselves  towards  a  denser  state  of  aggregation  round 
a  central  nucleus,  would  thus  be  in  some  sort  an  indication  of  age. 
Neither  is  there  any  variety  of  aspect  which  nebulae  oflFer,  which  stands  at 
all  in  contradiction  to  this  view.  Even  though  we  should  feel  ourselves 
compelled  to  reject  the  idea  of  a  gaseous  or  vaporous  "  nebulous  matter," 
it  loses  little  or  none  of  its  force.  Subsidence,  and  the  central  aggrega- 
tion consequent  on  subsidence,  may  go  on  quite  as  well  among  a  multi- 
tude of  discrete  bodies  under  the  influence  of  mutual  attraction,  and 
feeble  or  partially  opposing  projectile  motions,  as  among  the  particles  of  a 
gaseous  fluid.     / 

(872.)  The  "nebular  hypothesis,"  as  it  has  been  termed,  and  the 
theoTi/  of  sidereal  aggregation  stand,  in  fact,  quite  independent  of  each 
other,  the  one  as  a  physical  conception  of  processes  which  may  yet,  for 
aught  we  know,  have  formed  part  of  that  mysterious  chain  of  causes  and 
effects  antecedent  to  the  existence  of  separate  self-luminous  solid  bodies; 
the  other,  as  an  application  of  dynamical  principles  to  cases  of  a  very 
complicated  nature  no  doubt,  but  in  which  the  possibility  or  impossibility, 
at  least,  of  certain  general  results  may  be  determined  on  perfectly  legiti- 
mate principles.  Among  a  crowd  of  solid  bodies  of  whatever  size,  ani- 
mated by  independent  and  partially  opposing  impulses,  motions  opposite 
to  each  other  must  produce  collision,  destruction  of  velocity,  and  subsi- 
dence or  near  approach  towards  the  centre  of  preponderant  attraction; 
while  those  which  conspire,  or  which  remain  outstanding  after  such  con- 
flicts, must  ultimately  give  rise  to  circulation  of  a  permanent  character. 
Whatever  we  may  think  of  such  collisions  as  events,  there  is  nothing  in 
this  conception  contrary  to  sound  mechanical  principles.  It  will  be  recol- 
lected that  the  appearance  of  central  condensation  among  a  multitude  of 
separate  bodies  in  motion,  by  no  means  implies  permanent  proximity  to 
the  centre  in  each ;  any  more  than  the  habitually  crowded  state  of  a 


THEORY   OF  THE  FORMATION  OF  CLUSTERS. 


505 


pberoidal  forms, 
Assuming  that 
msation,  subordi- 
conceived  that  in 
tion  still  further 
I  in  its  immediate 
ae  whole  nebulae 
the  multitude  of 
process  might  be 
ication  of  form  to 
ly.  The  more  or 
into  discrete  stars 
aggregation  round 
indication  of  age. 
er,  which  stands  at 
ould  feel  ourselves 
*  nebulous  matter," 
le  central  aggrega- 
'ell  among  a  multi- 
;ual  attraction,  and 
ig  the  particles  of  a 

m  termed,  and  the 
idependent  of  each 
.which  may  yet,  for 
Ichain  of  causes  and 
linous  solid  bodies; 
to  cases  of  a  very 
ity  or  impossibility, 
on  perfectly  legiti- 
whatever  size,  ani- 
!8,  motions  opposite 
velocity,  and  subsi- 
raderant  attraction; 
ling  after  such  con- 
crmanent  character. 
1,  there  is  nothing  in 
It  will  be  recol- 
long  a  multitude  of 
janent  proximity  to 
crowded  state  of  a 


market-place,  to  which  a  largo  proportion  of  the  inhabitants  of  a  town 
frequently  or  occasionally  resort,  implies  the  permanent  residence  of  each 
individual  within  its  area.  It  is  a  fact  that  clusters  thus  centrally  crowded 
do  exist,  and  therefore  the  conditions  of  their  existence  must  be  dynami- 
cally possible,  and  in  what  has  been  said  we  may  at  least  perceive  some 
glimpses  of  the  manner  in  which  they  are  so.  The  actual  intervals  be- 
tween the  stars,  even  in  the  most  crowded  parts  of  a  resolved  nebula,  to 
he  seen  at  all  by  us,  must  be  enormous.  Ages,  which  to  us  may  well 
appear  indefinite,  may  easily  be  conceived  to  pass  without  a  single  instance 
of  collision,  in  the  nature  of  a  catastrophe.  Such  may  have  gradually 
hecome  rarer  as  the  system  has  emerged  from  what  must  be  considered  its 
chaotic  state,  till  at  length,  in  the  fulness  of  time,  and  under  the  pre- 
arranging guidance  of  that  Design  which  pervades  universal  nature,  each 
individual  may  have  taken  up  such  a  course  as  to  annul  the  possibility  of 
further  destructive  interference.  ■  ■ 

(873.)  But  to  return  from  the  regions  of  speculation  to  the  description 
of  facts.  Next  in  regularity  of  form  to  the  globular  clusters,  whose  con- 
sideration has  led  us  into  this  digression,  arc  elliptic  nebulae,  more  or  less 
elongated.  And  of  these  it  may  be  generally  remarked,  as  a  fact  un- 
doubtedly connected  in  some  very  intimate  manner  with  the  dynamical 
conditions  of  their  subsistence,  that  such  nebulae  are,  for  the  most  part, 
beyond  comparison  more  difficult  of  resolution  than  those  of  globular  form. 
They  are  of  all  degrees  of  excentricity,  from  moderately  oval  forms  to 
ellipses  so  elongated  as  to  bo  almost  linear,  which  are,  no  doubt,  edge- 
views  of  very  flat  ellipsoids.  In  all  of  them  the  density  increases  towards 
the  centre,  and  as  a  general  law  it  may  be  remarked  that,  so  far  as  we 
can  judge  from  their  telescopic  appearance,  their  internal  strata  approach 
more  nearly  to  the  spherical  form  than  their  external.  Their  resolva- 
bility,  too,  is  greater  in  the  central  parts,  whether  owing  to  a  real  supe- 
riority of  size  in  the  central  stars  or  to  the  greater  frequency  of  cases  of 
close  juxta-position  of  individuals,  so  that  two  or  three  united  appear  as 
one.  In  some  the  condensation  is  slight  and  gradual,  in  others  great  and 
sudden:  so  sudden,  indeed,  as  to  offer  the  appearance  of  a  dull  and 
blotted  star,  standing  in  the  midst  of  a  faint,  nearly  equable  elliptic  nebu- 
losity, of  which  two  remarkable  specimens  occur  in  R.  A.  12"  lO"  33% 
N.  P.  D.  41°  46',  and  in  IS''  27"  28»,  119°  (K  (1830). 

(874.)  The  largest  and  finest  specimens  of  elliptic  nebulae  which  the 
heavens  afford  are  that  in  the  girdle  of  Andromeda  (near  the  star  v  of 
that  constellation)  and  that  discovered  in  1788,  by  Miss  Carolina  Hersehel, 
in  R.  A.  0"  39-  12%  N.  P.  D.  116°  13'.  The  nebula  in  Andromeda 
(Plate  II.  fig.  3.)  is  visible  to  the  naked  eye,  and  is  continually  mistaken 


506 


OUTLINES  OF  ASTRONOMY. 


2f^ 


CIO 


for  a  comet  by  those  unacquainted  with  the  heavens.  Simon  Marius, 
who  noticed  it  in  1612  (though  it  appears  also  to  have  been  seen  and 
described  as  oval^  in  995),  describes  its  appearance  as  that  of  a  candle 
shining  through  horn,  and  the  resemblance  is  not  inapt.  Its  form,  as  seen 
through  ordinary  telescopes,  is  a  pretty  long  oval,  increasing  by  insensible 
gradations  of  brightness,  at  first  very  gradually,  but  at  last  more  rapidly, 
up  to  a  central  point,  which,  though  very  much  brighter  than  the  rest,  is 
decidedly  not  a  star,  but  nebula  of  the  same  general  character  with  the 
rest  in  a  state  of  extreme  condensation.  Casual  stars  are  scattered  over 
it,  but  with  a  reflector  of  18  inches  in  diameter,  there  is  nothing  to  excite 
any  suspicion  of  its  consisting  of  stars.  Examined  with  instruments  of 
superior  defining  power,  however,  the  evidence  of  its  resolvability  into 
stars,  may  be  regarded  as  decisive.  Mr.  Q.  P.  Bond,  assistant  at  the 
observatory  of  Cambridge,  U.  S.,  describes  and  figures  it  as  extending 
nearly  2^*^  in  length,  and  upwards  of  a  degree  in  breadth  (so  as  to  include 
two  other  smaller  adjacent  nebulae),  of  a  form,  generally  speaking,  oval, 
but  with  a  considerably  protuberant  irregularity  at  its  north  following  ex- 
tremity, very  suddenly  condensed  at  the  nucleus  almost  to  the  semblance 
of  a  star,  and  though  not  itsf 'f  clearly  resolved,  yet  thickly  sown  over 
with  visible  minute  stars,  so  numerous  as  to  allow  of  200  being  counted 
within  a  field  of  20'  diameter  in  the  richest  parts.  But  the  most  remark- 
able feature  in  his  description  is  that  of  two  perfectly  straight,  narrow, 
and  comparatively  or  totally  obscure  streaks  which  run  nearly  the  whole 
length  of  one  side  of  the  nebula,  and  (though  slightly  divergent  from 
each  other)  nearly  parallel  to  its  longer  axis.  These  streaks  (which 
obviously  indicate  b  stratified  structure  in  the  nebula,  if,  indeed,  they  do 
not  originate  in  the  interposition  of  imperfectly  transparent  matter  between 
us  and  it)  are  not  seen  on  a  general  and  cursory  view  of  the  nebula ;  they 
require  attention  to  distinguish  them,'  and  this  circumstance  must  be  borne 
in  mind  when  inspecting  the  very  extraordinary  engraving  which  illustrates 
Mr.  Bond's  account.  The  figure  given  in  our  Plate  II.  fig.  8,  is  from  a 
rather  hasty  sketch,  and  makes  no  pretensions  to  exactness.  A  similar, 
but  much  more  strongly  marked  case  of  parallel  arrangement  than  that 
noticed  by  Mr.  Bond  in  this,  is  one  in  which  the  two  semi-ovals  of  an 
elliptically  formed  nebula  appear  cut  asunder  and  separated  by  a  broad 
obscure  band  parallel  to  the  larger  axis  of  the  nebula,  in  the  midst  of 
which  a  faint  streak  of  light  parallel  to  the  sides  of  the  cut  appears,  is 
seen  in  the  southern  hemisphere  in  E.  A.  18"  IS"  31»,  N.  P.  D.  132°  8' 


*  Account  of  the  nebula  in  Andromeda,  by  G.  P.  Bond,  Assistant  at  the  Cambridge 
Observatory,  U.  S.    Trans.  American  Acad,,  vol.  ill.  p.  80. 


PLANETARY  NEBULA. 


607 


Simon  Marius, 
8  been  seen  and 
that  of  a  candle 
Its  form,  as  seen 
sing  by  insensible 
last  more  rapidly, 
!r  than  the  rest,  is 
jharacter  with  the 
are  scattered  over 
3  nothing  to  excite 
th  instruments  of 
3  resolvability  into 
d,  assistant  at  the 
res  it  as  extending 
th  (so  as  to  include 
■ally  speaking,  oval, 
north  following  ox- 
)8t  to  the  semblance 
t  thickly  sown  over 
f  200  being  counted 
ut  the  most  remark- 
tly  straight,  narrow, 
an  nearly  the  whole 
itly  divergent  from 
ese  streaks  (which 
I,  if,  indeed,  they  do 
urent  matter  between 
of  the  nebula  j  they 
stance  must  be  borne 
ing  which  illustrates 
!  II.  fig.  3,  is  from  a 
:actness.    A  similar, 
angement  than  that 
wo  semi-ovals  of  an 
separated  by  a  broad 
ila,  in  the  midst  of 
the  cut  appears,  is 
1.,  N.  P.  D.  132°  8' 

Listant  at  the  Cambridge 


<•,  63"  5',  and  12'  31»  11',  100°  40' 


(1830).    The  nebulse  in  12"  27-  3" 

present  analogous  features.  * 

(875.)  Annular  nebulae  also  exist,  but  are  among  the  rarest  objects  in 
the  heavens.  The  most  conspicuous  of  this  class  is  to  be  found  almost 
exactly  half  way  between  |3  and  y  Lyrse,  and  may  be  seen  with  a  telescope 
of  ro  derate  power.  It  is  small  and  particularly  well  defined,  so  as  to 
have  more  the  appearance  of  a  flat  oval  solid  ring  than  of  a  nebula.  The 
axes  of  the  ellipse  are  to  each  other  in  the  proportion  of  about  4  to  5,  and 
the  opening  occupies  about  half  or  rather  more  than  half  the  diameter. 
The  central  vacuity  is  not  quite  dark,  but  is  filled  in  with  faint  nebula, 
like  a  gauze  stretched  over  a  hoop.  The  powerful  telescopes  of  Lord 
Bosse  resolve  this  object  into  excessively  minute  stars,  and  show  filaments 
of  stars  adhering  to  its  edges. ' 

(87G.)  Planetary  nebulae  are  very  extraordinary  objficts.  They 
have,  as  their  name  imports,  a  near,  in  some  instances,  a  perttct  resem- 
blance to  planets,  presenting  discs  round,  or  slightly  oval,  in  some  quite 
sharply  terminated,  in  others  a  little  hazy  or  softened  at  the  borders. 
Their  light  is  in  some  perfectly  equable,  in  others  mottled  and  of  a  very 
peculiar  texture,  as  if  curdled.  They  are  comparatively  rare  objects,  not 
above  four  or  five  and  twenty  having  been  hitherto  observed,  and  of  these 
nearly  three-fourths  are  situated  in  the  southern  hemisphere.  Being  very 
interesting  objects,  we  subjoin  a  list  of  the  most  remarkable.'  Among 
these  may  be  more  particularly  specified  the  sixth  in  order,  situated  in  the 
Gross.  Its  light  is  about  equal  to  that  of  a  star  of  the  6-7  magnitude, 
its  diameter  about  12",  its  disc  circular  or  very  slightly  elliptic,  and  with 
a  clear,  sharp,  well-defined  outline,  having  exactly  the  appearance  of  a 
planet  with  the  exception  only  of  its  colour,  which  is  a  fine  and  full  blue 
verging  somewhat  upon  green.  And  it  is  not  a  little  remarkable  that  this 
phaenomenon  of  a  blue  colour,  whi(;h  is  so  rare  a^nong  stars  (except  when 
in  the  immediate  proximity  of  yellow  stars)  occurs,  though  less  strikingly, 
in  three  other  objects  of  this  class,  viz.  in  No.  4,  whose  colour  is  sky-blue, 

*  The  places  of  the  annular  nebulae,  at  present  known  (for  1830)  are, 


R.A. 

N.  P.  D. 

R.A. 

N.  P.  D. 

1. 

17h   lOm 

39* 

128°   18' 

3. 

18"  47" 

13' 

57°   11' 

2. 

17   19 

2 

113 

4. 

20    9 

33 

59   57 

'  Places  for  1330  of  twelve  of  the  most  remarkable  planetary  nebulae. 

R.A. 

N.  P.  n. 

R.  A. 

N.  P.  D. 

R.A. 

N.  P.  D. 

h.  m.  8. 

1.  7  34  2 

2.  9  16  39 

3.  9  59  52 

4.  10  16  36 

O    f 

104  20 
147  35 
129  36 
107  47 

h,  m.  8, 

5.  11  4  49 

6.  11  41  56 

7.  15  6  18 

8.  19  10  9 

0   / 

34  4 
146  14 
135  1 

83  46 

h.  m.  8. 
9.  19  34  21 

10.  19  40  19 

11.  20  54  53 

12.  23  17  44 

o  > 
104  33 

39  54 
102  2 

48  24 

^^! 


508 


OUTLINES   OF  ASTRONOMY. 


■«•« 


ih*—* 


•.♦iv; 


ri 


Snu0 


and  in  Nos.  11  and  12,  where  the  tint,  though  paler,  is  still  evident. 
Nos.  2,  7,  9,  and  12,  are  also  exceedingly  characteristic  objects  of  this 
class.  Nos.  3,  5,  and  11  (the  latter  in  the  parallel  of  p  Aquarii,  and 
about  S"  preceding  that  star),  are  considerably  elliptic,  and  (respectively) 
about  38",  30"  and  15"  in  diameter.  On  the  disc  of  No  3,  and  very 
nearly  in  the  centre  of  the  ellipse,  is  a  star  9",  and  the  texture  of  its  light, 
being  velvety,  or  as  if  formed  of  fine  dust,  clearly  indicates  its  resolvability 
into  stars.  The  largest  of  these  objects  is  No.  5,  situated  somewhat  south 
of  the  parallel  of  /3  Ursae  Majoris  and  about  12'"  following  that  star.  Its 
apparent  diameter  is  2'  40",  which,  supposing  it  placed  at  a  distance  from 
us  not  more  than  that  of  61  Oygni,  would  imply  a  linear  one  seven  times 
greater  than  that  of  the  orbit  of  Neptune.  The  light  of  this  stupendous 
globe  is  perfectly  equable  (except  just  at  the  edge  where  it  is  slightly 
softened),  and  of  considerable  brightness.  Such  an  appearance  would  not 
be  presented  by  a  globular  space  uniformly  filled  with  stars  or  luminous 
matter,  which  structure  would  necessarily  give  rise  to  an  apparent  increase 
of  brightness  towards  the  centre  in  proportion  to  the  thickness  traversed 
by  the  visual  ray.  We  might,  therefore,  be  induced  to  conclude  its  real 
constitution  to  be  either  that  of  a  hollow  spherical  shell  or  of  a  flat  disc, 
presented  to  us  (by  a  highly  improbable  coincidence)  in  a  plane  precisely 
perpendicular  to  the  visual  ray. 

(877.)  Whatever  idea  we  may  form  of  the  real  nature  of  such  a  body, 
or  of  the  planetary  nebulae  in  general,  which  all  agree  in  the  absence  of 
central  condensation,  it  is  evident  that  the  intriusic  splendour  of  their 
surfaces,  if  continuous,  must  be  almost  infinitely  less  than  that  of  the 
sun.  A  circular  portion  of  the  sun's  disc,  subtending  an  angle  of  1', 
would  give  a  light  equal  to  that  of  780  full  moons ;  while  among  all  the 
objects  in  question  there  is  not  one  which  can  be  seen  with  the  naked  eye. 
M.  Arago  has  surmised  that  they  may  possibly  be  envelopes  shining  by 
rejlected  light,  from  a  solar  body  placed  in  their  centre,  invisible  to  us  by 
the  effect  of  its  excessive  distance ;  removing,  or  attempting  to  remove 
the  apparent  paradox  of  such  an  explanation,  by  the  optical  principle  that 
an  illuminated  surface  is  equally  briffht  at  all  distances,  and,  therefore,  if 
large  enough  to  subtend  a  measurable  angle,  can  be  equally  well  seen, 
wiiereas  the  central  body,  subtending  no  such  angle,  has  its  effect  on  our 
u.ght  diminished  in  the  inverse  ratio  of  the  square  of  its  distance.'    The 


'  With  due  deference  to  so  high  an  authority  we  must  demur  to  the  conclusion. 
Even  supposing  the  envelope  to  reflect  and  scatter  (equally  in  all  directions)  all  the 
light  of  the  central  sun,  the  portion  of  the  light  so  scattered  which  would  fall  to  our 
share,  could  not  exceed  that  which  that  sun  itself  would  send  to  us  by  direct  radiation. 
But  this,  ex  hypotheii,  is  too  small  to  affect  the  eye  with  any  luminous  perception,  much 


DOUBLE  NEBULA. 


609 


,  is  Btill  evident, 
ic  objects  of  this 
of  V  Aquarii,  and 
and  (respectively) 
of  No  3,  and  very 
;exture  of  its  ligbt, 
tes  its  resolvability 
ed  somewhat  south 
ang  that  star.     Its 
1  at  a  distance  from 
;ar  one  seven  times 

of  this  stupendous 
where  it  is  slightly 
)pearance  vrould  not 
1  stars  or  luminous 
an  apparent  increase 

thickness  traversed 

to  conclude  its  real 

bell  or  of  a  flat  disc, 

)  in  a  plane  precisely 

ture  of  such  a  body, 

36  in  the  absence  of 

c  splendour  of  their 

jss  than  that  of  the 

ling  an  angle  of  1', 

while  among  all  the 

a  with  the  naked  eye. 

nvelopes  shining  by 

ire,  invisible  to  us  by 

fttempting  to  remove 

optical  principle  that 

jes,  and,  therefore,  if 

le  equally  vyell  seen, 

has  its  effect  on  our 

its  distance.'    The 

lemur  to  the  conclusion. 
[in  all  directiong)  all  the 
1  which  would  fall  to  our 
1  to  us  by  direct  radiation, 
ninoua  perception,  much 


assiduous  application  of  the  immense  optical  pov»ers  recently  brought  to 
bear  on  the  heavens,  will  probably  remove  some  portion  of  the  mystery 
which  at  present  hangs  about  these  enigmatical  objects. 

(878.)  Double  nebulce  occasionally  occur — and  when  such  is  the  case, 
the  constituents  most  commonly  belong  to  the  class  of  spherical  nebulae, 
and  are  in  some  instances  undoubtedly  globular  clusters.    All  the  varieties 
of  double  stars,  in  fact,  as  to  distance,  position,  and  relative  brightness, 
have  their  counterparts  in  double  nebulae;  besides  which  the  varieties  of 
form  and  gradation  of  light  in  the  latter  afford  room  for  combinations 
peculiar  to  this  class  of  objects.     Though  the  conclusive  evidence  of  ob- 
served relative  motion  be  yet  wanting,  and  though  from  the  vast  scale  on . 
which  such  systems  are  constructed,  and  the  probable  extreme  slowness 
of  the  angular  motion,  it  may  continue  for  ages  to  be  so,  yet  it  is  impos- 
sible, when  we  oast  our  eyes  upon  such  objects,  or  on  the  figures  which 
have  been  given  of  them,*  to  doubt  their  physical  connexion.     The  argu- 
ment drawn  from  the  comparative  rarity  of  the  objects  in  proportion  to 
the  whole  extent  of  the  heavens,  so  cogent  in  the  case  of  the  double  stars, 
is  infinitely  more  so  in  that  of  the  double  nebula).     Nothing  more  magni- 
ficent can  be  presented  to  our  consideration,  than  such  combinations. 
Their  stupendous  scale,  the  multitude  of  individuals  they  involve,  the 
perfect  symmetry  and  regularity  which  many  of  them  present,  the  utter 
disregard  of  complication  in  thus  heaping  together  system  upon  system, 
and  construction  upon  construction,  leave  us  lost  in  wonder  and  admira- 
tion at  the  evidence  they  afford  of  infinite  power  and  unfathomable 
design. 

(879.)  Nebulae  of  regular  forms  often  stand  in  marked  and  symmetri  al 
relation  to  stars,  both  single  and  double.  Thus  we  are  occasionally  pre- 
sented with  the  beautiful  and  striking  phaenomenon  of  a  sharp  and  bril- 
liant star  concentrically  surrounded  by  a  perfectly  circular  disc  or  atmo- 
sphere of  faint  light,  in  some  cases  dying  away  insensibly  on  all  sides,  in 
others  almost  suddenly  terminated.  These  are  Nebulous  Stars.  Fine 
examples  of  this  kind  are  the  45th  and  69th  nebulae  of  Sir  Wm.  Her- 
schel's  fourth  class*  (R.  A.  7"  19"  8%  N.  P.  D.  68°  45',  arid  3"  SS"  36% 

less  then  could  it  do  so  if  spread  over  a  surface  many  million  times  exceeding  in  angular 
area  the  apparent  disc  of  the  central  sun  itself.  (See  Annuaire  du  Bureau  des  Longi- 
tudes, 1842,  p.  409,  410,  411.)  M.  Arago  is  expresily  contending  for  reflected  light. 
If  the  envelope  be  self-luminous,  his  reasoning  is  perfectly  sound. 

•  Phil.  Trans.,  1833.    Plate  vii. 

'The  classes  here  referred  to  are  not  the  species  described  in  Art.  868,  but  lists  of 
nebulffi,  eight  in  number,  arranged  according  to  brightness,  size,  density  of  clustering, 
&c.,  in  one  or  other  of  which  all  nebulae  were  originally  classed  by  him.  Class  I. 
contains  "  Bright  nebula ;"  II.  "  Faint  do. ;"  III.  "  Very  faint  do. ;"  IV.  "  Planetary 


'4  i 


M 
^1  ! 


610 


OUTLINES   OF  ASTRONOMY. 


tl  "(a 


59°  40'),  in  which  stars  of  the  8th  magnitude  are  surrounded  by  photo- 
spheres of  the  kind  above  described  respectively  of  12"  and  25"  in  dia- 
meter. Among  stars  '^f  larger  magnitudes,  55  Andromedae  and  8  Canum 
Yenaticorum  may  be  named  as  exhibiting  the  same  phaenomenon  with 
more  brilliancy,  but  perh-ps  with  less  perfect  regularity. 

(880.)  The  connexion  of  nebulae  with  double  stars  is  in  many  instances 
extremely  remarkable.  Thus  in  R.  A.  18"  7-  1»,  N.  P.  D.  109°  56', 
occurs  an  elliptic  nebula  having  its  longer  axis  about  50",  in  which,  sym- 
metrically placed,  and  rather  nearer  the  vertices  than  the  foci  of  the  ellipse, 
are  the  equal  individuals  of  a  double  star,  each  of  the  10th  magnitude. 
In  a  similar  combination  noticed  by  M.  Strove  (in  R.  A.  18"  25",  N.  P.  D. 
25°  7'),  the  stars  are  unequal  and  situated  precisely  at  the  two  extremities 
of  the  major  axis.  In  R.  A.  13"  47-  33»,  N.  P.  D.  129°  9',  an  oval 
nebula  of  2'  in  diameter  has  very  near  its  centre  a  close  double  star,  the 
individuals  of  which,  slightly  unequal,  and  about  the  9*10  magnitude,  are 
not  more  than  2"  asunder.  The  nucleus  of  Messier's  64th  nebula  is 
«  strongly  suspected"  to  be  a  close  double  star — and  several  other  instances 
might  be  cited. 

(881.)  Among  the  nebulae  which,  though  deviating  more  from  sym* 
metry  of  form,  are  yet  not  wanting  in  a  certain  regularity  of  figure,  and 
which  seem  clearly  entitled  to  be  regarded  as  systems  of  a  definite  nature, 
however  mysterious  their  structure  and  destination,  by  far  the  most  re- 
markable are  the  27th  and  51st  of  Messier's  Catalogue.'  This  consists 
of  two  round  or  somewhat  oval  nebulous  masses  united  by  a  short  neck 
of  nearly  the  same  density.  Both  this  and  the  masses  graduate  off  how- 
ever into  a  fainter  nebulous  envelope  which  completes  the  figure  into  an 
elliptic  form,  of  which  the  interior  masses  with  their  connexion  occupy  the 
lesser  axis.  Seen  in  a  reflector  of  18  inches  in  aperture,  the  form  has 
considerable  regularity ;  and  though  a  few  stars  are  here  and  there  scat- 
tered over  it,  it  is  unresolved.  Lord  Rosse,  viewing  it  with  a  reflector  of 
double  that  aperture,  describes  and  figures  it  as  resolved  into  numerous 
stars  with  much  intermixed  nebula ;  while  the  symmetry  of  form  by  ren- 
dering visible  features  too  faint  to  be  seen  with  inferior  power,  is  rendered 
considerably  less  striking,  though  by  no  means  obliterated. 

(882.)  The  51st  nebula  of  Messier,  viewed  through  an  18-inch  re- 
flector, presents  the  appearance  of  a  large  and  bright  globular  nebula, 


nebulae,  stars  with  bars,  milky  chevelures,  short  rays,  remarkable  shapes,  &c. ;"  V. 
•'Very  large  nebulae;"  VI.  "  Very  compressed  rich  clusters;"  VII.  "Pretty  much 
compressed  do. ;"  VIII.  "  Coarsely  scattered  clusters." 

'  Place  for  1830 :  R.  A.  19*  52»  12',  N.  P.  D.  67"  44',  and  R.  A.  13"  22™  39',  N.  P. 
D.  41°56'. 


NEBULA  OF  PECULIAR  FORMS. 


611 


rounded  by  photo- 
2"  and  25"  in  dia- 
ledsB  and  8  Canum 
pheenomenon  with 

r- 

3  in  many  instances 
^.  P.  D.  109°  56', 
>0",  in  which,  sym- 
le  foci  of  the  ellipse, 
he  10th  magnitude. 
L18''25-,N.P.D. 
.  the  two  extremities 
).  129**  9',  an  oval 
lose  double  star,  the 
9*10  magnitude,  are 
ier's  64th  nebula  is 
veral  other  instances 

ing  more  from  sym- 
ularity  of  figure,  and 
}  of  a  definite  nature, 
by  far  the  most  re- 
)gue.'    This  consists 
lited  by  a  short  neck 
les  graduate  off  how- 
IS  the  figure  into  an 
lonnexion  occupy  the 
(erture,  the  form  has 
here  and  there  scat- 
it  with  a  reflector  of 
olved  into  numerous 
letry  of  form  by  ren- 
ir  power,  is  rendered 
grated. 

(Ugh  an  18-inch  re- 
;ht  globular  nebula, 

Ikable  shapes,  &c. ;"  V. 
i;"  VII.  "Pretty  much 

L.  A.  13*  22™  39',  N.  P. 


surrounded  by  a  ring  at  a  considerable  distance  from  the  globe,  very  une- 
qual in  brightness  in  its  different  parts,  s.nd  subdivided  through  about  two- 
fifths  of  its  circumference  as  if  into  two  laminae,  one  of  which  appears 
as  if  turned  up  towards  the  eye  out  of  the  plane  of  the  rest.  Near  it 
(at  about  a  radius  of  the  ring  distant)  is  a  small  bright  round  nebula. 
Viewed  through  the  6-feet  reflector  of  Lord  Rosse  the  aspect  is  much 
altered.  The  interior,  or  what  appeared  the  upturned  portion  of  the  ring, 
assumes  the  aspect  of  a  nebulous  coil  or  convolution  tending  in  a  spiral 
form  towards  the  centre,  and  a  general  tendency  to  a  spiroid  arrangement 
of  the  streaks  of  nebula  connecting  the  ring  and  central  mass  which  this 
power  brings  into  view,  becomes  apparent,  and  forms  a  very  striking, 
feature.  The  outlying  nebula  is  also  perceived  to  be  connected  by  a 
narrow,  curved  band  of  nebulous  light  with  the  ring,  and  the  whole,  if 
not  clearly  resolved  into  stars,  has  a  "  resolvable"  character  ^rhich  evi- 
dently indicates  its  composition.* 

(883.)  We  come  now  to  a  class  of  nebulae  of  totally  different  character. 
They  are  of  a  very  great  extent,  utterly  devoid  of  all  symmetry  of  form, 
—  on  the  contrary,  irregular  and  capricious  in  their  shapes  and  convolu- 
tions to  a  most  extraordinary  degree,  and  no  less  so  in  the  distribution  of 
their  light.  No  two  of  them  can  be  said  to  present  any  similarity  of 
figure  or  aspect,  but  they  have  one  important  character  in  common. 
They  are  all  situated  in,  or  very  ne.'w,  the  borders  of  the  Milky  Way. 
The  uiost  remote  from  it  is  that  in  the  sword  handle  of  Orion,  which 
being  20°  from  the  galactic  circle,  and  15°  from  the  visible  border  of  the 
Via  Lactea,  might  seem  to  forui  an  exception,  though  not  a  striking  one. 
But  this  very  situation  may  be  adduced  as  a  corroboration  of  the  general 
view  which  this  principle  of  localization  suggests.  For  the  place  in  ques- 
tion is  situated  in  the  prolongation  of  that  faint  offset  of  the  Milky  Way 
which  we  traced  (Art.  787.)  from  a  and  t  Persei  towards  Aldebaran  and 
the  Hyades,  and  in  the  zone  of  Great  Stars  noticed  in  Art.  785.  as  an 
appendage  of,  and  probably  bearing  relation  to  that  stratum. 

(884.)  From  thb  it  would  appear  to  follow,  almost  as  a  matter  of 
course,  that  they  must  be  regarded  as  outlying,  very  distant,  and  as  it 
were  detached  fragments  of  the  great  stratum  of  the  Galaxy,  and  this 
view  of  the  subject  is  strengthened  when  we  find  on  mapping  down  their 
places  that  they  may  all  be  grouped  in  four  great  masses  or  nebulous 
regions,  —  that  of  Orion,  of  Argo,  of  Sagittarius,  and  of  Cygnus.  And 
thus,  inductively,  we  may  gather  some  information  respecting  the  struc- 

'  This  description  13  from  the  recollection  of  a  sketch  exhibited  by  his  Lordship  at 
ihe  British  Association.  Every  astronomer  must  long  for  the  publication  of  his  own 
account  of  the  wonders  disclosed  by  this  magnificent  instrument. 


I 


a 


512 


OUTLINES   OP  A8TR0N0MY. 


ture  and  form  of  tbe  Galaxy  itself,  which,  could  we  view  it  as  a  whole, 
from  a  distaDce  such  as  that  which  separates  us  from  these  objects,  would 
ver3'  probably  present  itself  under  an  aspect  quite  as  complicated  and 
irregular. 

(885.)  The  great  nebula  surrounding  the  stars  marked  9  1  in  the  sword 
handle  of  Orion  was  discovered  by  Huyghens  in  1656,  and  has  been  re- 
peatedly %gurcd  and  described  by  astronomers  since  that  time.  Its 
appearance  varies  greatly  (as  that  of  all  nebulous  objects  does)  with  the 
instrumental  power  applied,  so  that  it  is  diflScult  to  recognize  in  represent* 
ations  made  with  inferior  telescopes,  even  principal  features,  to  say 
nothing  of  subordinate  details.  Until  this  became  well  understood,  it 
was  supposed  to  have  changed  very  materially,  both  in  form  and  extent, 
during  the  interval  elapsed  since  its  first  discovery.  No  doubt,  however, 
now  remains  that  these  supposed  changes  have  originated  partly  from  the 
cause  above-mentioned,  partly  from  the  difficulty  of  correctly  drawing, 
and,  still  more,  engraving  such  objects,  and  partly  from  a  want  of  suffi- 
cient care  in  the  earlier  delineators  themselves  in  faithfully  copying  that 
which  they  really  did  see.  Our  figure  (Plate  IV.,  Jl(/.  1,)  is  reduced 
from  a  larger  one  made  under  very  favourable  circumstances,  from  draw- 
ings taken  with  an  18-inch  reflector  at  the  Cape  of  Good  Hope,  where  its 
meridian  altitude  greatly  exceeds  what  it  has  at  European  stations.  The 
area  occupied  by  this  figure  is  about  one  25th  part  of  a  square  degree, 
extending  in  R.  A.  (or  horizontally)  2»  of  time,  equivalent  almost  ex- 
actly to  30'  in  arc,  the  object  being  very  near  the  equator,  and  24'  verti- 
cally, or  in  polar  distance.  The  figure  shows  it  reversed  in  both  direc- 
tions, the  northern  side  being  lowermost,  and  the  preceding  towards  the 
left  hand.  In  form,  the  brightest  portion  offers  a  resemblance  to  the  head 
and  yawning  jaws  of  some  monstrous  animal,  with  a  sort  of  proboscis  run- 
ning out  from  the  snout.  Many  stars  are  scattered  over  it,  which  for  the 
most  part  appear  to  have  no  connexion  with  it,  and  the  remarkable  sex- 
tuple star  e  1  Orionis,  of  which  mention  has  already  been  made  (Art. 
887),  occupies  a  most  conspicuous  situation  close  to  the  brightest  portion, 
at  i<lmost  the  edge  of  the  opening  of  the  jaws.  It  is  remarkable,  how- 
ever, that  within  the  area  of  the  tr-ipezium  no  nebula  exists.  The  general 
aspect  of  the  less  luminous  and  cirrous  portion  is  simply  nebulous  and 
irresolvable,  but  the  brighter  portion  immediately  adjacent  to  the  trape- 
zmm,  forming  the  square  front  of  the  head,  is  shown  with  tbe  IS-inch 
reflector  broken  up  into  masses  (very  imperfectly  represented  in  the  figure), 
whose  mottled  and  curdling  light  evidently  indicates  by  a  sort  of  granular 
texture  its  consisting  of  stars,  and  when  examined  under  the  great  light 
of  Lord  Bosse's  reflector,  or  the  exquisite  defining  power  of  the  great 


T: 


i-1 


NEBULA  OF   ARGO. 


518 


gr  it  as  a  whole, 
le  objects,  would 
complicated  and 

1 9  1  in  the  sword 
and  has  been  re- 
that  time.    Its 
jts  does)  with  the 
mize  in  represent- 
features,  to  say 
ell  understood,  it 
I  form  and  extent, 
lo  doubt,  however, 
ed  partly  from  the 
correctly  drawing, 
om  a  want  of  suffi- 
ifuUy  copying  that 
fig.  i,)  is  reduced 
stances,  from  draw- 
)od  Hope,  where  its 
)ean  stations.     The 
of  a  square  degree, 
uivalent  almost  ex- 
lator,  and  24'  verti- 
'ersed  in  both  direc- 
seeding  towards  the 
'mblance  to  the  head 
ort  of  proboscis  run- 
rer  it,  which  for  the 
ihe  remarkable  sex- 
ly  been  made  (Art. 
he  brightest  portion, 
is  remarkable,  how- 
lexists.   The  general 
imply  nebulous  and 
djacent  to  the  trape- 
In  with  the  18-inch 
sentcd  in  the  figure), 
»y  a  sort  of  granular 
ider  the  great  light 
power  of  the  great 


achromatic  at  Cambridge,  U.  S.,  is  evidently  perceived  to  consist  of  clus- 
tering stars.  There  can  therefore  bo  little  doubt  as  to  the  whole  consist- 
ing of  3tars,  too  minute  to  be  d'^cv-rned  individually  even  with  these 
powerful  aids,  but  which  become  visible  as  points  of  light  when  closely 
adjacent  in  the  more  crowded  parts  in  the  mode  already  more  than  once 
suggested. 

C886.)  The  nebula  is  not  confined  to  the  limits  of  our  figure.  North* 
ward  of  $  about  S3',  and  nearly  on  the  same  meridian  are  two  stars 
marked  C  1  and  C  2  Orionis,  involved  in  a  bright  and  branching  nebula 
of  very  singular  form,  and  south  of  it  is  the  star  t  Orionis,  which  is  also 
involved  in  strong  nebula.  Careful  examination  with  powerful  telescopes 
has  traced  out  a  continuity  of  nebulous  light  between  the  great  nebula 
and  both  these  objects,  and  there  can  be  little  doubt  that  the  nebulous 
region  extends  northwards,  as  far  as  t  in  the  belt  of  Orion,  which  is  in- 
volved in  strong  nebulosity,  as  well  as  several  smaller  stars  in  the  immedi- 
ate neighbourhood.  Professor  Bond  has  given  a  beautiful  figure  of  the 
great  nebula  in  Trans.  American  Acad,  of  Arts  and  Sciences,  new  series, 
vol.  iii. 

(887.)  The  remarkable  variation  in  lustre  of  the  bright  star  ri  in  Argo, 
has  been  already  mentioned.  This  star  is  situated  in  the  most  condensed 
region  of  a  very  extensive  nebula  or  congeries  of  nebular  masses,  streaks 
and  branches,  a  portion  of  which  is  represented  in  fig.  2,  Plate  IV.  The 
whole  nebula  is  spread  over  an  area  of  fully  a  square  degree  in  extent, 
of  which  that  included  in  the  'figure  occupies  about  one-fourth,  that  is  to 
say,  28'  in  polar  distance,  and  32'  of  arc  in  R.  A.,  the  portion  not  in- 
cluded being,  though  lainter,  even  more  capriciously  contorted  than  that 
here  depicted,  in  which  it  should  be  observed  that  the  preceding  side  is 
towards  the  right  hand,  and  the  southern  uppermost.  Viewed  with  an 
18-inch  reflector,  no  part  of  this  strange  object  shows  any  sign  of  resolu- 
tion into  stars,  nor  in  the  brightest  and  most  condensed  portion  adjacent 
to  the  singular  oval  vacancy  in  the  middle  of  the  figure  is  there  any  of 
that  curdled  appearance,  or  that  tenden;;y  to  bi'eak  up  into  bright  knots 
with  intervening  darker  portions  which  characterize  the  nebula  of  Orion, 
and  indicate  its  resolvability.  The  whole  i)3  situated  in  a  very  rich  and 
brilliant  part  of  the  Milky  Way,  so  thickly  strewed  with  stars  (omitted 
in  the  figure),  that  in  the  area  occupied  by  the  nebula,  not  less  than  1200 
have  been  actually  counted,  and  their  places  in  R.  A.  and  P.  D.  deter- 
mined. Yet  it  is  obvious  that  these  have  no  connexion  whatever  with 
the  nebula,  being,  in  fact,  only  a  simple  continuation  over  it  of  the  general 
ground  of  the  galaxy,  which  on  an  average  of  two  hours  in  Right  Ascen- 
I  sion  in  this  period  of  its  course,  contains  no  less  than  3138  stars  to  the 
33 


r 


614 


OUTLINES   OF  ASTRONOMY. 


sir: » 


square  degree,  all,  however,  diHtinct,  and  (except  where  the  object  in 
question  is  situated)  seen  projected  on  a  perfectly  dark  heaven,  without 
any  appearance  of  intermixed  nebulosity.  The  conclusion  can  hardly  bo 
avoided,  that  in  looking  at  it  we  see  through,  and  beyond  the  Milky  Way, 
far  out  into  space,  through  a  starless  region,  disconnecting  it  altogether 
from  our  system.  "  It  is  not  easy  for  language  to  convey  a  full  impres- 
sion of  the  beauty  and  sublimity  of  the  spectacle  which  this  nebula 
offers,  as  it  enters  the  field  of  view  of  a  telescope  fixed  in  Right  Ascen- 
sion, by  the  diurnal  motion,  ushered  in  as  it  is  by  so  glorious  and  innu- 
merable a  procession  of  stars,  to  which  it  forms  a  sort  of  climax,"  and  in 
a  part  of  the  heavens  otherwise  full  of  interest.  One  other  bright  and 
very  remarkably  formed  nebula  of  considerable  magnitude  precedes  it 
nearly  on  the  same  parallel,  but  without  any  traceable  connexion  between 
them. 

(888.)  The  nebulous  group  of  Sagittarius  consists  of  several  conspicuous 
nebulae'  of  very  extraordinary  forms,  by  no  means  easy  to  give  an  idea  of 
^y  mere  description.  One  of  them  (A,  1991')  is  singularly  trifid,  con- 
sisting of  three  bright  and  irregularly  formed  nebulous  masses,  graduating 
away  insensibly  externally,  but  coming  up  to  a  great  intensity  of  light  at 
their  interior  edges,  where  they  enclose  and  surround  a  sort  of  three-forked 
rift,  or  vacant  area,  abruptly  and  uncouthly  crooked,  and  quite  void  of 
nelulous  light.  A  beautiful  triple  star  is  situated  precisely  on  the  edge 
of  one  of  these  nebulous  masses  just  where  the  interior  vacancy  forks  out 
two  channels.  A  fourth  nebulous  mass  spreads  like  a  fan  or  downy  plume 
from  a  star  at  a  little  distance  from  the  triple  nebula. 

(889.)  Nearly  adjacent  to  the  last  described  nebula,  and  no  doubt  con- 
nected with  it,  though  the  connexion  has  not  yet  been  traced,  is  situated 
the  8th  nebula  of  Messier's  Catalogue.  It  is  a  collection  of  nebulous 
folds  and  masses,  surrounding  and  including  a  number  of  oval  dark  vacan- 
cies, and  in  one  place  coming  up  to  so  great  a  degree  of  brightness,  as  to 
ofiier  the  appearance  of  an  elongated  nucleus.  Superposed  upon  this 
nebula,  and  extending  in  one  direction  beyond  its  area,  is  a  fine  and  rich 
cluster  of  scattered  stars,  which  seem  to  have  no  connexion  with  it,  as  the 

•  About  R.A.  IT"  S'i",  N.P.D.  113°  1',  four  nebulm,  No.  41  of  Sir  Wm.  Herschel'i 
4th  class,  and  Nos.  1,  2,  3,  of  his  5th,  all  connected  into  one  great  complex  lebula.— 
In  R.A.  17"  53"  27',  N.P.D.  114°  21',  the  8th,  and  in  18"  11",  106°  15',  tho  17th  of 
Messier's  Cats' igue. 

*  This  numuer  refers  to  the  catalogue  of  nebulte  in  Phil.  Trans.,  1833.  The  reader 
will  find  figures  of  the  several  nebulae  of  this  group  in  that  volume,  pi.  iv.,  fig.  35,  in  the 
Author's  "  Results  of  Observations,  &c.,  at  the  Cape  of  Good  Hope,"  Plates  i.  fig.  1, 
and  ii.  figs.  1  and  2,  and  in  Mason's  Memoir  in  the  collection  of  the  American  Phil.  Soc, 
vol.  vii.  art.  xiii. 


»^)- 


THE  MAQELLANIO  CLOUDS. 


516 


ro  the  object  in 
:  heaven,  without 
ion  can  hardly  bo 
d  the  Milky  Way, 
sting  it  altogether 
ivcy  a  full  impres- 
which  this  nebula 
id  in  Right  Ascen- 
glorious  and  innu- 
of  climax,"  and  in 
e  other  bright  and 
gnitude  precedes  it 
,  connexion  between 

:  several  conspicuous 
jy  to  give  an  idea  of 
ingularly  trifid,  con- 
18  masses,  graduating 
intensity  of  light  at 
a  sort  of  three-forked 
1,  and  quite  void  of 
Precisely  on  the  edge 
ior  vacancy  forks  out 
tt  fan  or  downy  plume 

la,  and  no  doubt  con- 
aen  traced,  is  situated 
oUection  of  nebulous 
,er  of  oval  dark  vacan- 
se  of  brightness,  as  to 
luperposed  upon  this 
irea,  is  a  fine  and  rich 
.nexion  with  it,  as  the 

LlofSirWm.Herschel'T 
I  great  complex  lebula.- 
ir,  106*  15',  ih"  l''**  °' 

kans.,  1833.  The  reader 
|luine,pl.iv..fig.35,inthe 

|od  Hope,"  Plates  i.  fig-  h 
Ifthe  American  Phil.  Soc, 


nebula  does  no    as  in  the  region  of  Orion,  show  any  tendency  to  congre- 
gate about  the  stars. 

(890.)  The  19th  nebula  of  Messier's  Catalogue,  though  some  degree! 
remote  from  the  others,  evidently  belongs  to  this  group.  Its  form  is  very 
remarkable,  consisting  of  two  loops  like  capital  Greek  Omegas,  the  one 
bright,  the  other  exceedingly  faint,  connected  at  their  bases  by  a  broad 
and  very  bright  band  of  nebula,  insulated  within  which  by  a  narrow 
comparatively  obscure  border,  stands  a  bright,  resolvable  knot,  or  what  is 
probably  a  cluster  of  exceedingly  minute  stars.  A  very  faint  round  nebula 
stands  in  connexion  with  the  upper  or  convex  portion  of  the  brighter  loop. 

(891.)  The  nebulous  group  of  Cygnus  consists  of  several  large  and 
irregular  nebulae,  one  of  which  passes  through  the  double  star  k  Oygni, 
as  a  long,  crooked  narrow  streak,  forking  out  in  two  or  three  places.  The 
others,'  observed  in  the  first  instance  by  Sir  W.  Herschcl  and  by  the 
author  of  this  work  as  separate  nebulae,  have  been  traced  into  connexion 
by  Mr.  Mason,  and  shown  to  form  part  of  a  curiouA  and  intricate  nebuloos 
system,  consisting,  1st,  of  a  long,  narrow,  curved,  and  forked  streak,  and 
2dly,  of  a  cellular  effusion  of  great  extent,  in  which  the  nebula  occurs 
intermi/ed  with,  and  adhering  to  stars  around  the  borders  of  the  cellS| 
while  their  interior  is  free  from  nebula,  and  almost  so  from  stars. 

(892.)  The  Magellanic  clouds,  or  the  nubeculae  (major  and  minor,)  as 
they  are  called  in  the  celestial  maps  and  charts,  are,  as  their  name  imports, 
two  nebulous  or  cloudy  masses  of  light,  conspicuously  visible  to  the  naked 
eye,  in  the  southern  hemisphere,  in  the  appearance  and  brightness  of  their 
light  not  unlike  portions  of  the  Milky  Way  of  the  same  apparent  size. 
They  are,  generally  speaking,  round,  or  somewhat  oval,  and  the  larger,  which 
deviates  most  from  the  circular  form,  exhibits  the  appearance  of  an  axis 
of  light,  very  ill  defined,  and  by  no  means  strongly  distinguished  from  the 
general  mass,  which  seems  to  open  out  at  its  extremities  into  somewhat  oval 
sweeps,  constituting  the  preceding  and  following  portions  of  its  circumference. 
A  small  patch,  visibly  brighter  than  the  general  light  around,  in  its  follow- 
ing part,  indicates  to  the  naked  eye  the  situation  of  a  very  remarkable 
nebula  (No.  30  Doradus  of  Bode's  catalogue,)  of  which  more  hereafter. 
The  greater  nubecula  is  situated  between  the  meridians  of  4'>  40"  and  6" 
0"  and  the  parallels  of  156°  and  162°  of  N.P.D.,  and  occupies  an  area 
of  about  42  square  degrees.  The  lesser,  between  the  meridians'  O^*  28" 
and  1"  IS"  and  the  parallels  of  162°  and  165°  N.P.D.  covers  about  ten 
square  degrees.  Their  degree  of  brightness  may  be  judged  of  from  the 
effect  of  strong  moonlight,  which  totally  obliterates  the  lesser,  but  not 
quite  the  greater. 

'  R.A.20^49»20',  N.P.D.  58«'27'. 

*  It  is  laid  down  nenrly  an  hour  wrong  in  all  the  celestial  charts  and  globes. 


P;i 


.1  ' 


516 


OUTLINES   OP  ASTRONOMY. 


ST:  y 


IBS''"* 


CD 

CD 


(898.)  When  oxaniined  through  powerful  telescopes,  the  constitution 
of  the  nubecula),  and  cspcciully  of  the  nubecula  major,  is  found  to  be  of 
astonishing  complexity.  The  general  ground  of  both  consists  of  largo 
tracts  and  patches  of  nebulosity  in  every  stage  of  resolution,  from  light, 
irresolvable  with  18  inches  of  reflecting  aperture,  up  to  perfectly  separated 
stars  like  the  Milky  Way,  and  clustering  groups  sufficiently  insulated  and 
condensed  to  come  under  the  designation  of  irregular,  and  in  some  cases 
pretty  rich  clusters.  But  besides  those,  there  are  also  nebulae  in  abun- 
dance, both  regular  and  irregular;  globular  clusters  in  every  state  of 
condensation;  and  objects  of  a  nebulous  character  quite  peculiar,  and 
which  have  no  analogue  in  any  other  region  of  the  heavens.  Such  is  the 
concentration  of  these  objects,  that  in  the  area  occupied  by  the  nubecula 
major,  not  fewer  than  278  nebuloo  and  clusters  have  been  enumerated, 
besides  50  or  60  outliers,  which  (considering  the  general  barrenness  in 
such  objects  of  the  immediate  neighbourhood)  ought  certainly  to  be 
reckoned  as  its  appendages,  being  about  6}  per  square  degree,  which  very 
far  exceeds  the  average  of  any  other,  even  the  most  crowded  parts  of  the 
nebulous  heavens.  In  the  nubecula  minor,  the  concentration  of  such 
objects  is  less,  though  still  very  striking,  37  having  been  observed  within 
its  area,  and  6  adjacent,  but  outlying.  The  nubccultc,  then,  combine, 
each  within  its  own  area,  characters  which  in  the  rest  of  the  heavens  are 
no  less  strikingly  separated, — viz.,  those  of  the  galactic  and  the  nebular 
system.  Globular  clusters  (except  in  one  region  of  small  extent)  and 
nebulao  of  regular  elliptic  forms  are  comparatively  rare  in  the  Milky  Way, 
and  are  found  congregated  in  the  greatest  abundance  in  a  part  of  the 
heavens,  the  most  remote  possible  from  that  circle ;  whereas,  in  the  nube- 
culae,  they  are  indiscriminately  mixed  with  the  general  starry  ground,  and 
with  irregular  though  small  nebulae. 

(894.)  This  combination  of  characters,  rightly  considered,  is  in  a  high 
degree  instrnctive,  affording  an  insight  into  the  probable  comparative  dis- 
tance of  stars  and  nehulse,  and  the  real  brightness  of  individual  stars  as 
compared  one  with  another.  Taking  the  apparent  scmidiameter  of  the 
nubecula  major  at  3®,  and  regarding  its  solid  form  as,  roughly  speaking, 
spherical,  its  nearest  and  most  remote  parts  differ  in  their  distance  from 
us  by  a  little  more  than  a  tenth  part  of  our  distance  from  its  centre.  Thi 
brightness  of  objects  situated  in  its  nearer  portions,  therefore,  cannot  be 
much  exaggerated,  nor  that  of  ita  remoter  much  enfeebled,  by  their  differ- 
ence of  distance ;  yet  within  this  globular  space,  we  have  collected  upwards 
of  600  stars  of  the  7th,  8th,  9th,  and  10th  magnitudes,  nearly  800 
nebulae,  and  globular  and  other  clusters,  of  all  degrees  of  resoluhility,  and 
smaller  scattered  stars  innumerable  of  every  inferior  magnitude,  from  the 


»r\'\ 


THE   MAGELLANIC   CLOUDS. 


617 


,  the  constitution 
ia  found  to  bo  of 
consists  of  largo 
ution,  from  light, 
)crfcctly  separated 
otly  insulated  and 
nd  in  some  cases 
nebulsB  in  abun- 
in  every  state  of 
uite  peculiar,  and 
yens.     Such  is  the 
i  by  the  nubecula 
been  enumerated, 
icral  barrenness  in 
ht  certainly  to  be 
degree,  which  very 
rowded  parts  of  the 
ncentration  of  such 
een  observed  within 
alas,  then,  combine, 
of  the  heavens  are 
;ic  and  the  nebular 
small  extent)  and 
in  tho  Milky  Way, 
CO  in  a  part  of  the 
rhereas,  in  the  nube- 
1  starry  ground,  and 

isidered,  is  in  a  high 
able  comparative  dis- 
f  individual  stars  as 
semidiameter  of  the 
I,  roughly  speaking, 
their  distance  from 
Tom  its  centre.    Th^ 
therefore,  cannot  be 
>bled,  by  their  differ- 
;ve  collected  upwards 
rnitudes,  nearly  300 
's  ofresolubiUty,  and 
magnitude,  from  the 


10th  to  such  as  by  their  multitude  and  minuteness  constitute  irresolvable 
nebulosity,  extending  over  trnctH  of  many  square  degrees.  Were  there 
but  one  such  object,  it  might  be  muintaincd  without  utter  improbability 
that  its  apparent  sphericity  is  only  an  effect  of  foreshortening,  and  that  in 
reality  a  much  greater  proportional  difference  of  distance  between  its 
nearer  and  more  remote  parts  exists.  }{ut  such  an  adjustment,  improba* 
ble  enough  in  one  case,  must  bo  rejected  as  too  much  so  for  fair  argument 
in  two.  It  must,  therefore,  be  taken  as  a  demonstrated  fact,  that  stars  of 
tho  7th  or  8th  magnitude  and  irresolvable  nebula  may  co-exist  within 
limits  of  distance  not  differing  in  proportion  more  than  as  9  to  10,  a  con- 
elusion  which  must  inspire  some  degree  of  caution  iu  admitting,  as  certain^ 
many  of  the  consequences  which  have  been  rather  strongly  dwelt  upon  in 
the  foregoing  pages. 

(895.)  Immediately  preceding  the  centre  of  the  nubecula  minor,  and 
undoubtedly  belonging  to  the  same  group,  occurs  the  superb  globular 
cluster.  No.  47,  Toucani  of  Bode,  very  visible  to  the  naked  eye,  and  one 
of  the  finest  objects  of  this  kind  in  the  heavens.  It  consists  of  a  very 
condensed,  spherical  mass  of  stars,  of  a  pale  rose-colour,  concentrically 
enclosed  in  a  much  less  condensed  globe  of  white  ones,  15'  or  20'  in 
diameter.  This  is  the  first  in  order  of  the  list  of  such  clusters  in 
Art.  867. 

(896.)  Within  the  nubecula  major,  as  already  mentioned,  and  faintly 
visible  to  the  naked  eye,  is  the  singular  nebula  (marked  as  the  star  30 
Dorad(!ks  in  Bode's  Cataloguo)  Uotietd  by  Lacaille  as  resembling  the  nu- 
cleus of  a  small  comet.  It  occupies  about  one-500th  part  of  the  whole 
area  of  the  nubecula,  ami  is  ho  satisfactorily  represented  in  plate  Y.,  fig.  1, 
as  to  render  further  description  superfluous. 

(897.)  We  shall  concludo  this  chapter  by  the  mention  of  two  phseno- 
mena,  which  seem  to  indicate  the  existence  of  some  slight  degree  of  nebu- 
losity about  the  sun  itself,  and  even  to  place  it  in  the  list  of  nebulous 
stars.  The  first  is  that  called  the  zodiacal  light,  which  may  be  seen  any 
very  clear  evening,  soon  after  sunset,  about  the  months  of  March,  April, 
and  May,  or  at  the  opposite;  seasons  before  sunrise,  as  a  cone  or  lenticu- 
larly-shaped  light,  extending  from  tho  horizon  obliquely  upwards,  and 
following  generally  the  course  of  the  ecliptic,  or  rather  that  of  the  sun's 
equator.  The  apparent  angular  distance  of  its  vertex  from  the  sun  varies, 
according  to  circumstances,  from  40°  to  90°,  and  the  breadth  of  its  base 
perpendicular  to  its  axis  from  8°  to  30°.  It  is  extremely  faint  and  ill 
defined,  at  least  in  this  climate,  though  better  seen  in  tropical  regions,  but 
cannot  be  mistaken  for  any  atmospheric  meteor  or  aurora  borealis.  It  is 
manifestly  in  the  nature  of  a  lenticularly-formed  envelope,  surrounding 


518 


OUTLINES  OF  ASTRONOMT. 


\mmu 

2^: 


Plh'.IIr-' 

CD 


the  sun,  and  extending  beyond  the  orbits  of  Mercury  and  Venus,  and 
nearly,  perhaps  quite,  attaining  that  of  the  earth,  since  its  vertex  has  been 
seen  fully  90**  from  the  sun's  place  in  a  great  circle.  It  may  be  conjee- 
tured  to  be  no  other  than  the  denser  part  of  that  medium,  which,  we 
have  some  reason  to  bolieve,  resists  the  motion  of  comets;  loaded,  per- 
haps, with  the  actual  materials  of  the  tails  of  millions  of  those  bodies,  of 
which  they  have  been  stripped  in  their  succespive  perihelion  passages 
(Art.  566).  An  atmosphere  of  the  sun,  in  any  proper  sense  of  the  word, 
it  cannot  be,  since  the  existence  of  a  gaseous  envelope  propagating  pres- 
sure from  part  to  part;  subject  to  mutual  friction  in  its  strata,  and  there- 
fore rotating  in  the  same  or  nearly  the  same  time  with  the  central  body, 
and  of  such  dimensions  and  ellipticity,  is  utterly  incompatible  with  dyna- 
mical laws.  If  its  particles  have  inertia,  they  must  necessarily  stand  with 
respect  to  the  sun  in  the  relation  of  separate  and  independent  minute 
planets,  each  having  its  own  orbit,  plane  of  motion,  and  periodic  time. 
The  total  mass  being  almost  nothing  compared  to  that  of  the  sun,  mutual 
perturbation  is  out  of  the  question,  though  collisions  among  such  as  may 
cross  each  other's  paths  may  operate  in  the  course  of  indefinite  ages  to 
effect  a  subsidence  of  at  least  some  portion  of  it  into  the  body  of  the  sun 
or  those  of  the  planets.  .;  ,    ? 

(898.)  Nothing  prevents  that  these  particles,  or  some  among  them, 
may  have  some  tangible  size,  and  be  at  very  great  distances  from  each 
other.  Compared  with  planets  visible  in  our  most  powerful  telescopes, 
rocks  and  stony  masses  of  great  size  and  weight  would  be  but  as  the  im- 
palpable dust  which  a  sunbeam  renders  visible  as  a  sheet  of  light,  when 
streaming  through  a  narrow  chink  into  a  dark  chamber.  It  is  a  fact, 
established  by  the  most  indisputable  evidence,  that  stony  masses  and 
lumps  of  iron  do  occasionally,  and  indeed  by  no  means  unfrcquently,  fall 
upon  the  earth  from  the  higher  regions  of  our  atmosphere  (where  it  is 
obviously  impossible  they  can  have  been  generated),  and  that  they  have 
done  so  from  the  earliest  times  of  history.  Four  instances  are  recorded 
of  persons  being  killed  by  their  fall.  A  block  of  stone  fell  at  Mga 
Potamos,  B.  0. 465,  as  large  as  two  mill-stones;  another  at  Nami,  in  921, 
projected,  like  a  rock,  four  feet  above  the  surface  of  the  river,  into  which 
it  was  seen  to  fall.  The  emperor  Jehangire  had  a  sword  forged  from  a 
mass  of  meteoric  iron  which  fell,  in  1620,  at  Jahlinder,  in  the  Punjab.' 
Sixteen  instances  of  the  fall  of  stones  in  the  British  Isles  are  well  authen- 
ticated to  have  occurred  since  1620,  one  of  them  in  London.  In  1803, 
on  the  26th  of  April,  thousands  of  stones  were  scattered  by  the  explosion 

>  See  the  emperor's  own  very  remarkable  account  of  the  occurrence,  translated  in 
Phil.  Trans.  1793,  p.  202. 


UETEOROLITES  AND   SHOOTING  STARS. 


619 


J  and  Venus,  and 
ts  vertex  has  been 
lb  may  be  conjeo- 
aedium,  vhicb,  we 
metsj  loaded,  per- 
of  those  bodies,  of 
perihelion  passages 
sense  of  the  word, 
9  propagating  pres- 
bs  strata,  and  there- 
1  the  central  body, 
mpatible  with  dynsr 
Bcessarily  stand  with 
independent  minute 
,  and  periodic  time. 
A  of  the  sun,  mutual 
t  among  such  as  may 
of  indefinite  ages  to 
the  body  of  the  sun 

•  some  among  them, 
distances  from  each 
powerful  telescopes, 
uld  be  but  as  the  im- 
sheet  of  light,  when 
lamber.    It  is  a  fact, 
at  stony  masses  and 
ans  unfrcquently,  fall 
mosphere  (where  it  is 
),  and  that  they  have 
Qstances  are  recorded 
f  stone  fell  at  ^gos 
t,her  at  Nami,  in  921, 

the  river,  into  which 

a  sword  forged  from  a 

|nder,  in  the  Punjab.' 

Isles  are  well  authen- 

In  London.     In  1803, 

tered  by  the  explosion 

occunence,  iraMlatodin 


into  fragments  of  a  large  fiery  globe  over  a  region  of  twenty  or  thirty 
square  miles  around  the  town  of  L'Aigle,  in  Normandy.  The  fact  occurred 
at  mid-day,  and  the  circumstances  were  officially  verified  by  a  commission 
of  the  French  government.'  These,  and  innumerable  other  instances,' 
fally  establish  the  general  fact ;  and  after  vain  attempts  to  account  for  it 
by  volcanic  projection,  either  from  the  earth  or  the  moon,  the  planetary 
nature  of  these  bodies  seems  at  length  to  be  almost  generally  admitted. 
The  heat  which  they  possess  when  fallen,  the  igneous  phsenomena  which 
accompany  them,  their  explosion  on  arriving  within  the  denser  regions  of 
our  atmosphere,  &c.,  are  all  sufficiently  accounted  for  on  physical  princi- 
ples, by  the  condensation  of  the  air  before  them  in  consequence  of  their 
enormous  velocity,  and  by  the  relations  of  air  in  a  highly  attenuated  statie 
to  heat.* 

(899.)  Besides  stony  and  metallic  masses,  however,  it  is  probable  that 
bodies  of  very  different  natures,  or  at  least  states  of  aggregation,  are  thus 
circulating  round  the  sun.  Shooting  stars,  often  followed  by  long  trains 
of  light,  and  those  great  fiery  globes,  of  more  rare,  but  not  very  uncommon 
occurrence,  which  are  seen  traversing  the  upper  regions  of  our  atmosphere, 
sometimes  leaving  trains  behind  them,  remaining  for  many  minutes,  some- 
times bursting  with  a  loud  explosion,  sometimes  becoming  quietly  extinct, 
may  not  unreasonably  be  presumed  to  be  bodies  extraneous  to  our  planet, 
which  only  become  visible  when  in  the  act  of  grazing  the  confines  of  our 
atmosphere.  Among  the  last  mentioned  meteors  are  some  which  can 
hardly  be  supposed  solid  masses.  The  remarkable  meteor  of  Aug.  18, 
1783,  traversed  the  whole  of  Europe,  from  Shetland  to  Rome,  with  a 
velocity  of  about  30  miles  per  second,  at  a  height  of  50  miles  from  the 
surface  of  the  earth,  with  a  light  greatly  surpassing  that  of  the  full  moon, 
and  a  real  diameter  of  fully  half  a  mile.  Yet  with  these  vast  dimensions, 
it  changed  its  form  visibly,  and  at  length  quietly  separated  into  several 
distinct  bodies,  accompanying  each  other  in  parallel  courses,  and  each  fol- 
lowed by  a  tail  or  train. 

(900.)  There  are  circumstances  in  the  history  of  shooting  stars,  which 
very  strongly  corroborate  the  idea  of  their  extraneous  or  cosmical  origin, 
and  their  circulation  round  the  sun  in  definite  orbits.  On  several  occa- 
sions they  have  been  observed  to  appear  in  unusual,  and,  indeed,  astonish 

'  See  M.  Biot's  report  in  M6m.  de  rinstitut.  1806. 

*  See  a  list  of  upwards  of  200,  publinhed  by  Chladni,  Annales  du  Bureau  des  Lon 
gituden  de  France,  1825. 

'  Edinburgh  Review,  Jan.  1848,  p.  195.  It  is  very  remarkable  that  no  new  chemical 
element  has  been  detected  in  any  of  the  numerous  meteorolites  which  have  been  sub- 
jected to  analysis. 


'  1 


!  1 


Vi 


1 


620 


OUTLINES   OF  ASTRONOMY. 


'fmi 


^-s*' 
M.^1 


CD 


^ 
^ 


So 


ing  numbers,  so  as  to  convey  the  idea  of  a  shower  of  rockets,  or  of  snow- 
flakes  falling,  and  brilliantly  illuminating  the  whole  heavens  for  hours 
together,  and  that  not  in  one  locality,  but  over  whole  continents  and 
oceans,  and  even  (in  one  instance)  in  both  hemispheres.  Now  it  is  ex- 
tremely remarkable  that,  whenever  this  great  display  has  been  exhibited 
(at  least  in  modem  times),  it  has  uniformly  happened  on  the  night  be- 
tween the  12th  and  13th,  or  on  that  between  the  13th  and  14th  of  No- 
vember. Such  cases  occurred  in  1799,  1823,  1832,  1833,  and  1834. 
On  tracing  back  the  records  of  similar  phaenomena,  it  has  been  ascertained, 
moreover,  that  more  often  those  identical  nights,  but  sometimes  those 
immediately  adjacent,  have  been,  time  out  of  mind,  habitually  signalized 
by  such  exhibitions.  Another  annually  recurring  epoch,  in  which,  though 
far  less  brilliant,  the  display  of  meteors  is  more  certain  (for  that  of  No- 
vember is  often  interrupted  for  a  great  many  years),  is  that  of  the  10th 
of  August,  on  which  night,  and  on  the  9th  and  11th,  numerous,  large, 
and  bright  shooting  stars,  with  trains,  are  almost  sure  to  be  seen.  Other 
epochs  of  periodic  recurrence,  less  marked  than  the  above,  have  also  been 
to  a  certain  extent  established. 

(901.)  It  is  impossible  to  attribute  such  a  recurrence  of  identical  dates 
of  very  remarkable  phaenomena  to  accident.  Annual  periodicity,  irre- 
spective of  geographical  position,  refers  us  at  once  to  the  place  ocupied  by 
the  earth  in  its  annual  orbit,  and  leads  direct  to  the  conclusion  that  at  that 
place  the  earth  incurs  a  liability  to  freguent  encounters  or  concurrences 
with  a  stream  of  meteors  in  their  progress  of  circulation  round  the  sun. 
Let  us  test  this  idea  by  pursuing  it  into  some  of  its  consequences.  In 
the  first  places  then,  supposing  the  earth  to  plunge,  in  its  yearly  circuit, 
into  a  uniform  ring  of  innumerable  small  meteor-planets,  of  such  breadth 
as  would  be  traversed  by  it  in  one  or  two  days ;  since  during  this  small 
time  the  motions,  whether  of  the  earth  or  of  each  individual  meteor,  may 
be  taken  as  uniform  and  rectilinear,  and  those  of  all  the  latter  (at  the 
place  and  time)  parallel,  or  very  nearly  so,  it  will  follow  that  the  relative 
motion  of  the  meteors  referred  to  the  earth  as  at  rest,  will  be  also  uniform, 
rectilinear,  Kodi  parallel.  Viewed,  therefore,  from  the  centre  of  the  earth 
(or  from  any  point  in  its  circumference,  if  we  neglect  the  diurnal  velocity 
as  very  small  compared  with  the  annual)  they  will  all  appear  to  diverge 
from  a  common  point,  fixed  in  relation  to  the  celestial  sphere,  as  if  ema- 
nating from  a  sidereal  apex  (Art.  115).  t>  .  '     -. 

(902.)  Now  this  is  precisely  what  actually  happens.  The  meteors  of 
the  12th — 14th  of  November,  or  at  least  the  vast  majority  of  them,  de- 
scribe apparently  arcs  of  great  circles,  passing  through  or  near  y  Lconis. 
No  matter  what  the  situation  of  that  star  with  respect  to  the  horizon  or 


"vr 


PERIODICAL  APPEARANCE  OF   METEORS. 


621 


ts,  or  of  suow- 
vens  for  hours 
continents  and 

Now  it  is  ex- 
been  exhibited 
I  the  night  be- 
nd 14th  of  No- 
833,  and  1834. 
>een  ascertained, 
sometimes  those 
tually  signalized 
n  which,  though 

(for  that  of  No- 
that  of  the  10th 
numerous,  large, 

be  seen.  Other 
e,  have  also  been 

of  identical  dates 
,  periodicity,  irre- 
5  place  ocupied  by 
lusion  that  at  that 
s  or  concurrences 
>n  round  the  sun. 
jonsequences.    In 
its  yearly  circuit, 
J,  of  such  breadth 
during  this  small 
idual  meteor,  may 
the  latter  (at  the 
that  the  relative 
II  be  also  uniform, 
lentre  of  the  earth 
le  diurnal  velocity 
appear  to  diverge 
\  sphere,  as  if  ema- 

The  meteors  of 
fcority  of  them,  de- 

or  near  y  Leonis. 
It  to  the  horizon  or 


to  its  east  and  west  points  may  be  at  the  time  of  observation,  the  paths 
of  the  meteors  all  appear  to  diverge  from  that  star.  On  the  9th — 11th 
of  August  the  geometrical  fact  is  the  same,  the  apex  only  differing;  B 
Ouiaelopardali  being  for  that  epoch  the  point  of  divergence.  As  we  need 
not  suppose  the  meteoric  ring  coincident  in  its  plane  with  the  ecliptic; 
and  as  for  a  ring  of  meteors  we  may  substitute  an  elliptic  annulus  of  any 
reasonable  excentricity,  so  that  both  the  velocity  and  direction  of  each 
meteor  may  differ  to  any  extent  from  the  earth's,  there  is  nothing  in  the 
great  and  obvious  difference  in  latitude  of  these  apices  at  all  militating 
against  the  conclusion. 

(903.)  If  the  meteors  be  uniformly  distributed  in  such  a  ring  or  ellip- 
tic annulus,  the  earth's  encounter  with  them  in  every  revolution  will  be 
certain,  if  it  occur  once.  But  if  the  ring  be  broken,  if  it  be  a  succession 
of  groups  revolving  in  an  ellipse  in  a  period  not  identical  with  that  of  the 
earth,  years  may  pass  without  a  rencontre ;  and  when  such  happen,  they 
may  differ  to  any  extent  in  their  intensity  of  character,  according  as  richer 
or  poorer  groups  have  been  encountered. 

(904.)  ^^"^  ■'^ther  plausible  explanation  of  these  highly  characteristic 
features  i  .        mual  periodicity,  and  divergence  from  a  common  apex, 
ahcays  aUn-e  /or  eacJi  respective  epoch)  have  been  even  attempted,  and  ac- 
cordingly the  opinion  is  generally  gaining  ground  among  astronomers  that 
shooting  stars  belong  to  their  department  of  science,  and  great  interest  is 
excited  in  their  observation  and  the  further  development  of  their  laws. 
The  most  connected  and  systematic  series  of  observations  of  them,  having 
for  their  object  to  trace  out  their  relative  paths  with  respect  to  the  earth, 
are  those  of  Benzonberg  and  Brandos,  who,  by  noting  the  instants  and 
apparent  places  of  appearance  and  extinction,  as  well  as  the  precise  appa- 
rent paths  among  the  stars,  of  individual  meteors,  from  the  extremities 
of  a  measured  base  line  nearly  50,000  feet  in  length,  were  led  to  con- 
clude that  their  heights  at  the  instant  of  their  appearance  and  disappear- 
ance vary  from  16  miles  to  140,  and  their  relative  velocities  from  18  to 
36  miles  per  second,  velocities  so  great  as  clearly  to  indicate  an  indepen- 
dent planetary  circulation  round  the  sun.     [A  very  remarkable  meteor 
or  bolide,  which  appeared  on  the  19th  August,  1847,  was  observed  at 
Dieppe  and  at  Paris,  with  sufficient  precision  to  admit  of  calculation  of  the 
elements  of  its  orbit  in  absolute  space.    This  calculation  has  been  per- 
formed by  M.  Petit,  director  of  the  observatory  of  Toulouse,  and  the  fol- 
lowing hyperbolic  elements  of  its  orbit  round  the  sun  are  stated  by  him 
(Astr.  Nachr.  701)  as  its  result;  viz.,  Semimajor  axis  =  — 0-3240083; 
excentricity  =  8-95130;  perihelion  distance  =  0-95626;  inclination  to 
I  plane  of  the  earth's  equator,  18°  20'  18" ;  ascending  node  on  the  same 


I 


1 1],  i 


ij 


522 


OUTLINES  OV  ASTRONOMY. 


plane,  10°  34'  48" ;  motion  direct.  According  to  this  calculation,  the 
body  would  have  occupied  no  less  than  37340  years  in  travelling  from  tlie 
distance  of  the  nearest  fixed  star  supposed  to  have  a  parallax  of  1".] 

(905.)  It  is  by  no  means  inconceivable  that  the  earth  approaching  to 
such  as  r^iffer  but  little  from  it  in  direction  and  velocity,  may  have  at- 
tached aany  of  them  to  it  as  permanent  satellites,  and  of  these  there  mai/ 
be  some  so  large,  and  of  such  texture  and  solidity,  as  to  shine  by  reflected 
light,  and  become  visible  (sach,  at  least,  as  are  very  near  the  earth)  for  a 
brief  moment,  suffering  extinction  by  plunging  into  the  earth's  shadow ; 
in  other  words  undergoing  total  eclipse.  Sir  John  Lubboclc  is  of  opinion 
that  such  is  the  case,  and  ^as  given  geometrical  formulaa  for  calculating 
their  distances  from  observations  of  this  nature.*  The  observations  of  M. 
Petit  would  lead  us  to  believe  in  the  existence  of  at  least  one  such  body, 
revolving  round  the  earth,  as  a  satellite,  in  about  3  hours  20  minutes,  and 
therefore  at  a  distance  equal  to  2-513  radii  of  the  earth  from  its  centre, 
or  5000  miles  above  its  surface.'  ■   i     ^  «    ;     ,. 

'  Phil.  Mag.  Lond.  Ed.  Dub.  1848,  p.  80. 

*  Comptes  Rendus,  Oct.  12,  1846,  and  Aug.  9,  1847. 


.  .  i^  ■ .  I 


.'  y 


NATURAL  UNITS  OF  TIME. 


628 


i  calculation,  the 
•avelling  from  tLe 
allax  of  1".] 
th  approaching  to 
sity,  may  have  at- 
>f  these  there  way 
( shine  by  reflected 
at  the  earth)  for  a 
e  earth's  shadow; 
bboclt  is  of  opinion 
ul»  for  calcalating 
observations  of  M. 
east  one  such  body, 
urs  20  minutes,  and 
:th  fifom  its  centre, 


9, 1847. 


^.. 


PART  IV. 


OP    THE    ACCOUNT    OF    TIME. 


CHAPTER  XVm. 

NATURAL  UNITS  OP  TIME. — RELATION  OF  THE  SIDEREAL  TO  THE  SOLAR 
DAY  AFFECTED  BY  PRECESSION. — INCOMMENSURABILITY  OP  THE  DAY 
AND  YEAR. —  ITS  INCONVENIENCE. —  HOW  OBVIATED. — THE  JULIAN 
CALENDAR.  —  IRREGULARITIES  AT  ITS  FIRST  INTRODUCTION. — RE- 
FORMED BY  AUG08TU8. — GREGORIAN  REFORMATION.  —  SOLAR  AND 
LUNAR  CYCLES.  —  INDICTION. — JULIAN  PERIOD. — TABLE  OP  CHRO- 
NOLOGICAL ERAS.  —  RULES  FOR  CALCULATING  THE  DAYS  ELAPSED 
BETWEEN   GIVEN  DATES.  —  EQUINOCTIAL  TIME. 

(906.)  Time,  like  distance,  may  be  measured  by  comparison  with  stan- 
dards of  any  length,  and  all  that  is  requisite  for  ascertaining  correctly  the 
length  of  any  interval,  is  to  be  able  to  apply  the  standard  to  the  interval 
throughout  its  whole  extent,  without  overlapping,  on  the  one  hand,  or 
leaving  unmeasured  vacancies  on  the  other;  to  determine,  without  the 
possible  error  of  a  unit,  the  number  of  integer  standards  which  the  inter- 
val admits  of  being  interposed  between  its  be'nnning  and  end ;  and  to 
estimate  precisely  the  fraction,  over  and  above  an  integer,  which  remains 
when  all  the  p  jssible  integers  are  subtracted. 

(907.)  But  though  all  standard  units  of  time  are  equally  possible,  the- 
oretically speaking,  yet  all  are  not,  practically,  equally  convenient.  The 
solar  day  is  a  natural  internal  which  the  wants  and  occupations  of  man  in 
every  state  of  society  force  upon  him,  and  compel  him  to  adopt  as  his 
fundamental  unit  of  time.  Its  length  as  estimated  from  the  departure 
of  the  sun  from  a  given  meridian,  and  its  next  return  to  the  same,  is  sub- 
ject, it  is  true,  to  an  annual  fluctuation  in  excess  and  defect  of  its  mean 
value,  amounting  at  its  maximum  to  full  half  a  minute.  But  except  for 
astronomical  purposes,  this  is  too  small  a  change  to  interfere  in  the  slight- 
est degree  with  its  use,  or  to  attract  any  attention,  and  the  tacit  substitu* 


.ii;;!l 


a  ;' 


' 


!■! 


624 


OUTLINES  OF  ASTRONOMY. 


s: 


»M>1 


tioQ  of  its  mean  for  its  true  (or  variable)  value  may  be  considered  as 
having  been  made  from  the  earliest  ages,  by  the  ignorance  of  mankind 
that  any  such  fluctuation  existed. 

(908.)  The  time  occupied  by  one  complete  rotation  of  the  earth  on  its 
axis,  or  the  mean*  sidereal  day,  may  be  shown,  on  dynamical  principles,  to 
be  subjer!  ^o  no  variation  from  any  external  cause,  and  although  its  dura- 
tion wou  be  shortened  by  contraction  in  the  dimensions  of  the  globe 
itself,  i?uo  .  as  might  arise  from  the  gradual  escape  of  its  internal  heat, 
and  consequent  refrigeration  and  shrinking  of  the  whole  mass,  yet  theory, 
on  the  one  hand,  has  rendered  it  almost  certain  that  this  cause  cannot  have 
effected  any  perceptible  amount  of  change  during  the  history  of  the  human 
race ;  and,  on  the  other,  the  comparison  of  ancient  and  modern  observa- 
tions affords  every  corroboration  to  this  conclusion.  From  such  compari- 
sons, Laplace  has  concluded  that  the  sidereal  day  has  not  changed  by  so 
much  as  one  hundredth  of  a  second  since  the  time  of  Hipparchus.  The 
mean  sidereal  day  therefore  possesses  in  perfection  the  essential  quality  of 
a  standard  unit,  that  of  complete  invariabiliti/.  The  same  is  true  of  the 
mean  sidereal  year,  if  estimated  upon  an  average  sufficiently  large  to  com- 
pensate the  minute  fluctuations  arising  from  the  periodical  variations  of  the 
major  axis  of  the  earth's  orbit  due  to  planetary  perturbation  (Art.  668.) 

(909.)  The  mean  solar  day  is  an  immediate  derivative  of  the  sidereal 
day  and  year,  being  connected  with  them  by  the  same  relation  which  de- 
termines the  synodic  from  the  sidereal  revolutions  of  any  two  planets  or 
other  revolving  bodies  (Art.  418.)  The  excu:t  determination  of  ihe  ratio 
of  the  sidereal  to  the  solar  day,  which  is  a  point  of  the  utmost  importance 
in  astronomy,  is  however,  in  some  degree,  complicated  by  the  effect  of 
precession,  which  renders  it  necessary  to  distinguish  between  the  absolute 
time  of  the  earth's  rotation  on  its  axis,  (the  real  natural  and  invariable 
standard  of  comparison,)  and  the  mean  interval  between  two  successive 
returns  of  a  given  star  to  the  same  meridian,  or  rather  of  a  given 
meridian  to  the  same  star,  which  not  only  differs  by  a  minute  quantity 
from  the  sidereal  day,  but  is  actually  not  the  same  for  all  stars.  As 
this  is  a  point  to  which  a  little  difficulty  of  conception  is  apt  to  attach, 
it  will  be  necessary  to  explain  it  in  some  detail.  Suppose  then  n 
the  pole  of  the  ecliptic,  and  P  that  of  the  equinoctial,  A  B  C  D  the  sol- 
stitial and  equinoctial  oolures  at  any  given  epoch,  and  V pqr  the  small 
circle  described  by  P  about  h  in  one  revolution  of  the  equinoxes,  i.  e.  in 
25870  years,  or  9448300  solar  days,  all  projected  on  the  plane  of  the 

'  The  true  sidereal  day  is  variable  by  the  effect  of  nutation ;  but  the  variation  (an 
excessively  minute  fraction  of  tha  whole)  compensates  itself  in  a  revolution  of  the 
moon's  nodes. 


NATURAL   UNITS  OF  TIME. 


525 


je  considered  as 
ince  of  mankind 

f  the  earth  on  its 
lical  principles,  to 
lUhough  its  dura- 
ions  of  the  globe 
its  internal  heat, 
mass,  yet  theory, 
cause  cannot  have 
itory  of  the  human 
i  modern  observa- 
rom  such  compari- 
not  changed  by  so 
Hipparchus.     The 
essential  quality  of 
same  is  true  of  the 
iently  large  to  corn- 
eal variations  of  the 
■bation  (Art.  668.) 
ttive  of  the  sidereal 
relation  which  de- 
any  two  planets  or 
lination  of  i^e  ratio 
utmost  importance 
id  by  the  effect  of 
jtween  the  absolute 
[tural  and  invariable 
[ween  two  successive 
rather  of  a  given 
a  minute  quantity 
for  all  stars.    As 
ion  is  apt  to  attach, 
Suppose   then  n 
[,  A  B  C  D  the  sol- 
Ypq^r  the  small 
|e  equinoxes,  i.  c.  in 
in  the  plane  of  the 

f  j  but  the  variation  (an 
in  a  revolution  of  tho 


ecliptic  A  B  C  D.  Let  S  be  a  star  anywhere  situated  on  the  ecliptic,  or 
heticeen  it  and  the  small  circle  Vqr.  Then  if  the  pole  P  were  at  rest,  a 
meridian  of  the  earth  setting  out  from  P  S  and  revolving  in  the  direc- 
tion C  D,  will  come  again  to  the  star  after  the  exact  lapse  of  one  sidereal 
day,  or  one  rotation  of  the  earth  on  its  axis.  But  P  is  not  at  rest.  After 
the  lapse  of  one  such  day  it  will  have  come  into  the  situation  (suppose) 
p,  the  vernal  equinox  B  having  retreated  to  b,  and  tho  colure  P  0  having 
taken  up  the  new  position  p  c.  Now  a  conical  movement  impressed  on 
the  axis  of  rotation  of  a  globe  already  rotating  is  equivalent  to  a  rotation 
impressed  on  the  whole  globe  round  the  axis  of  the  cone,  in  addition  to 
that  which  the  globe  has  and  retains  round  its  own  independent  axis  of 
revolution.  Such  a  new  rotation,  in  transferring  P  to  p,  being  performed 
round  an  axis  passing  through  n,  will  not  alter  the  situation  of  that  point 
of  the  globe  which  has  it  in  its  zenith.  Hence  it  follows  that  pite  pass< 
ing  through  rt  will  be  the  position  taken  up  by  the  meridian  P  »t  C  after 
the  lapse  of  an  exact  sidereal  day.  But  this  does  not  pass  through  S,  but 
falls  short  of  it  by  the  hour-angle  »<pS,  which  is  yet  to  be  described 
before  the  meridian  comes  up  to  the  star.  The  meridian,  then,  has  lost 
so  much  on,  or  lagged  so  much  behind,  the  star  in  the  lapse  of  that  in- 
terval. The  same  is  true  whatever  be  the  arc  Pjp.  After  the  lapse  of 
any  number  of  days,  the  pole  being  transferred  to  p,  the  spherical  angle 
up  S  will  measure  the  total  hour-angle  which  the  meridian  has  lost  on  the 
star.  Now  where  S  lies  any  whore  between  C  and  r,  this  angle  con- 
tinually increases  (though  not  uniformly),  attaining  180°  when  p  comes 
to  r,  and  still  (as  will  appear  by  following  out  the  movement  beyond  r) 
increasing  thence  till  it  attains  360°  when  p  has  completed  its  circuit. 


\-m 


'   ■>! 


526 


OXTTLINES  OF  ASTRONOUT. 


»*■• 


Thus  in  a  whole  revolution  of  the  equinoxes,  the  meridian  will  have  lost 
one  exact  revolution  upon  the  star,  or  in  9448300  sidereal  days,  will  have 
re-attained  the  star  only  9448299  times :  in  other  words,  the  length  of  the 
day  measured  by  the  mean  of  the  successive  arrivals  of  any  star  outside 
of  the  circle  Fpqr  on  one  and  the  same  meridian  is  to  the  absolute  time 
of  rotation  of  the  earth  on  its  axis  as  9448300 :  9448299,  or  as  100000011 
tol. 

(910.)  It  is  otherwise  of  a  star  situated  within  this  circle,  as  at  cr.  For 
such  a  star  the  angle  ftp  a,  expressing  the  lagging  of  the  meridian,  in- 
creases to  a  maximum  for  some  situation  of  p  between  q  and  r,  and 
decreases  again  to  o  at  r ;  after  which  it  takes  an  opposite  direction,  and 
the  meridian  begins  to  get  in  advance  of  the  star,  and  continues  to  get 
more  and  more  so,  till  p  has  attained  some  point  between  a  and  P,  where 
the  advance  is  a  maximum,  and  thence  decreases  again  to  o  when  p  has 
completed  its  circuit.  For  any  star  so  situated,  then,  the  mean  of  all  the 
days  so  estimated  through  a  whole  period  of  the  equinoxes  is  an  absolute 
sidereal  day,  as  if  precession  had  no  existence. 

(911.)  If  we  compare  the  sun  with  a  star  situated  in  the  ecliptic,  the 
sidereal  year  is  the  mean  of  all  the  intervals  of  its  arrival  at  that  star 
throughout  indefinite  ages,  or  (without  fear  of  sensible  error)  throughout 
recorded  history.  Now,  if  we  would  calculate  the  synodic  sidereal  revo- 
lution of  the  sun  and  of  a  meridian  of  the  earth  by  reference  to  a  star  so 
situated,  according  to  the  principles  of  Art.  418,  we  must  proceed  as  fol- 
lows :  Let  D  be  the  length  of  the  mean  solar  day  (or  synodic  day  in 
question)  d  the  mean  sidereal  revolution  of  the  meridian  with  reference 
to  the  same  star,  and  y  the  sidereal  year.     Then  the  arcs  described  by  the 

sun  and  the  meridian  in  the  interval  D  will  be  respectively  360°  —  and 

360°  -^.    And  since  the  latter  of  these  exceeds  the  former  by  precisely 
a 

360°,  wehave  ,;v:.;^v>:..v ..  ;^^;--  -■  lA.-^-.  _-■,■.:,,,',_■_,.  .    ',-... 

^      360°--f360°;      * 


360°^ 
a 


whence  it  follows  thai 


2/ 


~=1  +  5=100273780, 
d  y 


\ 


taking  the  value  of  the  sidereal  year  y  as  given  in  Art  383,  viz.  365'  6^ 
9"  9*6*.  But,  as  we  have  seen,  d  is  not  the  absolute  sidereal  day,  but 
exceeds  it  in  the  ratio  1-00000011 : 1.  Hence  to  get  the  value  of  the 
mean  solar  as  expressed  in  absolute  sidereal  days,  the  number  above  set 
down  must  be  increased  in  the  same  ratio,  which  brings  it  to  1-00273791, 


NATURAL  UNITB  07  TIMB. 


627 


m  vill  have  lost 
I  days,  will  have 
the  length  of  the 
any  star  outside 
the  absolute  time 
or  as  100000011 

role,  as  at  «r.  For 
the  meridian,  in- 
een  q  and  r,  and 
>8ite  direction,  and 
i  continues  to  get 
sen  8  and  P,  where 
in  to  0  when  p  has 
ihe  mean  of  all  the 
koxes  is  an  absolute 

in  the  ecliptic,  the 
arrival  at  that  star 
ie  error)  throughout 
wnodic  sidereal  revo- 
eference  to  a  star  so 
must  proceed  as  fol- 
(or  synodic  day  in 
ridian  with  reference 
:c8  described  by  the 

ectively360°-and 
I  former  by  precisely 


^rt  383,  via.  365*  6" 
ate  stcZercaZ  day,  but 
.  get  the  value  of  the 
Ithe  number  above  set 
ags  it  to  100273791, 


which  is  the  ratio  of  the  solar  to  the  sidereal  day  actually  in  use  among 
astronomers. 

(912.)  It  would  be  well  for  chronology  if  mankind  would,  or  could 
have  contented  themselves  with  this  one  invariable,  natural,  and  conve- 
nient standard  in  their  reckoning  of  time.  The  ancient  Egyptians  did 
so,  and  by  their  adoption  of  an  historical  and  official  year  of  365  days 
have  afforded  the  only  example  of  a  practical  chronology,  free  from  all 
obscurity  or  complication.  But  the  return  of  the  seasons,  on  which  de- 
pend all  the  more  important  arrangements  and  business  of  cultivated  life, 
b  not  conformabe  to  suoh  a  multiple  of  the  diurnal  unit.  Their  return 
is  regulated  by  the  tropical  i/ear,  or  the  interval  between  two  successive 
arrivals  of  the  sun  at  the  vernal  equinox,  which,  as  we  have  seen  (Art. 
883),  differs  from  the  sidereal  year  by  reason  of  the  motion  of  the  equi* 
noctial  points.  Now  this  motion  is  not  absolutely  uniform,  because  the 
ecliptic,  upon  which  it  is  estimated,  is  gradually,  though  very  slowly, 
changing  its  situation  in  space  under  the  disturbing  influence  of  the  planets 
(Art.  640.)  And  thus  arises  a  variation  in  the  tropical  year,  which  is  de- 
pendent  on  the  place  of  the  equinox  (Art.  383.)  The  tropical  year  is 
actually  about  4-21*  shorter  than  it  was  in  the  time  of  Hipparchus.  This 
absence  of  the  most  essential  requisite  for  a  standard,  viz.  invariability, 
renders  it  necessary,  since  we  cannot  help  employing  the  tropical  year  in 
our  reckoning  of  time,  to  adopt  an  arbitrary  or  artificial  value  for  it,  so 
near  the  truth,  as  not  to  admit  of  the  accumulation  ox  itd  error  for  several 
centuries  producing  any  practical  mischief,  and  thus  satisfying  the  ordi- 
nary wants  of  civil  life ;  while,  for  scientific  purposes,  the  tropical  yet  r, 
so  adopted,  is  considered  only  as  the  representative  of  a  certain  number 
of  integer  days  and  a  fraction — the  day  being,  in  etfect,  the  only  standard 
employed.  The  case  is  nearly  analogous  to  the  reckoning  of  value  by 
guineas  and  shillings,  an  artificial  relation  of  the  two  coins  being  fixed  by 
law,  near  to,  but  scarcely  ever  exactly  coincident  with,  the  natural  one, 
determined  by  the  relative  market  price  of  gold  and  silver,  of  which 
either  the  one  or  the  other  —  whichever  is  really  the  most  invariable,  or 
the  most  in  use  with  other  nations, — may  be  assumed  as  the  true  theo- 
retical standard  of  value. 

(913.)  The  other  inconvenience  of  the  tropical  year  as  a  greater  unit 
is  its  incommensurability  with  the  lesser.  In  our  meat,  re  of  space  all 
our  subdivisions  are  into  aliquot  parts :  a  yard  is  three  feet,  a  mile  eight 
furlongi',  &o.  But  a  year  is  no  exact  number  of  days,  nor  an  integer 
number  with  any  exact  fraction,  as  one  third  or  one  fourth,  over  and  above; 
hut  the  surplus  is  an  incommenmrable  fraction,  composed  of  hours, 
minutes,  seconds,  &c.|  which  produces  the  same  kind  of  inconvenience  in 


,f  ii 


628 


OUTLINES  OP  ASTRONOMY. 


:ss. 


ITVJI 


i 


L"  ^ 


in  the  reckoning  of  time  that  it  would  do  in  that  of  money,  if  we  had 
gold  coins  of  tho  value  of  twenty-one  Hhillings,  with  odd  pence  and  far- 
things, and  a  fraction  of  a  farthing  over.  For  tliis,  however,  there  is  no 
remedy  but  to  keep  a  strict  register  of  the  surplus  fractions ;  and,  when 
they  amount  to  a  whole  day,  oast  them  over  into  the  integer  account. 

(914.)  To  do  this  in  the  simplest  and  most  convenient  manner  is  the 
object  of  a  well-adjusted  calendar.  In  the  Qregorian  calendar,  which  we 
follow,  it  is  accomplished  with  as  much  simplicity  and  neatness  as  the 
case  admits,  by  carrying  a  little  farther  than  is  done  above,  the  principle 
of  an  assumed  or  artificial  year,  and  adopting  two  such  years,  both  con- 
sisting of  an  exact  integer  number  of  days,  viz.  one  of  365  and  the  other 
of  366,  and  laying  down  a  simple  and  easily  remembered  rule  for  the 
order  in  which  these  years  shall  succeed  each  other  in  the  civil  reckoning 
of  time,  so  that  during  the  lapse  of  at  least  some  thousands  of  years  the 
sum  of  the  integer  artificial,  or  Gregorian,  years  elapsed  shall  not  differ 
from  the  same  number  of  real  tropical  years  by  a  whole  day.  By  this 
contrivance,  the  equinoxes  and  solstices  will  always  fall  on  days  similarly 
situated,  and  bearing  the  same  name  in  each  Gregorian  year;  and  the 
seasons  will  for  ever  coirespond  to  the  same  months,  instead  of  running 
the  round  of  the  whole  year,  as  they  must  do  upon  any  other  system  of 
reckoning,  and  used,  in  fact,  to  do  before  this  was  adopted  as  a  matter  of 
ignorant  haphazard  in  the  Greek  and  Roman  chronology,  and  of  strictly 
defined  and  superstitiously  rigorous  observance  in  the  Egyptian. 

(915.)  The  Gregorian  rule  is  as  follows  : — The  years  are  denominated 
aa  yean  current  (not  a»  years  elapsed)  from  the  midnight  between  the 
81st  of  December  and  the  1st  of  January  immediately  subsequent  to  the 
birth  of  Christ,  according  to  the  chronological  determination  of  that  event 
by  Dionysius  Exiguus.  Every  year  whose  number  is  not  divisible  by  4 
without  remainder,  consists  of  365  days ;  every  year  which  is  so  divisible, 
but  is  not  divisible  by  100,  of  366 ;  every  year  divisible  by  100,  but  not 
by  400,  again  of  365 ;  and  every  year  divisible  by  400,  ogain  of  366. 
For  example,  the  year  1833  not  being  divisible  by  4,  consists  of  365 
days;  1836  of  366;  1800  and  1900  of  365  each;  but  2000  of  366.  In 
order  to  see  how  near  this  rule  will  bring  us  to  the  truth,  let  us  see  what 
number  of  days  10000  Gregorian  years  will  contain,  beginning  with  the 
year  A.  D.  1.  Now,  in  10000,  the  numbers  not  divisible  by  4  will  be  |  of 
10000  or  7500 ;  those  divisible  by  100,  but  not  by  400,  will  in  like  manner 
be  I  of  100,  or  75 ;  so  that,  in  the  10000  years  in  question,  7575  consist 
of  366,  and  the  remaining  2425  of  365,  producing  in  all  3652425  days, 
which  would  give  for  an  average  of  each  year,  one  with  another,  365''-2425. 
The  actual  value  of  the  tropical  year,  (art.  383)  reduced  into  a  decimal 


NATURAL   UNITS  OF  TIME. 


529 


ancy,  if  we  had 
pence  and  far- 
■ever,  there  is  no 
ions ;  and,  when 
aev  account, 
tit  manner  is  the 
lendar,  which  we 
neatness  as  the 
ove,  the  principle 
years,  both  con- 
565  and  the  other 
ered  rule  for  the 
he  civil  reckoning 
lands  of  years  the 
jd  shall  not  differ 
iole  day.     By  this 
il  on  days  similarly 
ian  year;  and  the 
instead  of  running 
iny  other  system  of 
pted  as  a  matter  of 
)gy,  and  of  strictly 
iJgyptian. 

its  are  denominated 
Inight  between  the 
subsequent  to  the 
lation  of  that  event 
not  divisible  by  4 
rhich  is  so  divisible, 
jle  by  100,  but  not 
400,  again  of  366. 
4,  consists  of  365 
tt  2000  of  366.    In 
ith,  let  us  see  what 
beginning  with  the 
,le  by  4  will  be  |  of 
L  will  in  like  manner 
iestion,  7575  consist 
_  all  3652425  days, 
[another,  365'>-2425. 
luced  into  a  decimal 


fraction,  is  865 '24224,  80  the  error  in  the  Gregorian  rule  on  10000  of 
the  present  tropical  years,  is  2'6,  or  2'  lA^  24"' ;  that  is  to  say,  less  than 
a  day  in  8000  years ;  which  is  more  than  sufficient  for  all  human  purposes, 
those  of  the  astronomer  excepted,  who  is  in  no  danger  of  being  led  into 
error  from  this  cause.     Even  this  error  is  avoided  by  extending  the 
wording  of  the  Gregorian  rule  one  step  farther  than  its  contrivers  probably 
thought  it  worth  while  to  go,  and  declaring  that  years  divisible  by  4000 
should  consist  of  865  days.     This  would  take  off  two  integer  days  from 
the  above  calculated  number,  and  2 '5  from  a  larger  average;  making  the 
sum  of  days  in  100000  Gregorian  years,  36524225,  which  differs  only  by 
a  single  day  from  100000  real  tropical  years,  such  as  they  exist  at  present. 
(916.)  In  the  historical  dating  of  events  there  is  no  year  A.  d.  0.    The 
year  immediately  previous  to  A.  d.  1,  is  always  called  b.  o.  1.    This  must 
always  be  borne  in  mind  in  reckoning  chronological  and  astronomical 
intervals.     The  sum  of  the  nominal  years  b.  o.  and  a.  d.  must  be  dimin- 
ished  by  1.     Thus,  from  Jan.  1,  b.  o.  4713,  to  Jan.  1,  1582,  the  years 
elapsed  are  not  6295,  but  6294. 

(917.)  As  any  distance  along  a  high  road  might,  though  in  a  rather 
inconvenient  and  roundabout  way,  be  expressed  without  introducing  error 
by  setting  up  a  series  of  milestones,  at  intervals  of  unequal  lengths,  so 
that  every  fourth  mile,  for  instance,  should  be  a  yard  longer  than  the  rest, 
or  according  to  any  other  fixed  rule ;  taking  care  only  to  mark  the  stones 
so  as  to  leave  room  for  no  mistake,  and  to  advertise  all  travellers  of  the 
difference  of  lengths  and  their  order  of  succession  ;  so  may  any  interval 
of  time  be  expressed  correctly  by  stating  in  what  Gregorian  years  it  begins 
and  ends,  and  whereabouts  in  each.  For  this  statement  coupled  with  the 
declaratory  rule,  enables  us  to  say  how  many  integer  years  are  to  be 
reckoned  at  365,  and  how  many  at  366  days.  The  latter  years  arc  called 
bissextiles,  or  leap-years,  and  the  surplus  days  thus  thrown  into  the 
reckoning  are  called  intercalary  or  leap  days. 

(918.)  If  the  Gregorian  rule,  as  above  stated,  had  always  and  in  all 
countries  been  known  and  followed,  nothing  would  be  easier  than  to  reckon 
the  number  of  days  elapsed  between  the  present  time,  and  any  historical 
recorded  event.  But  this  is  not  the  case ;  and  the  history  of  the  calendar, 
with  reference  to  chronology,  or  to  the  calculation  of  ancient  observations, 
may  be  compared  to  that  of  a  clock,  going  regularly  when  left  to  itself, 
but  sometimes  forgotten  to  be  wound  up ;  and  when  wound,  sometimes 
sot  forward,  sometimes  backward,  either  to  serve  particular  purposes  and 
private  interests,  or  to  rectify  blunders  in  setting.  Such,  at  least,  appears 
to  have  been  the  case  with  the  Roman  calendar,  in  which  our  own  origi- 
nates, from  the  time  of  Numa  to  that  of  Julius  Caesar,  when  the  lunar 
84 


■'i" 


680 


OUTLINES  OP  ASTRONOMY. 


*m4 


year  of  18  months,  or  856  days,  was  augmented  at  pleasare  to  correspond 
to  tho  solar,  by  which  the  seasons  arc  determined,  by  the  arbitrary  inter- 
oalations  of  the  priests,  and  the  usurpations  of  the  decemvirs  and  other 
magistrates,  till  the  confusion  became  inextricable.  To  Julius  Caosar, 
assisted  by  Sosigenos,  an  eminent  Alexandrian  astronomer  and  mathema- 
tician, wo  owe  the  neat  contrivance  of  the  two  years  of  865  and  860  days, 
and  the  insertion  of  one  bissextile  after  throe  common  years.  This  im- 
portant change  took  place  in  the  45th  year  before  Christ,  which  he  ordered 
to  commence  on  the  1st  of  January,  being  the  day  of  the  new  moon  im- 
mediateh/  following  the  winter  aohtice  oftfie  year  before.  We  may  judge 
of  the  state  into  which  the  reckoning  of  time  had  fallen,  by  the  fact,  that 
to  introduce  the  new  system  it  was  necessary  to  enact  that  the  previous 
year,  46  b.  o.,  should  consist  of  445  days,  a  circumstance  which  obtained 
for  it  the  epithet  of  "  the  year  of  confusion."  '. 

(919.)  Had  Caesar  lived  to  carry  out  into  practical  effect,  as  Chief 
Pontiff,  hb  own  reformation,  an  inconvenience  would  have  been  avoided, 
which  at  the  very  outset  threw  the  whole  matter  into  confusion.  The 
words  of  his  edict  establishing  the  Julian  system  have  not  been  handed 
down  to  us,  but  it  is  probable  that  they  contained  some  expression  equi- 
valent to  "  every  fourth  year,"  which  the  priests  misinterpreting  after  Lis 
death  to  mean  (according  to  the  sacerdotal  system  of  numeration)  as 
counting  the  leap  year  newly  elapsed  a«  No.  1  of  the  four,  intercalated 
every  third  instead  of  every  fourth  year.  This  erroneous  practice  con- 
tinued during  36  years,  in  which  therefore  12  instead  of  9  days  were 
intercalated,  and  an  error  of  three  days  produced ;  to  rectify  which,  Au- 
gustus  ordered  the  suspension  of  all  intercalation  during  three  complete 
guadriennia,  —  thus  restoring,  as  may  be  presumed  his  intention  to  have 
been,  the  Julian  dates  for  the  future,  and  re-establishing  the  Julian 
system,  which  was  never  afterwards  vitiated  by  any  error,  till  the  epoch 
when  its  own  inherent  defects  gave  occasion  to  the  Gregorian  reformation. 
According  to  the  Augustan  reform,  the  years  A.  v.  o.  761,  765,  769,  &c., 
which  we  now  call  A.  D.  8,  12,  16,  &c.,  are  leap  years.  And  starting 
from  this  as  a  certain  fact,  (for  the  statements  of  the  transaction  by  clas- 
sical authors  are  not  so  precise  as  to  leave  absolutely  no  doubt  as  to  the 
previous  intermediate  years,)  astronomers  and  chronologists  have  agreed 
to  reckon  backwards  in  unbroken  succession  on  this  principle,  and  thus  to 
carry  the  Julian  chronology  into  past  time,  as  if  it  had  never  suffered 
such  interruption,  and  as  if  it  were  certain  (which  it  is  not,  though  we  con- 
ceive the  babnce  of  probabilities  to  incline  that  way')  fhat  Caesar,  by  way 

*  With  Scaliger,  Ideler,  and  all  the  best  authorities.    Yet  it  has  been  argued  that 
Cssar  would  naturally  begin  his  first  quadriennium  with  three  ordinary  years,  defer- 


'T'f- 


LUNAR  OYCLR. 


681 


of  securing  the  intercalation  as  a  matter  of  precedent,  made  his  initial 
year  45  b.  o.  a  leap  year.  Whenever,  therefore,  in  the  relation  of  any 
event,  either  in  ancient  history  or  in  modern,  previous  to  the  change  of 
stylo,  the  time  is  specified  in  our  modern  nomenclature,  it  is  always  to  be 
understood  as  having  been  identified  with  the  assigned  date  by  threading 
the  mazes  (often  very  tangled  and  obscure  ones)  of  special  and  national 
chronology,  and  referring  the  day  of  its  occurrence  to  its  place  in  the 
Julian  system  to  interpreted. 

(920.)  Different  nations  in  different  ages  of  the  world  have  of  course 
reckoned  their  time  in  different  ways,  and  from  different  epochs,  and  it  in 
therefore  a  matter  of  great  convenience  that  astronomers  and  chronologists 
(as  they  have  agreed  on  the  uniform  adoption  of  the  i^ulian  system  of 
years  and  months)  should  also  agree  on  an  epoch  antecedent  to  them  all, 
to  which,  as  to  a  fixed  point  in  time,  the  whole  list  of  chronological  eras 
can  be  differentially  referred.  Such  an  epoch  is  the  noou  of  th;,  1st  of 
January,  B.C.  4713,  which  is  called  the  epoch  of  the  Julian  period,  a  cycle 
of  7980  Julian  years,  to  understand  the  origin  of  which  we  must  explain 
that  of  three  subordinate  cycles,  from  whose  combination  it  take''  iw*^  rise, 
by  the  multiplication  together  of  the  numbers  of  years  severally  onttuned 
in  them,  viz. : — the  Solar  and  Lunar  cycles,  and  that  of  the  indiotions. 

(921.)  The  Solar  cycle  consbts  of  28  Julian  years,  after  the  lapse  of 
which  the  same  days  of  the  week  on  the  Julian  system  would  always 
return  to  the  a  iie  days  of  each  mouth  throughout  the  year.  For  four 
such  years  consisting  of  1461  days,  which  is  not  a  multiple  of  7,  it  is 
evident  that  the  least  number  of  years  which  will  fulfil  this  condition 
must  be  seven  times  that  interval,  or  28  years.  The  place  in  this  cycle 
for  any  year  A.  D.,  as  1849,  is  found  by  adding  9  to  the  year,  and  divi- 
ding by  28.    The  remainder  is  the  number  sought,  0  being  counted  as  28. 

(922.)  The  Lunar  cycle  consists  of  19  years  ov  ??^  lunations,  which 
differ  from  19  Julian  years  of  365^  days  only  by  ul  >ut  an  hour  and  a 
half,  so  that,  supposing  the  new  moon  to  happen  on  the  first  of  January, 
in  the  first  year  of  the  cycle,  it  will  happeu  on  that  day  (or  within  a  very 
short  time  of  its  beginning  or  ending)  again  after  a  lapse  of  19  years,  and 
almost  certainly  on  that  day,  and  within  an  hour  and  a  half  of  the  same 
hour  of  the  day,  after  the  lapse  of  four  such  cycles,  or  76  years ;  and  all 
the  new  moons  in  the  interval  will  run  on  the  same  days  of  the  month  as 
in  the  preceding  cycle.  This  period  of  19  years  is  sometimes  called  the 
Metonic  cycle,  from  its  discoverer  Meton,  an  Athenian  mathematician,  a 

ring  the  rectification  of  their  accumulated  error  to  the  fourth,  by  inserting  there  the 
intercalary  day.  For  the  correction  of  Roman  dates  during  the  fifty-two  years  between 
the  Julian  and  Augustan  reformations,  see  Ideler,  "  Handbuch  der  Mathematischen 
und  Technischen  Chronologie,"  which  we  take  for  our  guide  throughout  this  chapter. 


ri 


hi. 


582 


OUTLINES  OF  ASTRONOMY. 


CO' 


discovery  duly  appreciated  by  bis  countrymen,  as  ensuring  the  correspon- 
dence between  the  lunar  and  solar  years,  the  former  of  which  was  followed 
by  the  Greeks.  Public  honours  were  decreed  to  him  for  this  discovery, 
a  circumstance  very  expressive  of  the  annoyance  which  a  lunar  year  of 
necessity  inflicts  on  a  civilized  people,  to  whom  a  regular  and  simple 
calendar  is  one  of  the  first  necessities  of  life.  The  cycle  of  76  years,  a 
great  improvement  on  the  Metonic  cycle,  was  first  proposed  by  Callippus, 
and  is  therefore  called  the  Callippic  cycle.  To  find  the  place  of  a  given 
year  in  the  lunar  cycle,  (or  as  it  is  called  the  Golden  Number,)  add  1  to 
the  number  of  the  year  a.  d.,  and  divide  by  19,  the  remainder  (or  19  if 
exactly  divisible)  is  the  Golden  Number. 

(923.)  The  cycle  of  the  indictions  is  a  period  of  15  years  used  in  the 
courts  of  law  and  in  the  fiscal  organization  of  the  Roman  empire,  under 
Constantine  and  his  successors,  and  thence  introduced  into  legal  dates,  as 
the  Golden  Number,  serving  to  determine  Easter,  was  in  to  ecclesiastical 
ones.  To  find  the  place  of  a  year  in  the  indiction  cycle,  add  3  and  divide 
by  15.  The  remainder  (or  15  if  0  remain)  is  the  number  of  the  indic- 
tional  year. 

(924.)  If  we  multiply  together  the  numbers  28,  19,  and  15,  we  get 
7980,  and  therefore,  a  period  or  cycle  of  7980  years  will  bring  round  the 
years  of  the  three  cycles  again  in  the  same  order,  so  that  each  year  shall 
hold  the  same  place  in  all  the  three  cycles  as  the  corresponding  year  in 
the  foregoing  period.  As  none  of  the  three  numbers  in  question  have  any 
common  factor,  it  is  evident  that  no  two  years  in  the  same  compound 
period  can  agree  in  all  the  three  particulars :  so  that  to  specify  the  numbers 
of  a  year  in  each  of  these  cycles  is,  in  fact,  to  specify  the  year,  if  within 
that  long  period;  which  embraces  the  entire  of  authentic  chronology. 
The  period  thus  arising  of  7980  Julian  years,  is  called  the  Julian  period, 
and  it  has  been  found  so  useful,  that  the  most  competent  authorities  have 
not  hesitated  to  declare  that,  through  its  employment,  light  and  order 
were  first  introduced  into  chronology.'  We  owe  its  invention  or  revival 
to  Joseph  Scaliger,  who  is  said  to  have  received  it  from  the  Greeks  of  Con- 
stantinople. The  first  year  of  the  current  Julian  period,  or  that  of  which 
the  number  in  each  of  the  three  subordinate  cycles  is  1,  was  the  year  4713 
B.  c,  and  the  noon  of  the  1st  of  January  of  that  year,  for  the  meridian 
of  Alexandria,  is  the  chronological  epoch,  to  which  all  historical  eras  are 
most  readily  and  intelligibly  referred,  by  computing  the  number  of  integer 
days  intervening  between  that  epoch  and  the  noon  (for  Alexandria)  of  the 
day,  which  is  reckoned  to  be  the  first  of  the  particular  era  in  question. 
The  meridian  of  Alexandria  is  chosen  as  that  to  which  Ptolemy  refers  the 
commencement  of  the  era  of  Nabonassar,  the  basis  of  all  his  calculations. 
*  Ideler,  Handbuch,  Sic,  vol.  1,  p.  77. 


•M— 


GHRONOLOaiOAL   ERAS. 


538 


ig  the  conrcspon- 
lich  was  followed 
>r  this  discovery, 
a  lunar  year  of 
rular  and  simple 
3le  of  76  years,  a 
sed  by  Callippus, 
I  place  of  a  given 
[umber,)  add  1  to 
mainder  (or  19  if 

years  used  in  the 
lan  empire,  under 
into  legal  dates,  as 
in  to  ecclesiastical 
!,  add  3  and  divide 
mber  of  the  indic- 

.9,  and  15,  we  get 
rill  bring  round  the 
;hat  each  year  shall 
Tesponding  year  in 
I  question  have  any 
le  same  compound 
ipecify  the  numbers 
the  year,  if  within 
hentio  chronology, 
the  Julian  period, 
mt  authorities  have 
t,  light  and  order 
invention  or  revival 
the  Greeks  of  Con- 
I,  or  that  of  which 
was  the  year  4713 
',  for  the  meridian 
|l  historical  eras  are 
number  of  integer 
Alexandria)  of  the 
ir  era  in  question. 
Ptolemy  refers  the 
ill  bis  calculations. 


(925.)  Qiven  the  year  of  the  Julian  period,  those  of  the  subordinate 
cycles  are  easily  determined  as  above.  Conversely,  given  the  years  of  the 
solar  and  lunar  cycles,  and  of  the  indietion,  to  determine  the  year  of  the 
Julian  period  proceed  as  follows :  —  Multiply  the  number  of  the  year  in 
the  solar  cycle  by  4845,  in  the  lunar  by  4200,  and  in  the  Cycle  of  the 
Indictions  by  6916,  divide  the  sum  of  the  products  by  7980,  and  the 
remainder  is  the  year  of  the  Julian  period  sought. 

(926.)  The  following  table  contains  these  intervals  for  some  of  the  more 
important  historical  eras :  — 
Intervals  in  Days  bettoeen  the  Commencement  of  the  Julian  Period,  and 

that  of  some  other  remarkable  I'lironological  and  astronomical  Eras.  . 


Names  by  which  the  Era  is  usually  cited. 


First  day 

current  of 

tlio  era. 


Julian  Epochs.  Julian  Dales. 

Julian  period Jan.  1. 

Creation  of  the  world  (Usher)  (Jan.  1.) 

Era  of  the  Deluge  ( Aboulhassnn  Kus- 
ohiar) 

Ditto  Vulgar  Computation 

Era  of  Abrah.ani  (Sir  II.  Nicholus) .... 

Destruction  of  Troy,  (ditto) 

Dedication  of  Solomon's  Temple 

Olymptadti  (mean  epoch  in  gcnernl 
use)  

Building  of  Home  (Varrunian  epoch, 
u.  0.) 

Era  of  Nabonassar 

Metonic  cycle  (Astronomienl  epoch)... 

Callippic  cycle,        do.     (liiot) 

Philippic  era,  or  era  of  Philip  Aridasus 

Era  of  the  Seleucidoo 

Csesarcan  era  of  Antioch 

Julian  reformation  of  the  Calendar... 

Spanish  era 

Actian  era  in  Rome 

Aotian  era  of  Alexandria 

Vulgar  or  Dionysian  era 

Era  of  Diocletian 

Hejira    (astronomical    epoch,    new 
moon) 

Era  of  Yezdogird 

Gelalaean  era  (Sir  H.  Nicholas) 

Last  day  of  Old  Style  (Catholic  na- 
tions)   

Last  day  of  Old  Style  in  England).... 

Gregorian  Epocha. 
New  Style  in  Catholic  nations , 

Ditto      in  England 

Commencement  of  the  19th  century, 

epoch  of  Bode's  catalogue  of  stars.. 
Epoch  of  the  catalogue  of  stars  of  the 

R.  Astronomical  Society , 

Epoch  of  the  catalogue  of  the  British 

Association 


Ohronolog'l 
designation 
,of  the  year. 


Current  year 
of  the  Ju- 
lian Period. 


Feb.  18. 
(.Tan.  1.) 
Oct.  1. 
July  12. 
(May  1.) 

July  1. 

AprU  22. 
Feb.  26. 
July  15. 
June  28. 
Nov.  12. 

Oct.  1. 

Sept.  1. 

Jan.  1. 

Jan.  1. 

Jan.  1. 
Aug.  29. 

Jan.  1. 
Aug.  20. 

July  16. 
June  16. 
March  14. 

Oct.  4. 
Sept.  2. 
Oreijnrian 
I)ate». 
Oct.  15. 
Sept.  14. 

Jan.  1. 

Jan.  1. 

Jan.  1. 


B.C.4713 
4004 

3102 
2348 
2015 
1184 
1015 

776 

753 

747 

432 

330 

324 

312 

49 

45 

38 

30 

30 

A.  D.   1 

284 

622 

632 

1079 

1582 
1752 


1582 
1752 

1801 

1830 

1850 


1 
710 

1612 
2366 
2699 
3530 
3699 

3938 

3961 
3967 
4282 
4384 
4390 
4402 
4665 
4669 
4676 
4684 
4684 
4714 
4997 

5335 
5345 
679^ 

6295 
6465 


6295 
6465 

6514 

6543 

6563 


Interval 
days. 


0 
258,963 

588,466 

863,817 

985,718 

1,289,160 

1,350,815 

1,438,171 

1,446,502 
1,448,638 
1,563,831 
1,599,608 
1,603,398 
1,607,739 
1,703,770 
1,704,987 
1,707,544 
1,710,466 
1,710,706 
1,721,424 
1,825,030 

1,948,439 
1,952,063 
2,115,285 

2,299,160 
2,361,221 


2,299,161 
2,361,222 

2,378,862 

2,389,454 

2,396,759 


■:-| 


••;H 


ISI 


I 

I'; 


If    ill 


■■■'1 


ii ' 


'ir    ■'. 


684 


OUTLINES  OF  ASTRONOMY. 


VX3f 

o 


N.  B.  The  civil  epochs  of  the  Metonic  cycle,  and  the  Hejira,  are  each  one  day  later 
than  the  astronomical,  the  latter  being  the  epochs  of  the  absolute  new  moon*,  the  former 
those  of  the  earliest  possible  visibility  of  the  lunar  crescent  in  a  tropical  sky.  M.  Biot 
has  shown  that  the  solstice  and  new  moon  not  only  coincided  on  the  day  here  set  down 
as  the  commencement  of  the  Callippio  cycle,  but  that,  by  a  happy  coincidence,  a  bare 
possibility  existed  of  seeing  the  crescent  moon  at  Athens  wt(At»  that  day,  reckoned  from 
midnight  to  midnight.  ,  i-, 

(927.)  The  determination  of  the  exact  interval  between  any  two  given 
dates  is  a  matter  of  such  importance,  and,  unless  methodically  performed, 
is  so  very  liable  to  error,  that  the  following  rules  will  not  be  found  out  of 
place.  In  the  first  place  it  must  be  remarked,  generally,  that  a  date, 
whether  of  a  day  or  year,  always  expresses  the  day  or  year  current  and  not 
elapsed,  and  that  the  designation  of  a  year  by  A.  D.  or  b.  o.  is  to  be  re- 
garded as  the  name  of  that  year,  and  not  as  a  mere  number  uninterrupt- 
edly designating  the  place  of  the  year  in  the  scale  of  time.  Thus,  in 
the  date,  Jan.  5,  b.  c.  1,  Jan.  5  does  not  mean  that  5  days  of  January  in 
the  year  in  question  have  elapsed,  but  that  4  have  elapsed,  and  the  5th  is 
current.  And  the  B.  c.  1,  indicates  that  the  first  day  of  the  year  so 
named,  (the  first  year  current  before  Christ,)  preceded  the  first  day  of  the 
vulgar  era  by  one  year.  The  scale  of  A.  D.  and  B.  0.  is  not  continuous, 
the  year  0  in  both  being  wanting )  so  that  (supposing  the  vulgar  reckon- 
ing correct)  our  Saviour  was  bom  in  the  year  b.  o.  1. 

(928.)  To  find  the  year  current  of  the  Julian  period,  (j.  p.)  corre- 
sponding  to  any  given  year  current  B.  C.  or  A.  D.  If  B.  0.,  subtract  the 
number  of  the  year  from  4714 :  if  a.  d.,  add  its  number  to  4713.  For 
example,  see  the  foregoing  table. 

(929.)  To  find  the  day  current  of  the  Julian  period  corresponding  to 
any  given  date,  Old  Style.  Convert  the  year  B.  0.  or  A.  D.  into  the  cor- 
responding year  J.  p.  as  above.  Subtract  1  and  divide  the  number  so 
diminished  by  4,  and  call  Q  the  integer  quotient,  and  R  the  remainder. 
Then  will  Q  be  the  number  of  entire  quadriennia  of  1461  days  each,  and 
R  the  residual  years,  the  first  of  which  is  always  a  leap'year.  Convert 
Q  into  days  by  the  help  of  the  first  of  the  annexed  tables,  and  R  by  the 
second,  and  the  sum  will  be  the  interval  between  the  Julian  epoch,  and 
the  commencement,  Jan.  1,  of  the  year.  Then  find  the  days  intervening 
between  Ihe  beginning  of  Jan.  1,  and  that  of  the  date-day  by  the  third 
table,  using  the  cofiumn  for  a  leap-year,  where  R  =  0,  and  that  for  a  com- 
mon year  when  R  is  1,  2,  or  3.  Add  the  days  so  found  to  those  in 
Q  -f  R,  and  the  sum  will  be  the  days  elapsed  of  the  Julian  period,  the 
number  of  whioh  increased  by  1  gives  the  day  current. 


:•«!. 


ire  each  one  day  later 
new  moon»,  the  former 
tropical  sky.  M.  Biot 
the  day  here  set  down 
py  coincidence,  a  bare 
hat  day,  reckoned  from 


reen  any  two  given 
odically  performed, 
kot  be  found  out  of 
orally,  that  a  date, 
ear  current  and  not 
or  B.  0.  is  to  be  re- 
umber  uninterrupt- 
of  time.    Thus,  in 

days  of  January  in 
psed,  and  the  5th  is 
iay  of  the  year  so 

the  first  day  of  the 
.  is  not  continuous, 
I  the  vulgar  reckon- 

eriod,  (J.  P.)  corre- 
f  B.  0.,  subtract  the 
ober  to  4713.     For 

od  corresponding  to 
>r  A.  D.  into  the  cor- 
ride  the  number  so 
d  B  the  remainder. 
1461  days  each,  and 
leap-year.     Convert 
ables,  and  R  by  the 
e  Julian  epoch,  and 
he  days  intervening 
Eite-day  by  the  third 
and  that  for  a  corn- 
found  to  those  in 
e  Julian  period,  the 
It. 


CHRONOLOGICAL  INTERVALS. 


535 


Table  L  Multiples  of  1461, 

the  days  in  a 

Table  2.  Days  in 
Residual  years. 

0 
1 
2 
3 

0 

366 

731 

1096 

1  ' 

2 

3 

1461 
2922 
4383 

4 
5 
6 

6844 
7305 
8766 

7 
8 
9 

10227 
11688 
13149 

Tablb  3.  Days  elapsed  from  Jan.  1  to  the  Ist  of  each  Month. 

' .  ■    ■' 

In  a  com. 
men  year. 

In  a  leap 
year. 

In  a  com- 
mon year. 

In  a  leap 
year. 

Jan. 1 

0 

31 

59 

90 

120 

151 

0 

31 

60 

91 

121 

152 

July  1 

181 
212 
243 
273 
304 
334 

182 
213 
244 
274 
306 
335 

Feb.  1 

Aug.  1 

March  1 

Sept.  1 

April  1 

Oct.  1 

May  1 

Nov.  1 

June  1 

Deo.  1 

Example. — What  is  the  current  day  of  the  Julian  period  correspond- 
ing to  the  last  day  of  Old  Style  in  England,  on  Sept.  2,  A.  D.  1752  ? 

1752  •        t     1000                 .     1,461,000 

4713             '     ■  600                        876,600 

6463  year  current.  10                         14,610 

1_  6                           8,766 

4)6464  years  elapsed.  R=0                                  0 

Q=1616p  Jan.  1  to  Sept.  1,                  244 

R  =      05  Sept.  1  to  Sept.  2, 1 

2,361,221  days  elapsed. 

■^      '  Current  day  the  2,361,222''. 

(930.)  To  find  the  same  for  any  given  date,  New  Style.  Proceed  as 
above,  considering  the  date  as  a  Julian  date,  and  disregarding  the  change 
of  style.    Then,  from  the  resulting  days,  subtract'  as  follows : — 

For  any  date  of  New  Style,  antecedent  to  March  1,  a.  d.  1700 10  days. 

After  Feb.  28,  1700,  and  before  March  1,  a.  d.  1800 11  days. 

"  1800  "  '•  1900 12  days. 

••  1900  "  "  2100 13  days,  &c. 

(931.)  To  find  the  interval  between  any  tico  dates,  whctlier  of  Old  or 
New  Style,  or  one  of  one,  and  one  of  the  other.  Find  the  day  current 
of  the  Julian  period  corresponding  to  each  date,  and  their  difference  is 
the  interval  required.  If  the  dates  contain  hours,  minutes,  and  seconds, 
they  must  be  annexed  to  their  respective  days  current,  and  the  subtraction 
performed  as  usual. 

(932.)  The  Julian  rule  made  every  fourth  year,  without  exception,  a 
bissextile.  This  is,  in  fact,  an  over-correction ;  it  supposes  the  length  of 
the  tropiflal  year  to  be  365^%  which  is  too  great,  and  thereby  induces  an 


;t 


if 


m 


!i  1 


!     in 

1'     ;!    ' 


586 


OUTLINES  OF  ASTRONOMY. 


fcfcw'' 


^'i   la 


CD 


error  of  7  days  in  908  years,  as  'srill  easily  appear  od  trial.  Accordingly, 
80  early  as  the  year  1414,  it  began  to  bo  perceived  that  the  equinoxes 
were  gradually  creeping  away  from  the  21st  of  March  and  Septediber, 
where  they  ought  to  have  always  fallen  had  the  Julian  year  been  exact, 
and  happening  (as  it  appeared)  too  early.  The  necessity  of  a  fresh  and 
effectual  reform  in  the  c  dendar  was  from  that  time  continually  urgc^,  and 
at  length  admitted.  The  change  (which  took  place  under  the  popedom 
of  Gregory  XIII.)  consisf  d  in  the  omission  .f  ten'  nominal  days  after 
the  4th  of  October,  1582,  (so  that  the  next  day  wa.^  called  the  15th,  and 
not  the  5th,)  and  the  promulgation  of  the  rule  already  explained  for  future 
regulation.  The  change  was  adopted  immediately  in  all  Catholic  coun- 
tries; but  more  slowly  in  Protestant.  In  England,  "the  change  of  style," 
as  it  was  called,  took  place  after  the  2d  of  September,  1752,  eleven  no- 
minal days  being  then  struck  out ;  so  that,  the  last  day  of  Old  Style  being 
the  2d,  the  first  of  New  Style  (the  next  day)  was  called  the  14th,  instead 
of  the  8d.  The  same  legislative  enactment  which  established  the  Gre- 
gorian year  in  England  in  1752,  shortened  the  preceding  year,  1751,  by 
a  full  quarter.  Previous  to  that  time,  the  year  was  held  to  ^  )gin  with 
the  2&th  March,  and  the  year  A.  D.  1751  did  so  accordingly;  but  that 
year  was  not  suffered  to  run  out,  but  was  supplanted  on  the  1st  of  January 
by  the  year  1752,  which  it  was  enacted  should  commence  on  that  day,  as 
well  as  every  subsequent  year.  Russia  is  now  the  ouly  country  in 
Europe  in  which  the  Old  Style  is  still  adhered  to,  and  (another  secular 
year  having  elapsed)  the  difference  between  the  European  and  Russian 
dates  amounts,  zt  present,  to  12  days. 

(933.)  It  is  fortunate  for  astronomy  that  the  confusion  of  dates,  and 
the  irreconcilable  contradctions  which  historical  statements  too  often  ex- 
hibit, when  confronted  with  the  best  knowledge  we  possess  of  the  ancient 
reckonings  of  time,  affect  recorded  observations  but  little.  An  astrono- 
mical observation,  of  any  striking  and  well-marked  phaenomenon,  carries 
with  it,  in  most  cases,  abundant  means  of  recovering  its  exact  date,  when 
any  tolerable  approximation  is  afforded  to  it  by  chronological  records; 
and,  so  far  from  being  abjectly  dependent  on  the  obscure  and  often  con- 
tradictory dates,  which  the  comparison  of  ancient  authorities  indicates,  is 
often  itself  the  surest  and  most  convincing  evidence  on  which  a  chrono- 
logical epoch  can  be  brought  to  rest.  Remarkable  eclipses,  for  instance, 
now  that  the  lunar  theory  is  thoroughly  understood,  can  be  calculated 
back  for  several  thousands  of  years,  without  the  possibility  of  mistaking 
the  day  of  their  occurrence.     And,  whenever  any  such  eclipse  is  so  inter- 

'  See  note  at  the  end  of  this  chapter,  p.  540. 


.1 


I- 


LUNAR  YEAR. 


687 


[.  Accordingly, 
t  the  equinoxes 
and  Septeihber, 
year  been  exact, 
y  of  a  fresh  and 
aually  urgc^,  and 
der  the  popedom 
)minal  days  after 
led  the  15th,  and 
plained  for  future 
ill  Catholic  coun- 
change  of  style," 
1752,  eleven  no- 
)f  Old  Style  being 
.  the  14th,  instead 
tablished  the  Gre- 
ng  year,  1751,  by 
leW  to  ■  )gin  with 
>rdinglyj  but  that 
the  Ist  of  January 
ice  on  that  day,  as 
!  ouly  country  in 
id  (another  secular 
pean  and  Russian 

ision  of  dates,  and 
lents  too  often  ex- 
llsess  of  the  ancient 
Ittle.     An  astrono- 
iaenomenon,  carries 
_  exact  date,  when 
)nological  records; 
lire  and  often  cou- 
)rities  indicates,  is 
)n  which  a  chrono- 
lipses,  for  instance, 

can  be  calculated 
|bility  of  mistaking 

eclipse  is  so  inter- 


woven with  the  account  given  by  an  ancient  author  of  some  historical 
event,  as  to  indicate  precisely  the  interval  of  time  between  the  eclipse  and 
the  event,  and  at  the  same  time  completely  to  identify  the  eclipse,  that 
date  is  recovered  and  fixed  for  ever.' 

(934.)  The  days  thus  parcelled  out  into  years,  the  next  step  to  a  per- 
fect knowledge  of  time  is  to  secure  the  identification  of  each  day,  by  im- 
posing on  it  a  name  universally  known  and  employed.  Since,  however, 
the  days  of  a  whole  year  are  too  numerous  to  admit  of  loading  the 
memory  with  distinct  names  for  each,  all  nations  have  felt  the  necessity 
of  breaking  them  down  into  parcels  of  a  more  moderate  extent ;  giving 
(  imes  to  each  of  these  parcels,  and  particularizing  the  days  in  each  by 
numbers,  or  by  some  special  indication.  The  lunar  month  has  been  re- 
sorted to  in  many  instances ;  and  some  nations  have,  in  fact,  preferred  a 
lunar  to  a  solar  chronology  altogether,  as  thu  Turks  and  Jews  continue  to 
do  to  this  day,  making  the  year  consist  of  12  lunar  months,  or  354  days. 
Our  own  division  into  twelve  unequal  months  is  entirely  arbitrary,  and 
often  productive  of  confusion,  owing  to  the  equivoque  between  the  lunar 
and  calendar  month.'  The  intercalary  day  naturally  attaches  itself  to 
February  as  the  shortest. 

(935.)  Astronomical  time  reckons  from  the  noon  of  the  current  day, 
civil  from  the  preceding  midnight,  so  that  the  two  dates  coincide  only 
during  the  earlier  half  of  the  astronomical,  and  the  later  of  the  civil  day. 
This  is  an  inconvenience  which  might  be  remedied  by  shifting  the  astro- 
nomical epoch  to  coincidence  witb  the  civil.  There  is,  however,  another 
inconvenience,  and  a  ver^  serious  one,  to  which  both  are  liable,  inherent 
in  the  nature  of  the  day  itself,  which  is  a  local  pheenomenon,  and  com- 
mences at  different  instants  of  absolute  time,  under  different  meridians, 
whether  we  reckon  from  noon,  midnight,  sunrise,  or  sunset.  In  conse- 
quence all  astronomical  observations  require,  in  addition  to  their  date,  to 
render  them  comparable  with  each  other,  the  longitude  of  the  place  of 
observation  from  some  meridian,  commonly  respected  by  all  astronomers. 
For  geographical  longitudes,  the  Isle  of  Ferroe  has  been  chosen  by  some 
as  a  common  meridian,  indifferent  (and  on  that  very  account  offensive)  to 
all  nations.  Were  astronomers  to  follow  such  an  example,  they  would 
probably  fix  upon  Alexandria,  as  that  to  which  Ptolemy's  observations 

i 

'  See  the  remarkable  calculations  of  Mr.  Baily  relative  to  the  celebrated  solar  ecIipM 
which  put  an  end  to  the  battle  between  the  kings  of  Media  and  Lydia,  b.  c.  610, 
Sept.  30.    Phil.  Trans,  ci.  2-^0. 

*  "A.  month  in  law  is  a  lunar  month  or  twenty-eight  days,  (! !)  unless  otherwise  ex- 
pressed."— Blackilone,  ii,  chap.  9.  "A  lease  for  twelve  months  ia  only  for  forty-eight 
weeks."— /kid. 


n 


ii  'I 
m 


588 


on  LINES  OF  ASTRONOMY. 


SCI 


ti  ■ 


and  computations  were  reduced,  and  as  claiming  on  that  account  the  re- 
spect of  all  while  offending  the  national  egotism  of  none.  But  even  this 
will  not  meet  the  whole  difficulty.  It  will  still  remain  doubtful,  on  a 
meridian  180°  remote  from  that  of  Alexandria,  what  dyy  is  intend'?*.!  by 
any  given  date.  Do  whaj  we  will,  when  it  is  the  Mondn;  the  1st  of 
January,  1849,  in  one  part  of  the  world,  it  will  be  Sunday,  the  31st  of 
December,  1848,  in  anothtjr,  so  long  as  time  iii  reckon -d  by  Ivoal  u.iars. 
This  equivoque,  and  the  necessity  of  specifying  the  geO;(*raphical  locality 
as  an  element  of  the  date,  caxs  only  be  uot  over  b^^  a  reckoning  of  time 
which  refers  itself  to  some  event,  real  or  imaginary,  common  to  all  the 
globe.  Such  an  event  is  the  passage  of  th(?  sun  tbrough  thu  vf'r:;al 
oquinox,  or  rather  the  passage  of  an  iniaginary  sun,  supposed  to  move 
with  perfoct  equality,  through  a  vernal  equinox  supposed  free  v.ui  the 
inequalit  i'  s  of  nutation,  and  receding  upon  the  ecliptic  wi.i'.  perfect  uni- 
formity. The  rtc  ;nal  equiwox  is  variable,  not  only  by  the  effect  of  nuta- 
tion, but  by  tb'.t  of  thrt  inequality  of  precession,  resulting  from  the  change 
in  the  plane  of  the  ecliptic  due  to  planetary  perturbation.  Both  varia- 
tions are,  however,  periodical ;  the  one  in  the  short  period  of  19  years, 
the  other  in  a  period  of  enormous  length,  hitherto  uncalculated,  and 
whose  maximum  of  fluctuation  is  also  unknown.  This  would  appear,  at 
first  sight,  to  render  impracticable  the  attempt  to  obtain  from  the  sun's 
motion  any  rigorously  uniform  measure  of  time.  A  little  consideration, 
however,  will  satisfy  ua  that  such  is  not  the  case.  The  solar  tables,  by 
which  the  apparent  place  of  the  sun  in  the  heavens  is  represented  with 
almost  absolute  precision  from  the  earliest  ages  to  the  present  time,  are 
constructed  upon  the  supposition  that  a  certain  angle,  which  is  called  "  the 
sun's  mean  longitude,"  (and  which  is,  in  effect,  the  sum  of  the  mean  side- 
real motion  of  the  sun,  pl%ia  the  mean  sidereal  motion  of  the  equinox  in 
the  opposite  direction,  as  near  as  it  can  he  obtained  from  the  accumu- 
lated observations  of  twenty-five  centuries,)  increases  with  rigorous  uni- 
formity as  time  advances.  The  conversion  of  this  mean  longitude  into 
time  at  the  rate  of  860°  to  the  mean  tropical  year,  (such  as  the  tables 
assume  it,)  will  therefore  give  us  both  the  unit  of  time,  and  the  uniform 
measure  of  its  lapse  which  we  seek.  It  will  also  furnish  us  with  an  epoch, 
not  indeed  marked  by  any  real  event,  but  not  on  that  account  the  less 
positively  fixed,  being  connected,  through  the  medium  of  the  tables,  with 
every  single  observation  of  the  sun  on  which  they  have  been  constructed 
and  with  which  compared.  .     .  r         -i     -  ^,  ,.-     -i-  * 

(936.)  Such  is  the  simplest  abstract  conception  of  equinoctial  time.  It 
is  the  mean  longitude  of  the  sun  of  some  one  approved  set  of  solar  tables, 
converted  into  time  at  the  rate  of  360°  to  the  tropical  year.    Its  unit  is 


ri-;V 


account  the  re- 
But  even  thia 
doubtful,  on  a 
ia  intended  by 
dav  tjbe  Ist  of 
lay,  tho  3l8t  of 
by  k-jal  ii.tors, 
-aphical  locality 
iickoning  of  time 
ijiDon  to  all  the 
■ough  th:i  vcr;al 
upposed  to  mcve 
ed  free  .^- ni  th* 
I  v?i.i\  perfect  uni- 
the  effect  of  nuta- 
g  from  the  change 
tion.    Both  varia- 
)eriod  of  19  years, 
uncalculated,  and 
s  would  appear,  at 
ain  from  the  sun's 
ittle  consideration, 
["he  solar  tables,  by 
is  represented  with 
e  present  time,  are 
which  is  called  "the 
m  of  the  mean  side- 
1  of  the  equinox  in 
\  from  the  accumu- 
J  with  rigorous  uni- 
nean  longitude  into 
(such  as  the  tables 
me,  and  the  uniform 
Ish  us  with  an  epoch, 
hat  account  the  less 
n  of  the  tables,  with 
lave  been  constructed 

■  equinoctial  time.   It 
;erfsc<o/so?ar  tables, 

eal  year.    Its  unit  is 


EQUINOCTIAL  TIMB. 


589 


the  mean  tropical  year  which  those  tables  assume  and  no  other^  and  its 
epoch  is  the  mean  vernal  equinox  of  these  tables  for  the  current  year,  or 
the  instant  when,  the  mean  longitude  of  the  tables  is  rigorously  0,  accord- 
ing to  the  assumed  mean  motion  of  the  sun  and  equinox,  the  assumed 
epoch  of  mean  longitude,  and  the  assumed  equinoctial  point  on  which  the 
tables  have  been  computed,  and  no  otJier.  To  give  complete  effect  to  this 
idea,  it  only  remains  to  specify  the  particular  tables  fixed  upon  for  the 
purpose,  which  ought  to  be  of  great  and  admitted  excellence,  since,  once 
decided  on,  the  very  essence  of  the  conception  is  that  no  subsequent  altera- 
tion in  any  respect  should  he  madcy  even  when  the  continual  progress  of 
astronomical  science  shall  have  shown  any  one  or  all  of  the  elements  con- 
cerned to  be  in  some  minute  degree  erroneous  (as  necessarily  they  must,) 
and  shall  have  even  ascertained  the  corrections  they  require  (to  be  them- 
selves again  corrected,  when  another  step  in  refinement  shall  have  been 
made.) 

(937.)  Delambre's  solar  tables  (in  1828)  when  this  mode  of  reckoning 
time  was  first  introduced,  appeared  entitled  to  this  distinction.  According 
to  these  tables,  the  sun's  mean  longitude  was  0°,  or  the  mean  vernal  equi- 
nox occurred,  in  the  year  1828,  on  the  22d  of  March  at  1"  2'»  59*  05 
mean  time  at  Greenwich,  and  therefore  at  1"  12"  20»-55  mean  time  at 
Paris,  or  1"  56"  34'*55  mean  time  at  Berlin,  at  which  instant,  therefore, 
the  equinoctial  time  was  0"*  0"  O"  0»00,  being  the  commencement  of  the 
1828th  year  current  of  equinoctial  time^  if  we  choose  to  date  from  the 
mean  tabular  equinox,  nearest  to  the  vulgar  era,  or  of  the  6541st  year  of 
the  Juliau  period,  if  we  prefer  that  of  the  first  year  of  that  period. 

(938.)  Equinoctial  time  tLen  dates  from  the  mean  vernal  equinox  of 
Delambre's  solar  tables,  and  its  unit  is  the  mean  tropical  year  of  these 
tables  (365*'242264.)  Hence,  having  the  fractional  part  of  a  day  ex- 
pressing the  difference  between  the  mean  local  time  at  any  place  (suppose 
Greenwich)  on  any  one  day  between  two  consecutive  moan  vernal  equi- 
noxes, that  difference  will  be  the  same  for  every  other  day  in  the  same 
interval.  Thus,  between  the  mean  equinoxes  of  1828  and  1829,  the 
difference  between  equinoctial  and  Greenwich  time  is  0'''956261  or  O"" 
22"  57"  0»-95,  which  expresses  the  equinoctial  day,  hour,  minute,  and 
second,  corresponding  to  mean  noon  at  Greenwich  on  March  23,  1828, 
and  for  the  noons  of  the  24th,  25th,  &o.,  we  havtt  only  to  substitute  Id, 
2d,  &c.,  for  0',  retaining  the  same  decimals  of  a  day,  or  the  same  hours, 
minutes,  &c.,  up  to  and  including  March  22, 1829.  Between  Greenwich 
noon  of  the  22d  and  23d  of  March,  1829,  the  1828th  equinoctial  year 
terminates,  and  the  1829tb  commences.  This  happens  at  0'''286003,  or 
at  G"  51"  50*-66  Greenwich  mean  time,  after  which  hour,  and  until  the 


m 

U 


540 


OUTLINES  OF  ASTRONOMY. 


o 


next  noon,  the  Greenwich  hour  added  to  equinoctial  time  864'-056261 
will  amount  to  more  than  865-242264,  a  complete  year,  which  has  there- 
fore to  be  subtracted  to  'got  the  equinoctial  date  in  the  next  year,  cor- 
responding to  the  Greenwich  time.  For  example,  at  12^  0*  0*  Greenwich 
mean  time,  or  O'-dOOOOO,  the  equinoctial  time  will  be  864-956261 -f 
0-500000= 365-456261,  which  being  greater  than  865-242264,  shows 
that  the  equinoctial  year  current  has  changed,  and  the  latter  number 
being  subtracted,  we  get  0''-218977  for  the  equinoctial  time  of  the 
1829th  year  current  corresponding  to  March  22,  12^  Greenwich  mean 
time. 

(989.)  Having,  therefore,  the  fractional  part  of  a  day  for  any  one  year 
expressing  the  equinoctial  hour,  &c.,  at  the  mean  noon  of  any  given  place, 
that  for  succeeding  years  will  be  had  by  subtracting  0' -242264,  and  its 
multiples,  from  such  fractional  part  (increased  if  necessary  by  unity,)  and 
for  preceding  years  by  adding  them.  Thus,  having  found  0-198525  for 
the  fractional  part  for  1827,  we  find  for  tuo  fractional  parts  for  succeeding 
years  up  to  1853  as  follows': —  .^       *         .    „  , 

•110981 
•868717 
•626453 
•384189 
•141925 
•899661 

*  These  numbers  differ  from  those  in  the  Nautical  Almanack,  and  would  require  to 
be  substituted  for  them,  to  carry  out  the  idea  of  equinoctial  time  as  above  laid  down. 
In  the  years  1828-1833,  the  late  eminent  editor  of  that  work  used  an  equinox  slightly 
differing  from  that  of  Delambre,  which  accounts  for  the  difference  in  those  years.  In 
1834,  it  would  appear  that  a  deviation  both  from  the  principle  of  the  text  and  from  the 
previous  practice  of  that  ephemeris  took  place,  in  deriving  the  fraction  for  1834  from 
that  for  1833,  which  has  been  evei  since  perpetuated.  It  consisted  in  rejecting  the 
mean  longitude  of  Delambre's  tables,  and  adopting  Bessel's  correction  of  that  element. 
The  effect  of  this  alteration  was  to  i.isert  3"  3**68  of  purely  imaginary  time,  between 
the  end  of  the  equinoctial  year  1833  and  the  beginning  of  1834,  or,  in  other  words,  to 
make  the  interval  between  the  noons  of  March  22  and  23,  1834, 24i>  3"  3i'68,  when 
reckoned  by  equinoctial  time.  In  1835,  and  in  all  "ubsequent  years,  a  further  depar- 
ture from  the  principle  of  the  text  took  place  by  substituting  Bessel's  tropical  year  of 
365-2422175,  for  Delambre's.    Thus  the  whole  subject  has  fallen  into  confusion. 

[Note  on  Art.  932. 
The  reformation  of  Gregory  was,  after  all,  incomplete.  Instead  of  ID  days  lie  ought 
to  have  omitted  12.  The  interval  from  Jan.  1,  a.  d.  1,  to  Jan.  1,  a.d.  1582,  reckoned 
as  Julian  years,  is  577460  days,  and  as  tropical,  577448,  with  an  error  not  exceeding 
O'-Ol,  the  difference  being  12  days,  whose  omission  would  have  completely  restored  the 
Julian  epoch.  But  Gregory  assumed  for  his  fixed  point  of  departure,  not  that  epoch, 
but  one  later  by  324  years,  viz.  Jan.  1,  *  <«.  325,  the  year  of  the  Council  of  Nice; 
assuming  which,  the  difference  of  the  two  reckonings  is  S'-SOS,  or,  to  the  nearest  whole 
number,  10  days.] 


1828 

•956261 

1835 

•260413 

1842 

•664665 

1848 

1829 

•713997 

1836 

•018149 

1843 

•322301 

1849 

1830 

•471733 

1837 

-775885 

1844 

•080037 

1850 

1831 

•229469 

1838 

-533621 

1845 

•837773 

1851 

1832 

•987205 

1839 

•291357 

1846 

•595509 

1852 

1833 

•744941 

1840 

-049093 

1847 

•363245 

1853 

1834 

•602677 

1841 

•806829 

1849 
1850 
1851 
1852 
1853 


•384189 
•141925 


m  864«-956261 
^hich  has  there-     I  H 

le  next  year,  cor-     •  B 

>  0*  0*  Qreenwich 
»e  864-956261  + 
;5-242264,  shows 
he  latter  number    I  g 

3tial  time  of  the    ■  ;         | 
Qreenwich  mean    ■  ^ 

y  for  any  one  year 

of  any  given  place, 

0O-242264,  and  its 

Hupy  by  unity,)  and    |  2  ^ 

ound  0198525  for  '^ 

)arts  for  succeeding    ■  ^aa 

3  «      . 

1848  \  -110981  ■  X      H  ^       '^ 

IDiO         •SAa717  ■    M         ^     -4 


868717  I  M      ^   ^ 

626453  ■  Q       p   g 


;?   fcf 


899661  1^^      „^g       g 


,  and  would  require  to 
le  M  above  Iwd  down, 

led  an  equinox  slightly  ■  pj  q 

nee  in  those  years.    In  ■  g  « 

f  the  text  and  from  the  ■  ho 

a  fraction  for  1834  from  ■  §  >• 

nsisted  in  rejecting  the  ■  M 

rrectionof  that  element.  ■  q 

Mfftnary  time,  between  |  ^ 

I,  or,  in  other  words,  to 

L834,  24"  3»  3.-68,  when  _ 

t  years,  a  further  depar-  ^         g 

Jessel's  tropical  year  of 

en  into  confusion. 

tead  of  10  days  he  ought 
1,  A.D.  1582,  reckotied  ■         oj, 
an  error  not  exceeding  B        g 
completely  restored  the  ■ 
—sparture,  not  that  epoch, 
>f  the  Council  of  Nice; 
,  or,  to  the  nearest  whole 


I 


I 


541 


:   1  «  : 

i  11  i  ■ 

W  W  O  C^  W  M  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  00  CO  CO  CO  CO  CO  CO 


a  a 


-  as 


,^  e^. 


•s 


Vi  JZ  *^  ' 


^/^^--L-SiS  §a,>;S3J)«  aajfcgiiSlS-C  M^ 


I 


03 


e0'(»<»oeoeoeo-*"'*»««'*«o«ooe^oo-<o»i-ic0'00>ow 
a>9>o>oooooooooo.7i>7i.H^^cpeoiOcp'^'^ 

C4  C^  C^  SO  CO  CO  CO  cO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO 


N^»-o»M*«McocococO'«.«o»i-i»-oeooe^'^090Ji-H 


i 

1 
a 

•     » 

*1 

■s 
a  , 

s 

'I  : 

=     Of. 

.S|.SgSi 

S.aS.|>  j-s  j-SS.  . _ 

•a  J; '3  a^  «  «*  a '2  "3  P  «  3  S  8  S—  "ja  a.B-='7  - 

ty^OO-^fcOJOw  «  fc  PM  O  tJ  tJ  P5  O  O  M  J  <  u  C3 
}i,  0  a  >s      w  >«.5a  a  oa  >s  a  '53.  «  >«.'Si  w  «   «s  a .«  x'w  * 


^^ 


£ 


i-4'^^'«t<^>n<ooococococO'^l<>n'<)co<st-ooaococco 


i*»e<«NN*«C*WMNC<»»e^e^ff«e<»s)M 


t» 00  ••  ••  o  ^  o  «o  h-  oo  00  oc  ce  »!<  ©  CO  -n  »  o 

t-oooo<-<e^««oo»o»o»o»oi-i-<wesco-*'^-*-r'0 


re^e^Mc^e^e^e^e^c^iMe^ 


ejs 


s.a 


•9  rS  a  a 


>> 


a    :  S 


•3  ai  £  m£ 


M 


542 


APPENDIX. 


>''•« 


Ot! 
H 

ta 


t 


I 


£ 


I 


I' 


I 


J  . 

Id 


CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  CO  cO 


f-lP-l'^K»«s<et~^.co0>oel-llft^.aE>ao•-lc«co^>Aoe 


u  »  k  oa^ea.  »■'>*-»> 


^co»*i*-e^r3t>.i~.ioo>oe^o»Neoo»i-ieoeo<o«t»Oi-i 
^^e^^Me^Me^f^c^e^w««coeoeo«MMPSWWMM 


oNco«e»-ie<)«oeO'toce»i-ioo"-iwoooMNi«io«oo»o 
coeOfOM"*^^1^'ft'<^lrt«©«o^-^_■-^-cpop(»ooaoQO<»o» 


=2 

5 


-a  •-  ?  •§  .tJ  «»    •  O  -a . 


5. 


5.2 


i    :    =   -C j 

2    ■  .S  .2  3  :a  _ 
<S5.2gg3e'<Su<p  •- «j  .age 

^S4&7hiait>«c9CC«S  i<  •'3  hS«ctC7'oA<0 


.5 

&•  o 


a*e 


«  B-ca»o  e  >s 


9  O  CO  O  00  a>  O  00  »•  ^  >0  »>  CO  04 '^  o»  a>  ^  b- o 


ie^»«e4e^(Ne4e^Me^»4e4e^ 


CO      a><n»4a>^  ao  ^  t~>  <o  eo '^  <e  t- i-i  co  oo  co  eo  «e  a> 

o   I  e^  >o  «>  o  i-(  c^  e^  CO  >A  o  <o  t- CO  OD  00  o  e  e  i-i  04  94  04 


I  04  C4  04  94  04  04  04 


^ 

> 


Ifg 


•  *c    :  •*;   •  3    •   t   •   •    : 

SS^S!^"     2-3  J 
-I  -3  "3  S  g  s  -c  r§  9  -2 


»      ■•       Menu  s^o^sMV/K  ^^<c%  >.  w  a  W  o 


««a  « 


't'ilT 


APPBN    ^X. 


548 


}  oo  00  o>  9* 
}  M  eo  rs  « 

i|<  ■«f  •^  -fs  >£> 
o  M  fo  eo  eo 


•       •       • 

:  :   : 
:  :  ! 


I  ^1  ift  «e '-'  »i 

)  PS  PS  p5  eo  eo 

3  »H  »H  r^  M  M 

}  M  M  8*9  O  W 


H 

CO 

GQ 


5 


m 

H 

Ph 

O 

QQ 

H 

H 
H 

n 

H 

Pt4 

O 

pa 


M  N  «  w  e<  e^ 


03 


^9^      >()  e  (0  <e  <e  »•  >A  M  «e  1-4  ^  ^  <e  ».  »<  e» ';^  ^^ « 

P9  ^  »-l  W  e<S  ^  O  e<9  O  IH         M  ■>*  ■*  i«  M  1-1  PS  M  rt 


e  00  ao  PS 


ooaops«^aoei-tusb-iH^oeps»i<e«ea»xs 

FH  M  »4  ^  »«  PS        W  PS  lO  Xi -♦  •^  <0  N  ii»  US 


O  i«  "I"    OO  O  US  PS 
"»*»-.   •*  rH  PS  O  US  «  PS  *»  -^ 
i-«  N  iH  W    il  fH  iH 


^usi-ips<oaoe^f->aoi-ie4e 

»*  00  «■•  OC;  h- 00  0»  1-1  »»  PS 


a>  00 


»4aops^•o^cpfH^^efH'^M»4ep^-'^7 

l0^usa>^'4•IH^^4^^-^4^•PS'^•Huso30» 

rH  *»  rH  us    >*N^'^e^    PS  i-t  us  PS  W  us 


^eps      •-•cor*ooooust^«e£nususc)S»>»-t>ooe><e<e 

C4   us  us  e^   W  PS  ■«»<  PS  rH  us      PS  w '(t  fh  w  ^  ^ 

O  t»P>    fH  us  CO  t«US  KS '^  ^  us  us  0»  PS  e  ^  OS  IH  ei  O  FH 

fH  fH        f4  fH  O 


o»^-«oooO'it«OF^e^us<ooo^.PS«F^|-^us^us 
itOP5t-.i^e')0>MMooo>ooMcO'»f"e-i>'S«oe^oo»o» 
F^«ooooi(S(Mtoc^e^>no>"stoiooO'fsi-H'^<ou5t>.FH 
usoot^P8uso4'<SMoouspso"sooao'*ooe^F-iFH«o»>. 
inco«ops<oi~~9>Me^ocoaoF-it>'«t<toa>a>c«:>to«ooo 
oorHO»usi-cooPse^oo><»'-<«ou»t-.PSao'>*u)'»)<o 
e40ooFHe4(3C4ri»40FHF-iF4^9^ooe^o 

oooooooeooooeooeeeoeoo 


00  <o 

us  OS 

*»  t^ 

0>  o 
<o  o 
a>  ^* 

oo  »< 

C4 


»«  ao 

FH  us 

PS  CO 

us  to 
^  a> 
Jt  (^ 
2  00 

OS  <D 


o»oot>e<so^o»ust-us«euso 

■»(t»*<^0'»)IODF-(0»FHt-0»e^r-( 

Ni^FH'*)(osi7it-©NO»WMus 

PSPS'OUsi>Ot-F<P<t--^W<J9 

09oe^->*'^ooo»i-ii-iFHO»oooo 

i-IPSPSPSPSC4PSUSUSUSUS«0<0 


FH 

fH  ^ 
«0  00 

*•  us 

O  ») 

e^  PS 

O  PS 


t>  ea 

FH  M 

00  00 
FH  N 

eq  CO 

OS  i 

us  00 

to  te 


FH  PS  <o 


If 


I 


ii 


:<k-     ■ 

FH  <e  e  PS  e  e  e  e>  e  e  e  e  e  o  e  o  e  o  o  F"  ;>  v. 

ooFHe»itotoFHOt>e^totoususto  —  oootO'v:.  r^<r 

o>PSoe>ooi>-aooo»FHr-iHti<ooPSusi(saitoooc»a 

epso<o<oooooooFHusoc«so>oooooootot»r':cio 

*>.psopSFHH»<pHus«o«©«etoOD-»«<oooMoe<»ooN«o 

oofr>o»»«PS«eoooDMH*t-t-aot-«ot-.e^oMoopS 

PSt»OUS»«PSC»SPSPS"<(<'^UJ>flU5«t-t-FHMU5FHO 

ooiHFH»4e4»4»«»4»4»4C4e4^^^»4PSusd»e>9 

r^  OS 


O 

I 


b  :   :   :   :.S   M   : 


:  ®   : 

:  a.  : 

:  *   : 

•  o  J 


.3 


4> 

-  _  C  5  !* 


544 


APPENDIX. 


o 


i 

H 
xa 

•< 

H 
H 
H 

O 
P4 


•88 

II 


a'  ao  lA  i-l  9  to 
■*     n     w 


,  t^  "¥  t^  M*  ^ 
A  O  M  »*  M  M 


si:; 


IC  M  M  O  O 

»«  T"  a>  ^  4* 

e  l-l  O  >H  9 


o  e  e  < 


[1 

MM  ^~^^^ 

ill 


e  e  e  <o  e 
e  ^  o  M  o 
e  f4  00  s>  f-i 
e^  CO  t<  to  ^ 


Sg 


ssss 

e  Fri  i4  lO 
to  gt  ^  i-i 
o«  tort  <« 


<-4  0>  oil  to 

•o  M  "rt  eo 

to  oc  'fl  eo 
iH  >o  f4  a>  e 
<e  e  CO  « 


^ 


•«*  CO  < 


M 


«?3g 

to  t-l  0»  to 

■><<  O  ^  00 

e  o  »<  i-( 

1-1  CO 


l-»  Hi  O  "-a  S  l->  •-,  S  •-»  Sli;  Hj  •<  OQ  ■<  Hj  H»  H, 

1-4  ooee>ei-<t<^e«eo^oooa>-^  op 

o  ^  o  x)  >o  m  '^  >r>  ^  >o  o  lo  >n  >A  -f  o  '* 

00  ooaoaoaoaocoaoaciaoaoasoocococio  oo 


s 


<fiOM>A«fHOOaO^O'^fOH<^00>A«>A9>(teojS 

1)1        1-1  lO        iH  fH  CO  •^  CO  W  ■*  t-l  *<  iH  eo  w        w^ 

ecoa>»4ooM^''»0>co^>r<<4*^iH«pHtoi/)ooD<^ 

COCOM^S^^iHCOpHCO^iH         CO         CfiAlHM^^ 

«Oi-io^i<»©'OOeo'«i-iooiHu»^o»to^Miotoo 
«i-ie<oeo^e^0>aotoaoi-ie>me4i-ii-i'4<i-icotoco 

pS         pH  »<  i-<  iH  M  94  CO  e4         — <  M  W  CO  iH  l-l  IH  CO 

II  II  II 


i 

! 


e>iHO^OpO>9«iHe»0>^>eCOCO(>9otl>pO>«QprH»o 

Wco•a^o•^^«50o7^^>o6>c«^a96>ot•9a««b 

■^  US        irj  ^  CO  CO  11  pH  C«  •^ 'il  ^  i-l  1-H  1-t  ^ '♦I  CO  ff<  rH  «o 

p4coocoo«o<o^coa>eeooo^«ei-i»iQoe>i-He4 
e^  ^  CO  c<      lA  ^  e^  CO  ^      »<  »<  i-*  m  ^  m  e^  co  ih 

'^aoe>»4co-4O>HiH'^to>/tioo>'^topHiii-t0>toto 

t-e<10>COCOO'0^toi-lpHCOrHtoiO'^NMi-IOO«^ 
iH         CO        COM  CO  II  pH  1-t         i-l  pH  N  pH 


e 

i 

as 


a  S.2  a 


o 
A 

o 
a 


•       .     4*     *     w       •        • 

s^  t;  i:  fe  B  2 


§.S  «  a 


—    m    "    O 
03    B    1    1 

"■-22 

-  o. 

« 


»'■»•»■ 


APPENDIX. 


515 


II 


JVbfe.— The  elements  of  the  orbits  of  Mercury,  Venus,  the  Earth,  Mars,  Jupiter, 
Saturn,  and  Uranus,  are  those  given  by  the  late  F.  Baily,  Esq.,  in  his  "  Astronomical 
Tables  and  Formulas,"  and  are  the  same  with  those  which  form  the  basis  of  Uelam- 
bru's  tables,  embodying  the  formulae  of  Laplace.  'I'ho  elements  of  Uranus  and  Nop* 
tune  can  only  be  regarded  os  provisional;  those  of  the  former  requiring  consideruble 
corrections,  necessitated  by  the  discovery  of  Nopiuiie,  but  which,  not  being  yet  finally 
ascertained,  by  reason  of  the  uncertainty  still  attending  on  the  mass  and  elenionts  of 
the  latter  planet,  it  was  thought  better  to  leave  the  old  elements  untouched  than  to  give 
an  imperfect  rectification  of  them.  The  masses  of  the  planets  are  those  most  recently 
adopted  by  Encke  (Ast.  Nachr.  No.  443),  on  mature  consideration  of  all  the  ouiho< 
rities,  that  of  Neptune  excepted,  which  is  I'rof.  Pierce's  determination  from  Bund's 
and  Lassell's  observation  of  the  satelliio  discovered  by  the  latter.  The  densities  are 
Hansen's  (A.N.  443.) 

The  elements  of  Vesta,  Juno,  Ceres,  and  Pallas,  are  the  osculating  elements  for 
1850,  computed  by  Encke  (A.  N.  636.)  [Those  of  Flora  ore  from  the  computotions 
of  Brunnow  (A.  N.  645);  of  Victoria,  Villarceaux  (A.  N.  741);  of  Iris,  Schubers 
(A.  N.  730);  of  Metis,  Wolfers  (A.  N.  764);  of  Hebe,  Luther  (A.  N.  -21);  of  Par- 
thenope,  Galen  (A.  N.  757);  of  Aslraea,  D' Arrest  (A.  N.  6vJ6);  of  Egeria,  D' Arrest 
(A.  N.  749);  of  Irene,  Vogel  and  Riimker  (.\.  N.  765);  and  of  Hygeia,  Santini  (A. 
N.  702.) 

Of  these  last>mentioned  small  planets,  Hygeia,  Pnrthcnope,  and  Egeria  were  dis- 
covered by  Dr.  Gasparis,  at  Naples,  on  April  12,  1849,  May  11  and  Nov.  2,  1850, 
respectively;  Iris,  Flora,  Victoria,  and  Irene,  by  Mr.  Hind,  on  Aug.  13  and  Oct.  18, 
1847,  Sept.  13,  1850,  and  May  19,  1851,  respectively.  The  elements  of  the  recently- 
discovered  small  planets  may  undergo  material  corrections  from  further  observation. 
Irene  has  a  blue  colour  and  a  faint  nebulous  envelope.  The  orbits  of  Astrtea  and 
Hygeia  approach  at  one  point  (their  common  node)  within  0'006  of  the  radius  of  the 
earth's  orbit.  It  will  not  be  long  before  the  planets  themselves  come  within  that  prox- 
imity to  each  other  (A.  N.  752.)  Victoria  and  Aetriea  are  subject  to  variations  of 
brightness,  which  indicate  rotations  on  their  axes,  and  dark  spots  (A.  N.  760.)  D'  Arrest 
(A.  N.  752)  remarks  that  a  relation  subsists  between  the  excentricities  of  the  orbits  of 
the  small  planets,  and  the  inclinations  of  the  planes  in  which  they  lie  to  the  sun's 
equator,  the  more  excentric  orbits  being  the  more  inclined.  While  these  sheets  pass 
through  the  press,  another,  yet  unnamed,  is  announced  by  M.  do  Gasparis.] 

III. 

Synoptio  Table  of  the  Elements  of  the  Orbits  of  the  Satel- 
lites, so  FAR  AS  THEY  ARE  KNOWN.  14 

1.  The  Moon. 

Mean  distance  from  earth 59'-96435000 

Mean  sidereal  revolution 27''-321661418 

Mean  synodical  ditto 29^*530588715 

Exoentricity  of  orbit 0054844200 

Moan  revolution  of  node 6793''-39]OSO 

Mean  revolution  of  apogee 3232<*-575343 

Mean  longitude  of  node  at  epoch 13°  53'  17"'7 

Mean  longitude  of  peri^e  at  do 266    10     7*5 

Mean  ineUnation  of  orbit 5     8  47  *9 

Mean  longitude  of  moon  at  epoch 118    17     8*3 

Mass,  thatof earth  being  1 0011399 

Diameter  in  miles 2153 

Density,  (hat  of  the  earth  being  1 0*5657 

*  The  distances  are  expressed  in  equatorial  radii  of  the  primaries.  The  epoch  is  Jan.  1, 
1801,  unless  otherwiae  expressed.    "The  periods,  &.c.  are  expressed  in  mean  solar  dayf . 
36 


H,  t 


546 


APPENDIX. 


& 

O 

09 

s 


&t3 


-1" 


"S  S. 
|§« 
II 

d 


CO  >Q  ^-  0> 

e^  CO  0>  o 
e<s  M  <r  «o 
t«  n  CO  M 
f-te^  oo '« 


e4  o  o 

'f  o>  o 

l-H  W  O 

?  ^  ? 

o>  4<  i-l 
M  ■^  CO 


*«>«*«■«* 


O  iH  i«  ■^ 
04 


O  O  o  o  o 


%  e  e  o  00 
o  e^  >o 


w  rt  i-i 


o  oe  o  o 


o  '^  e^  eo 

00  CO  O  00 
^  94  lO  e> 

O  to  CO  9> 


«eco  04  M 
o  ea  <o  o 

•fl  eo  CO  t» 

•    •    •    • 

a  CO  CO  60  ^ 

CO  cO  CO  ^ 

^  00  CO  CO  CD 

■OiHcot-te 


^ 


a 

a 

.S3 

5 


o 
u 

« 

9 

« 

a 
e 
a 


.a 

4i» 
S 

.a 


a 

CO 
CO 

« 

O 
O 

.a 


H 

■< 
GO 

O 
M 
H 


2  g 


rHNCO  ■* 


a 

n 

.9 


13 

OQ 

3 


•3 


o 

tS 


S  a 

*>  .s 


CO 


^» 

1 

00 

1 

»                                 CO 

^4  ^^  G^ 

0     sgas 

^ 

#" 

*S 

M 

E 

C^  »«  ^.  gg[ 

Til  e<i  04 »« 

fl 

?999 

g 

ooeo 

H 

o 

A 

•** 

•s 

.  oocooDooo'^    :oo 

Q) 

^  -^eoTf-td      M    :■* 

-S  . 

It 

-S5!5§^S  Ito 

l« 

<e t- CO »-co t>    .o> 

o>n«>-«e^>Qco    :« 

i 

«>«      eoeoeoiH    "m 

» 

o  o              e      o 

o«S3.S9   :o 

otco-M'M'Mco    :ea 

1' 

J^SfiftOS   :S 

^ 

. 

9 

i»iA<oao  w  e      e 

.  * 

e  94  0>  a>  M  X)      o» 

J9 

«0  f-l  CO  CO  >A  ^     1    X) 
CO  CO  CO  00  XJ  PH  ■+•« 

•3 

§ 

"'♦^••SJSS 

* 

d 

•O  0»  *- *- 0»  00  M         <* 

1 

•m       M       fHN        ■<# 

1 

M»«CO  00  r-l  lAi-)         CO 
g  CO  XS  i-t  1^  M  ■«  ».  >A 

i 

-o»ooi-it-Ne4ff«*» 

1 

•0erHi-te4^>A«4A 
^  ©4  *^ 

«4 

O 

tarn 

1 

i 

E 

K 

1 

1   e 

1 

s 

!i 

•1 

^ 

!8WP';fiP3HWV3 

■   ••«•••• 

p^e^co'^ocet^oo 

^2    -s 


4)    V 

s-s. 
»:! 

-1 

!•§ 

OB 
OB    O 

« 

«  e 
"  m 
-u  « 

A  « 


1  £ 

u 

«  o  S 

_r  *  j3 

1  fe  ■ 

■3  «  a 

a  ® 
-W  S 

•.op    Ji    § 


o  ^ 


55 


«  2^  a<«.S 

^^s«"  - 
S'g.'i'aJ. 

;2  C  a  «  S  'S 

grfj  a-  a-" 

_.  a  B  Sag 

a-M^atsl 

o 


1 


■?  ©  5  3  B-a 

^'  -9  w  u  ®      ' 

r:    A     Z     Ik    41  . 


5  o  a  *'C  g 
•*•  o  .a  «  g 

« "O  '■§  -^  **  I 

B-a  " 

.S  00  •     "a  2 
?  2.5.3  3  g 

B  ■*    _  a        <a 

2«-  2.2      " 

-  H  !.,_•  s 

•a.    ^P  -5 


Ba«g.«    - 
_   m   «    ► 


to 


B    •."B  3      -a 
«  ►»  ,  2  _«  a 


a  o 


o     2  y- 


"  s 
si, 

o 

go 

l-s 

eg  O 

»  o 

"  m 

IS  3 

43   « 


^2 

*  o  © 


a."  o 
•S  2 


8 

h5 


a 


•■ago.' 


£.2 


■g'S  « -"^ 


(3  a 


•I      ^ 

o  "  So »  5  *s 


11  s^  a-. 


S       8 


•c 


«»«  U)«a 


5-- 


■3  --    Q«  a 
•"•   ^   >   © 


»*  8 

B 


©•Bo 


"S  -O  ■■§  ^  **  ® 

•t!    5    ?    b    41  ^ 


B  o 


•'•  *    S    _        .B 


5 

CO 


«>  •B  ^ 
B^         B 


""■aa^ 


a 

B 
CO  c-"   Ci-:   9 


SSw 


*S'S.g'"g 


i»   B  <Q       .„ 


la 


4  > 


U) 


§0  ® 


B    .,5  5"*  ja 


U) 


2 1*^  5 -0.5 
»-      MS 


APPENDIX. 


647 


fl 
i 

•a 

s 

I 


"S  2.J.  « 

®  «  2.  B 
,A  A  C  B 

,2  i«  £ 
B  "» ,5 

-•sill 

-.sill 

•3  "•"EH  g 
a  (D  »      fl 

•••  -fl  "W  fll 

„«  ©-:.S 

£  _  Boo  a 

-S '«  H  o  « 

00     S  M  « 

5,00   w  oJ3 

ja" 
H 


isg 


n 

I 

O 
n 


B 

a  . 


1 


0 

n 

*-H 

00 

»< 

0 

n 

, 

0 

A 

, 

to 

.a 

rH 

t- 

^ 

B 

0) 

m 

;>< 

»? 

. 

»^ 

^. 

00 

00 

O  CO  OS  It)  o 
/-  OS  N  ift  »H 

•H  T-i  e^  '^  at 


I 


i 


s  a 

a 

us  cw   c«>  0. 

•««- 

H  N  1H    ft 

•0-* 

00  0  n  00  h» 

iH  iH  eo  0 

O 


13 


3* 

•f 


tH  fr)  C4 '<4I  u»  «e 


! 


f 


s 
a 

o 
o 


iih 


W 


t 
I.I' 


548 


APPENDIX. 


o 
"•^l 


P3 


< 
H 

CO 

H 

H 
H 

H 

cc 
H 
» 

O 

A 
o 

M 

H 

o 

OQ 
H 
IZ! 

H 


'0 

1846.  Feb.  25. 

9"  13m  35" 

116°  28'  34" 

102    39    36 

30    55      7 

3-15021 

0-793629 

2042-24 

Direct. 

1844,  Sept.  2. 

11"  36"  53« 

342°  31'   15" 

63    49    31 

2    54    45 

3-09946 

0-617256 

1993^-09 

Direct. 

t 

1843.  Oct.  17. 
3"  42y  16* 
19°  34    19" 
209    29    19 
11    22     31 

3-81179       . 
0-555962 
2718''-26 
Direct. 

i 

1846.  Feb.  11. 

0"    2"  50« 

109°    5'   47" 

245    56     58 

12    34    14 

3-50182 

0-755471 

2393''-52 

Direct 

1 

1845.  Aug.  9. 

15"  11"  11" 

157°  44'   21" 

334    19     33 

13      7     34 

2-21640 

0-847436 

1205''.23 

Direct 

•n  ,  5 

l-H  (M  «<»  o>  ift                       « 

.  W  eO  O         «0  rH  M<  ^ 

l>                      o»  OS^  g 

•  -  o            K.  OS  oo  -3 
geso-orH           e^PiH 

,      ••   3  d   •i  (t  <•  Oi 

d 

I 

o 

.a 


o 
o 


a 

s> 

O 

a 
'3 

a 

a 
o 


O    00 

5.2 


«s  a  "  «  § 

£  o  *sPh     . 
g  .2  fc  o;  o- 

«^*o. 


o 
o: 


-I 


«  «  £  TS  2 


o  0  g  3 


.53  0)  Q  ^  ^ 
'S  .a  <"  .^.S  ._ 
:g  s  ®  to  o  § 

■*»  a-o  §«g«g 

»  o   «         ®   * 

2  «  *  a  .-S  -3 


a.2'S 


n  _ 
0*0 


»r.9  .t;  -3  _  . 

o^  nag 
g  M  M  go  W) 

"3  S  a  _  a  2 
•a  3  «a  ^  .2  ■§ 

i2i*^°  - 


-3 
a  -  «« 

.tH  ^     iO  jfl 

^  ^  .s  « -S 

.-  =:    a  .2  o 

^  "  ^  ~  a 


pq  a  rt  35  k 

•  .2  V  o  o  9 

ns  jr «».  o  a 
«M  o  SH 


CO 


*  a  Ir„« 

a  "^ 

O  *s  W 

^  2  ®  o 

gag* 
-  a  •>! 

-SI'S.!  . 


o 


arH  a  2 


go 


o  o 


0) 

"  *  » -S  .S 
S  « .2  -S  « 
.9  .-2  ■§  o  -a 

I  III? 


O  3' 

a  g  " 

.3  "  a 

'.2  '■*^  o  M  ® 


■13  «"  iH 

r   4)  q  *! 


I  >si  .a  a  -2  o 

a  "  "  fl  § 

o   S   S   cS   >. 

-°  o  MS:? 

f-i  ,-.   j3   ^ 


3  a 


y  SI 


<i> 


ja  o  M  « •"* 


ad  a  5 

©O  o  »  • 

'S     ,  a  fl  9 


INDEX. 


N,  B.  The  referencos  are  to  the  articles,  not  to  the  pages. 

...  attached  to  a  reference  number  indicates  that  the  reference  extends  to  the  article  cited,  and 
several  subsequent  in  succession. 


M.^ 


Aberration  of  light  explained,  329.  Its 
uranographical  effects,  333.  Of  an 
object  in  motion,  335.  How  distin- 
guished from  parallax,  805.  System- 
atic, 862. 

Aboul  We/a,  705. 

Acceleration,  secular,  of  moon's  mean 
motion,  740. 

Adams,  606.  767. 

Adjustment,  errors  of,  in  instruments, 
136.  Of  particular  instruments.  (See 
those  instruments.) 

JEtna,  portion  of  earth  visible  from,  32. 
Height  of,  32.  note. 

Air,  rarefaction  of,  33.  Lav  of  density, 
87.  Refractive  power  affected  by 
moisture,  41. 

Airy,  O.  B.  Esq.,  his  results  respecting 
agure  of  the  earth,  220.  Researches 
on  perturbations  of  the  earth  by  Ve- 
nus, (  .6.  Rectification  of  the  muss 
of  Jupiter,  757. 

Algol,  821. 

Altitude  and  azimuth  instrument,  187. 
— s.  Equal,  method  of,  188. 

Andromeda,  n^ebula  in,  874. 

Angl/f  of  position,  204.  Of  situation,  311. 

AngUf.  measurement  of,  163. 167.  Hour, 
107 

Anjiilar  velocity,  law  of,  variation  of, 
350. 

Anomalistic  year,  384. 

AnoM/ily  '•a  planet   499. 

AnniUyir  nebulae,  875. 

Aper  </  ftberrs»»:ion,  ZAZ. 
343.     '/trefrmtioti,  UZ 


Of  parallax, 
Solar,  854. 


Of  abofyiflg  stmrt,  Wi. 

A]^'^'''  '4  mt»ftt>  4i¥i.     Period  of  its  re- 

V',l<ition,  ml. 
Apsides,  4CMt      Motion  of  investigated, 

#76.     Application   to  lunar,   676 ... 

Motion  of,  inu8trat«i4  by  experiment, 


692.  Of  planetary  orbits,  694.  Li- 
bration  of,  G94.  Motion  in  orbits 
very  near  to  circles,  696.  In  excen- 
tric  orbits,  697... 

Areas,  Kepler's  law  of,  490. 

Argelander,  his  researches  on  variable 
stars,  820...,  on  sun's  proper  motion, 
854. 

Argo,  nebulae  in,  887.  Irregular  star  n 
in  constellation,  880. 

Ascension,  right,  108.  {See  Right  ascen- 
sion.^ 

Asteroids,  their  existence  suspected  pre- 
vious to  their  discovery,  505.  Ap- 
pearance in  telescopes,  525.  Gravity 
on  surface  of,  625.  Elements,  Appen- 
dix, Synoptic  Table. 

Astrcea,  discovery  of,  605. 

Astrometer,  783,  784. 

Astronomy.  Etymology,  11.  General 
notions,  11. 

Atmosphere,  cornHhition  of,  33...  Possi- 
ble limit  of,  30.  its  waves,  37.  Strata, 
37.  Causes  refraction,  38.  Twi- 
light, 44.  Total  mass  of,  148.  Of 
Jupiter,  613. 

Attraction  of  a  sphere,  445 — 450.  (See 
Gravif  'iin.) 

Avgmtntaiion  of  moon's  apparent  dia- 
meter, 404. 

Augustus,  his  reformation  of  iwistakes 
in  the  Julian  calendar,  (919).  Era 
of,  926. 

Australia,  excessive  summer  tempera- 
ture of,  369. 

Axis  of  the  earth,  82.  Rotation  perma- 
nent, 56.  Miy  .'  of  the  earth's  orbit, 
373.     Of  sun's  rotation,  392. 

Axis  of  a  planetary  orbit.  Momentary 
vaination  of,  caused  by  the  tangential 
force  only,  058.  660.  Its  variationg 
periodical,  601...  invariability  of, 
and  how  understoof'.,  668. 


Azimuth,  103.- 
187. 


-and  ultitude  instrument, 
(549) 


660 


INDEX. 


o 


fc».. 


B. 

Barometer,  natixre  of  its  indication,  33. 

Use  in  calculating  refraction,  43.    In 

determining  heights,  287. 
Belts  of  Jupiter,  512,     Of  Saturn,  614. 
Benzenberff's   principle    of   coUimation, 

179. 
Bessel,  his  results  respecting  the  figure 

of  the  earth,  220.     Discovers  parallax 

of  61  Cygni,  812. 
Biela's  comet,  579... 
Biot,  his  aeronautic  .isccnt,  32. 
Bode,  his  (so  called)  law  of  planetary 

distonces,  505.     Violated  in  the  case 

of  Neptune,  507. 
Borda,  his  principle  of  repetition,  198. 
E'Uvard,   his   suspicion   of  extraneous 

influence  on  Uranus,  760. 


CoBsar,  his  reform  of  the  Soman  calen- 
dar, 917. 

Calendar,  Julian,  917.    Gregorian,  014... 

Cause  and  effect,  439,  and  note. 

Centre  of  the  earth,  80.  Of  the  sun,  462. 
Of  gravity,  3G0.  Revolution  about, 
452. 

Centrifugal  force.  Elliptic  form  of  earth 
produced  by,  224.  Illustrated,  225. 
Compared  with  gravity,  229.  Of  a 
body  revolving  on  the  earth's  surface, 
452. 

Ceres,  discovery  of,  505. 

ChMis,  Prof.,  506,  note. 

Charts,  celestial.  111.  Construction  of, 
291...     Bremiker's,  506,  and  note. 

Chinese  records  of  comets,  574.  Of  ir- 
regular stars,  831. 

Chronometers,  how  used  for  determining 
differences  of  longitude,  255. 

Circle,  arctic  and  antarctic,  94.  Verti- 
cal, 100.  Hour,  106.  Divided,  163. 
Meridian,  174.  Reflecting,  197.  Re- 
peating, 198.     Galactic,  793. 

ClepsK/drc,  loO. 

Clock,  151.  Error  and  rate  of,  how 
found,  253. 

^louds,  greatest  height  of,  34.  Magel- 
lanic, 892... 

Clusters  of  stars,  804...  Globular,  867. 
Irregu'ir,  869. 

CoUimation,  lino  of,  155. 

CoUtmaior,  178... 

Coloured  stars,  851... 

Coiures,  ':>07. 

Comets f  554.    Set^n  in  daytime,  655. 


590.  Tails  of,  556... 566.  599.  Ex- 
treme tenuity  of,  558.  General  de- 
scription of,  560.  Motions  of,  and 
described,  561...  Parabolic,  564.  El- 
liptic, 567...  Hyperbolic,  5G4.  Di- 
mensions of,  565.  Of  Halley,  567... 
Of  Cffisar,  573.  Of  Encke,  576.  Of 
Biela,  579.  Of  Fnye,  584.  Of  Lex- 
ell,  585.  Of  De  Vico,  586.  Of  Bror- 
sen,  587.  Of  Peters,  588,  Synopsis 
of  elements  (Appendix).  Increase  of 
visible  dimensions  in  receding  from 
the  sun,  571.  580.  Grout,  of  1843, 
589...  Its  supposed  identity  with 
many  others,  594...  Interest  attached 
to  subject,  597.  Cometary  statistics, 
and  conclusions  therefrom,  001. 

Gommensurabiliiif  (near)  of  mean  mo- 
tions ;  of  Saturn'.s  satellites,  550.  Of 
Uranus  and  Neptune,  669,  and  note. 
Of  Jupiter  and  Saturn,  720.  Earth 
and  Venus,  726.     Effects  of,  719. 

Compensation  of  disturbances,  how  ef- 
fected, 719.  725. 

Compression  of  terrestrial  spheroid,  221. 

Configurations,  inequalities  depending 
on,  655... 

Conjunctions,  superior  and  inferior,  473. 
Perturbations  chiefly  produced  at,  713. 

Consciousness  of  effect  when  force  is  ex- 
erted. 430. 

Constellations,  60.  301.  How  brought 
into  view  by  change  of  latitude,  52. 
Rising  and  setting  of,  58. 

Copernican  explanation  of  diurnal  mo- 
tion, 76.  Of  apparent  motions  of  sun 
and  planets,  77. 

Correction  of  astronomical  observations, 
324...  s.  Uranographical  summary, 
view  of,  342... 

Culminations,  125.  Upper  and  lower, 
126. 

Cgcle,  of  conjunctions  of  disturbing  and 
disturbed  planets,  719.  Metonic,  926. 
Callippic,  ib.  Solar,  921.  Lunar  922. 
Of  indictious,  923. 


Day,  solar,  lunar,  and  sidereal,  143. 
Ratio  of  sidereal  to  solar,  305.  909. 
Oil.  Solar  unequal,  146.  Mean 
ditto  invariable,  908.  Civil  and  astro- 
nomical, 147.     Intercalary,  916. 

Bai/s  elapsed  between  principal  chrono- 
logical eras,  92(5.  Rules  for  reckon- 
ing between  given  dates,  927. 


i...566.  699.     Ex- 
568.     General  de- 
Motions   of,  and 
'arabolic,  564.    El- 
lerbolic,  6G4.     Di- 
Of  Halley,  567... 
f  Encke,  576.     Of 
ye,  684.     Of  Lex- 
co,  586.     Of  Bror- 
rs,  688.     Synopsis 
idix).     Increase  of 
in  receding  from 
.     Great,  of  1843, 
sed    identity   with 
.  Interest  attached 
!ometary  statistics, 
erefrom,  601. 
sar)   of  mean  mo- 
satellites,  650.    Of 
me,  669,  and  note, 
iturn,  720.     Earth 
Effects  of,  719. 
turbances,  how  ef- 

itrial  spheroid,  221. 
ualities    depending 

r  and  inferior,  473. 
fly  produced  at,  713. 
it  when  force  is  ex- 

01.  How  brought 
ige  of  latitude,  52. 

of,  68. 

on  of  diurnal  mo- 
rent  motions  of  sun 

mical  observations, 
raphical  summary. 

Upper  and  lower, 

of  disturbing  and 
^9.    Metonic,926. 
921.  Lunar  922. 


ind  rddereal,  143. 

to  solar,  305.  909. 

[ual,    146.      Mean 

8.    Civil  and  astro- 

ercalary,  916. 
principal  chrono- 
llules  for  reckon- 

dates,  927< 


INDEX. 


551 


Declination,  106.     How  obtaine'l,  296. 

Definilionii,  82... 

Degree  of  meridian,  how  measured,  210... 
Error  admissible  in,  216.  Length  of 
in  various  latitudes,  216.  221. 

Diameters  of  the  earth,  220,  221.  Of 
planets,  synopsis,  Appendix.  {See 
also  each  planet.) 

Dilatation  of  comets  in  receding  from 
the  sun,  578. 

Dione,  548. 

Discs  of  stars,  316. 

Distance  of  the  moon,  403.;  the  sun,  357.; 
fixed  stars,  807.  812... ;  polar,  106. 

Districts,  natural,  in  heavens,  302. 

Disturbing  forces,  nature  of,  609...  Ge- 
neral estimation  of,  611,  Numerical 
values,  6  J  2.  Unresolved  in  direction, 
614.  Resolution  of,  in  two  modes, 
616.  618.  EflFects  of  each  resolved 
portion,  616...  On  moon,  expressions 
of,  676.  Geomtrical  representations 
of,  676.  717. 

Diurnal  motion  explained,  58.  Paral- 
lax, 339.     Rotation,  144. 

Double  refraction,  202.  Image  micro- 
meter, a  new,  described,  203.  Comet, 
580.     NebuliB,  878. 

Double  Stars,  833...  Specimens  of  each 
class,  835.  Orbitual  motion  of,  839. 
Subject  to  Newtonian  attraction,  843. 
Orbits  of  particular,  843.  Dimen- 
sions of  these  orbits,  844.  848.  Co- 
loured, 851...  Apparent  periods  af- 
fected by  motion  of  light,  863. 

Dove,  his  law  of  temperature,  370. 


E. 


Earth.  Its  motion  admissible,  15.  Sphe- 
rical form  of,  18.  22...  Optical  eflect 
of  its  curvature,  25.  Diurnal  rot.ition 
of,  62.  Uniform,  56.  Permanence 
of  its  axis,  57.  Figure  spheroidal, 
219...  Dimensions  of,  220.  Elliptic 
figure  a  result  of  theory,  229.  Tem- 
perature of  surface,  how  maintained, 
366.  Appearance  as  seen  from  moon, 
436.  Velocity  in  its  orbit,  474.  Dis- 
turbance by  Venus,  726. 

Eclipses,  411...  Solar,  420.  Lunar,  421... 
Annular,  425.  Periodic  return  of, 
426.  Number  possible  in  a  year,  426. 
Of  .Jupiter's  witellites,  538.  Of  Sa- 
turn's, 549. 

h-'riptit,  305...  Its  plane  slowly  varia- 
sle,  306.     Cause  of  this  variation  ex- 


plained, 640.    Poles  of,  307.    Limits, 
solar,  412.     Lunar,  427. 

Egyptians,  ancient,  their  chronology,  912. 

Elements  of  a  planet's  orbit,  493.  Varia- 
tions of,  662...  Of  doable  star  orbits, 
843.  Synoptic  tablo  of  planetary, 
&c..  Appendix 

Ellipse,  variable,  of  a  plunet,  653.  Mo- 
mentary or  osculating,  C54. 

Elliptic  notion  a  consequence  of  gravi- 
tation, 446.  Laws  of,  489...  Their 
theoretical  explanation,  491. 

Ellipticity  of  the  earth,  221. 

Elongation,  341.  Greatest,  of  Mercury 
and  Venus,  467. 

Enceladus,  548,  note. 

Encke,  comet  of,  676.  His  hypothesis 
of  the  resistance  of  the  ether,  577. 

Epoch,  one  of  the  elements  of  a  planet's 
orbit,  496.  Its  variation  not  inde- 
pendent, 730.  Variations  incident 
on,  731.  744. 

Equation  of  light,  335.  Of  the  centre, 
876.  Of  time,  379.  Lunar,  452. 
Annual,  of  the  moon,  738. 

Equator,  84. 

Equatorial,  185. 

Equilibrium,  figure  of,  in  a  rotating  body, 
224. 

Equinoctial,  97.     Time,  935. 

Equinox,  293.  303. 

Equinoxes,  precession  of,  312.  Its  ef- 
fects, 313.  In  what  consisting,  314... 
Its  physical  cause  explained,  642... 

Eras,  chronological  list  of,  926. 

Errors,  classification  of,  133.  Instru- 
mental, 135...  Their  detection,  140. 
Destruction  of  accidental  ones  by  tak- 
ing means,  137.  Of  clock,  how  ob- 
tained, 293. 

Establishment  of  a  port,  754, 

Ether,  resistance  of,  577. 

Evection  of  moon,  748. 

Excenfricities,  stability  of  Lagrange's 
theorem  respecting,  701. 

Excentricily  of  earth's  orbit,  354.  How 
ascertained,  377.  Of  the  moon's,  405. 
Momentary  perturbation  of,  investi- 
gated, 670.  Application  to  lunar 
theory,  688.  Variations  of,  in  orbits 
nearly  circular,  696.  In  exccntric 
orbits,  697.  Permanent  inequalities 
depending  on,  719. 


Facula,  338. 

Faye,  comet  of,  584,  and  Appendix. 


i  jM 


552 


INDEX. 


; 

.< 

m 

:5^ 

U) 

tMTW 

»H 

»< 

O 

f' 

'*if'l 

i- 

r 

**•-»? 

i 

•tt'ij^ 

•fW*, 

-f 

|<UIK« 

t 

O 

1 

i 

C9 

i 

^ 

S» 

Flora,  discovery  of,  606. 

Focus,  upper.  Its  momentary  change  of 
place,  670,  671.  Path  of,  in  virtue  of 
both  elements  of  disturbing  force,  704. 
Traced  in  the  case  of  the  moon's  vari- 
ation, 706...  And  parallactic  inequa- 
lity, 712.  Circulation  of,  about  a 
mean  situation  in  planetary  perturba- 
tions, 727. 

Force,  metaphysical  conception  of,  439. 

Forced  vibration,  principle  of,  650. 

Forces,  disturbing.   See  Disturbing  force. 


CK 


Galactic  circle,  793.  Polar  distance, 
lb. 

Galaxy  composed  of  stars,  302.  Sir  W. 
Herschel's  conception  of  its  form  and 
structure,  780.  Distribution  of  stars 
generally  referable  to  it,  786.  Its 
course  among  the  constellations,  787... 
Difficulty  of  conceiving  its  real  form, 
792.  Telescopic  analysis  of,  797.  In 
some  directions  unfathomable,  in 
others  not,  798. 

Galle,  Dr.,  606.  Finds  Neptuno  in  place 
indicated  by  theory,  768. 

Galloivay,  his  researches  on  the  sun's 
proper  motion,  856. 

Gasparis,  Sig.  De.  discovers  a  new  pla- 
net (Appendix). 

Gauging  the  heavens,  793. 

Gay  Lussac,  his  aeronautic  ascent,  32. 

Geocentric  longitude,  603.  Place,  371, 
497. 

Geodesical  jieasurements,  —their  nature, 
247... 

Geography,  111,  205... 

Globular  clusters,  865.  Their  dynami- 
cal stability,  866.  Specimen  list  of, 
807. 

Golden  number,  922. 

Goodricke,  his  discovery  of  variable  stars, 
821... 

Gravitation,  how  deduced  from  phacno- 
mena,  444...  Elliptic  motion  a  con- 
sequence of,  490... 

Gravity,  centre  of,  tee  Centre  of  gra- 
vity. 

Gravity  diminished  by  centrifugal  force, 
231.  Measures  of,  statical,  234.  Dy- 
namical, 235.  Force  of,  on  the  moon, 
433...  On  bodies  at  surface  of  the 
sun,  440.  Of  other  planets,  see  their 
names. 

Gregorian  reform  of  calendar,  915... 


H. 


Ilalley.     His  comet,  567.     First  notices 
proper  motions  of  the  stars,  852. 

Hansen.     His  detection  of  long  inequa- 
lities in  the  moon's  motions,  745... 

Harding  discovers  Juno,  605. 

Heat,  supply  of,  from  sun  alike  in  sum- 
mer and  winter,  368.     How  kept  up, 
400.    Sun's  expenditure  of,  estimated 
397.     Received  from  ttt  sun  by  di/ 
ferent  planets,  508.     Endured  by  or 
mets  in  perihelio,  592. 

Ilebe,  discovery  of,  505. 

Heights  above  the  sea,  bow  measured 
286.     Mean,  of  the  continents,  289. 

Heliocentric  place,  500. 

Heliorneirr,  201. 

Hemispheres,  terrestrial  and  aqueous,  284. 

Uerschel,  Sir  Wm.,  discovers  Uranus, 
605,  and  two  satellites  of  Saturn,  548. 
His  method  of  gauging  the  henveus, 
793.*  Views  of  the  structure  of  the 
Milky  Way,  786.  Of  nebular  subsi- 
dence*, and  sidereal  aggregation,  869, 
874.  His  catalogues  of  double  stars, 
835.  Discovery  of  their  binary  con- 
nexion, 839.  Of  the  sun's  proper  mo- 
tion, 854.  Classifications  of  nebulso, 
868,  879,  note. 

Horizon,  22.  Dip  of,  23, 195.  Rational 
and  sensible,  74.  Celestial,  98.  Arti- 
ficial, 163. 

Horizontal  point  of  a  mural  circle,  how 
determined,  176... 

Hour  circles,  106 ;  angle,  107 ;  glass, 
150. 

Hyperion,  Appendix,  Saturn's  satellites. 


lo'petus,  648.  :' 

Inclination  of  the  moon's  orbit,  400.  Of 
planet's  orbits  disturbed  by  orthogo- 
hil  force,  619.  Physical  importance 
of,  as  an  element,  632.  Momentary 
variation  of,  estimated,  033.  Crite- 
rion of  momentary  increase  or  dimi- 
nution, 635.  Its  changes  periodical 
and  self-correcting,  636.  Application 
to  case  of  the  moon,  638. 

Inclinations,  stability  of,  Lagrange  s  the- 
orem, 639.  Analogous  in  their  per- 
turbations to  exceutriciJes,  699. 

Indictions,  923. 

Inequality.  Parallactic  of  moon,  712. 
GreiU,  of  Jupiter  and  Saturn,  720... 


rial  and  aqueous,  284. 
,  'Jiscovers  Uranus, 
Bllites  of  Saturn,  548. 
auging  the  heavens, 
the  structure  of  the 
.  Of  nebular  subsi- 
eal  aggregation,  809, 
gues  of  double  stars, 
of  their  binary  con- 
■  the  sun's  proper  mo- 
jifications  of  nebula;. 


a  mural  circle,  how 
;  angle,  107;  glass, 
s,  Saturn's  satellites. 


INDEX. 


558 


vctic  of  moon,  712. 
•  and  Saturn,  720... 


Inequalities,  independent  of  excentricity, 
theory  of,  702..,     Dependent  on,  719. 
Intercalation,  916. 
Iris,  discovery  of,  605. 
Iron,  meteoric,  888. 

J. 

Julian  Period,  924.  Date,  930.  Re- 
formation. 918. 

Juno,  discofiry  of,  505. 

Jupiter,  physical  appearance  and  de- 
scription of  511.  Ellipticity  of,  512. 
Belts  of,  512.  Gravity  on  surface, 
508.  Satellites  of,  510.  Seen  without 
satellites,  543.  Recommended  as  a 
photometric  standard,  783.  Elements 
of,  &c.  {See  Synoptic  Table,  Appen- 
dix.) 

Jupiter  and  Saturn,  their  mutual  pertur- 
bations, 700,  720... 

K. 

Kater,  his  mode  of  measuring  small  in- 
tervals of  time,  150.  His  collimator, 
178. 

Ktplcr,  his  laws,  352,  487,  489.  Their 
pliysical  interpretation,  490... 


Lagging  of  tides,  753. 

Lagrange,  his  theorems  respecting  the 
stability  of  the  planetai-y  system,  669, 
639,  701. 

Laplace  accounts  for  the  secular  accele- 
ration of  the  mu>on,  740. 

Lassell,  his  discovery  of  the  satellite  of 
Neptune,  524.  Of  an  eighth  satellite 
of  Saturn,  Appendix.  Re-discovers 
two  of  Ihe  satellites  of  Uranus,  551. 

Latitude,  terrestrial,  88.  Parallels  of, 
89.  How  ascertained,  119,  129.  R6- 
mer's  mode  of  obtaining,  248.  On  a 
spheroid,  247.  Celestial,  308.  Helio- 
centric, how  calculated,  500.  Geo- 
centric, 503. 

Laws  of  nature  how  arrived  at,  139. 
Subordinate,  appear  first  in  form  of 
errors,  139.     Kepler's,  352,  487... 

Level,  spirit,  176.  Sea,  285.  Strata,  287. 

Leverrier,  50»;,  507,  767. 

Lexell,  com«t  «f,  685. 

Libration  of  liM  moon,  435.  Of  apsides, 
694. 

Light,  aberration  of,  331.    Velocity  of, 


831.  How  ascertained,  545.  Equa- 
tion of,  335.  Extinction  of,  in  tra- 
versing space,  798.  Distance  mea- 
sured by  its  motion,  802...  Of  certain 
stars  compared  wiUi  the  sun,  817... 
Effect  of  its  motion  in  altering  appa- 
rent period  of  a  double  star,  863. 
Zodiacal,  897. 

Local  time,  252. 

London,  centre  of  the  terrestrial  hemi- 
sphere, 284. 

Longitude,  terrestrial,  90.  How  deter- 
mined, 121,  251...  By  chronometers, 
265.  By  signals,  264.  By  electric 
telegraph,  262.  By  shooting  stars, 
265.  By  Jupiter's  satellites,  &c.,  266. 
By  lunar  observations,  267...  Celes- 
tial, 308.  Mean  and  true,  875.  He- 
liocentric, 500.  Geocentric,  503.  Of 
Jupiter's  satellites,  curious  relations 
of,  542. 

Lunation  (synodic  revolution  of  the 
moon),  its  duration,  418. 

M. 

Magellanic  clouds,  892... 

Magnitudes  of  stars,  780...  Common 
and  photometric  scales  of,  780...  and 
Appendix. 

Maps,  geographical,  construction  of,  273. 
Celestia:,  290...     Of  the  moon,  437. 

Mars,  phases  of,  484.  Gravity  on  sur- 
face, 508.  Continents  and  seas  of, 
510.     Elements  (Appendix). 

Masses  of  planets  determined  by  their 
satellites,  532.  By  their  mutual  per- 
turbations, 757.  Of  Jupiter's  satel- 
lites, 758.     Of  the  moon,  759. 

Menstrual  equation,  628. 

Mercator's  projections,  283. 

Mercury,  synodic  revolution  of,  472.  Ve- 
locity in  orbits,  474.  Stationary  points 
of,  476.  Phases,  477.  Greatest  elon- 
gations, 482.  Transits  of,  483.  Heat 
received  from  sun,  608.  Physical  ap- 
pearance and  description,  509.  Ele- 
ments of  (Appendix). 

Meridian,  terrestrial,  85.  Celestial,  101. 
Line,  87,  190.  Circle,  174.  Marc, 
190.  Arc,  how  measured,  213.  Arcs, 
lengths  of,  in  various  latitudes,  216. 

Messier,  his  catalogue  of  nebulae,  865. 

Meteors,  S98.  Periodical,  900...  Heights 
of,  904. 

Metis,  discovery  of,  505. 

Micrometers,  199. 


I 


Iji 


554 


INDEX. 


mmmt 

■Hi 
P 


ifi%  way.    (5m  Qalazy,  802.) 

Mimas,  560,  and  note. 

Mira  Geti,  820. 

i/bon,  her  motion  among  the  stars,  401. 
Distance  of,  403.  Magnitude  and  ho- 
rizontal parallax,  404.  Augmeuta- 
tion,  404.  Her  orbit,  406.  Revolution 
of  nodes,  407.  Apsides,  409.  Oc- 
oultation  of  stars  by,  414.  Phases 
of,  416;  Brightness  of  surface,  417, 
note.  Redness  in  eclipses,  422.  Phy- 
sical constitution  of,  429...  Destitute 
of  sensible  atmosphere,  431.  Moun- 
tains of,  480.  Climate,  431...  Inha- 
bitants, 434.  Influence  on  weather, 
482,  and  note.  Rotation  on  axis,  435. 
Appearance  from  earth,  436.  Maps 
and  models  of,  437.  Real  form  of 
orbit  round  the  sun,  452.  Gravity  on 
surface,  508.  Motion  of  her  nodes 
and  change  of  inclination  explained, 
638...  Motion  of  apsides,  676...  Va- 
riation of  excentricity,  688...  Paral- 
lactic inequality,  712.  Annual  equa- 
tion, 738.  Evection,  748.  Variation, 
705...     Tides  produced  by,  751. 

Motion,  apparent  and  real,  15.  Diurnal, 
62.  Parallactic,  68.  Relative  and 
absolute,  78...  Angular,  how  mea- 
sured, 149.  Proper,  of  stars,  862... 
Of  sun,  864. 

Mountains,  their  proportion  to  the  globe, 
29.     Of  the  moon,  430. 

Moiona  Roa,  32. 

Mural  circle,  168. 

N. 

Nabonassar,  era  of,  926. 

Nadir,  99. 

Nebulce,  classifications  of,  868,  879,  note. 
Law  of  distribution,  86i8.  Resolvable, 
870.  Elliptic,  873.  Of  Andromeda, 
874.  Annular,  876.  Planetary,  876. 
Coloured,  ib.  Double,  878.  Of  sub- 
regular  forms,  881,  882.  Irregular, 
883.  Of  Orion,  885.  Of  Argo,  887. 
Of  Sagittarius,  888.    Of  Cygnus,  891. 

Nebular  hypothesis,  872. 

Neiml&m  matter,  871.     Stars,  880. 

Nq^iwie,  discovery  of,  606,  768.  Pertur- 
bations produced  on  Uranus  by,  ana- 
lysed, 765...  Place  indicated  by  the- 
ory, 767.  Elements  of,  771...  Per- 
|k  turbing  forces  of,  on  Uranus,  geome- 
trically exhibited,  778.  Their  effects, 
774.., 


Newton,  his  theory  of  gravitation,  490... 
et  passim. 

Nodes  of  the  sun's  equator,  890.  Of  the 
moon's  orbit,  407.  Passage  of  pla- 
nets through,  460.  Of  planetary  or- 
bits, 495.  Perturbation  of,  620... 
Criterion  of  their  advance  or  recess, 
622.  Recede  on  the  disturbing  orbit, 
624...  Motion  of  the  moon's  theory 
of,  638.  Analogy  of  theur  variations 
to  those  of  perihelia,  69W 

Nomenclature  of  Saturn's  satellites,  648, 
note. 

Nonagesimal  point,  how  found,  310. 

Normal  disturbing  force  and  its  effects, 
618  Action  on  excentricity  and  pe- 
rihelion, 673.  Action  on  lunar  ap- 
sides, 676.  Of  Neptune  on  Uranus, 
its  effects,  776. 

Nnbeeulce,  major  and  minor,  892... 

Number,  golden,  922. 

Nutation,  in  what  consisting,  321.  Pe- 
liod,  322.  Common  to  all  celestial 
bodies,  323.  Explained  on  physical 
principles,  648. 

0. 

Obliquity  of  ecliptic,  303.  Produces  the 
variations  of  season,  362.  Slowly 
diminishing,  and  why,  640. 

Observation,  astronomical,  its  peculiari- 
ties, 138. 

Occultation,  perpetual,  circle  of,  118. 
Of  a  star  by  the  moon,  413...  Of  Ju- 
piter's satellites  by  the  body,  541. 
Of  Saturn's,  649. 

Olbers  discovers  Pallas  and  Vesta,  605. 
His  hypothesis  of  the  partial  opacity 
of  space,  798. 

Opacity,  partial,  of  space,  798. 

Oscillations,  forced,  principle  of,  650. 

Orbits  of  planets,  their  elements  (Ap- 
pendix) of  double  stars,  843.  Of 
comets.     {See  Comets.) 

Orthogonal  disturbing  force,  and  its  ef- 
fects, 616,  619. 

Orthographic  projection,  280. 

P. 

Palitzch  discovers  the  variability  of  Al- 
gol, 821. 

Pallas,  discovery  of,  606. 

Parallactic  instrument,  186.  Inequality 
of  the  moon,  712.  Of  planets,  718. 
Unit  of  sidereal  distances,  804.  Mo- 
tion, 68. 


r  gravitation,  490... 

uator,  890.    Of  the 

.  Passage  of  pla- 
Of  planetary  or- 

irbation  of,  620... 
advance  or  recess, 

;he  disturbing  orbit, 
the  moon's  tlieory 
of  tli^  variatioua 

Ua,  69# 

urn's  satellites,  648, 

low  found,  310. 
orce  and  its  effects, 
excentricity  and  pe- 
.ction  on  lunar  ap- 
leptune  on  Uranus, 

i  minor,  »92... 

i. 

onsisting,  321.     Pe- 

mon  to  all  celestial 

plained  on  physical 


,  303.     Produces  the 
ason,    362.      Slowly 
why,  640. 
micalj  its  peculiari- 

aal,   circle  of,   118. 

uoon,  413...     OfJu- 

by  the  body,  641. 

lias  and  Vesta,  605. 
the  partial  opacity 

space,  798. 

principle  of,  650. 

their  elements  (Ap- 

)le  stars,   843.     Of 

nets.) 

Qg  force,  and  its  ef- 

tion,  280. 


he  variability  of  Al- 

;  505. 

snt,  185.  Inequality 
Of  planets,  713. 
iistances,  804.     Mo- 


^!-" 


INDEX. 


555 


Parallax,  70.  Geocentrio  or  diurnal, 
889.  Heliocentric,  341.  Horizontal, 
855.  Of  the  moon,  404.  Of  the  sun, 
857,  479,  481.  Annual,  of  stars,  800. 
How  investigated,  805...  Of  particu- 
lar stars,  812,  818,  815.  Systematic, 
862. 

Peak  of  Teneriffe,  82. 

Pendulum-o\ock,  89.  A  measure  of  gra- 
vity, 285. 

Penumbra,  420. 

Perigee  of  moon,  406. 

Perihelia  and  exeentricities,  theory  of, 
670... 

Perihelion,  368.  Longitude  of,  495. 
Passage,  496.  Heat  ebdured  by  co- 
mets in,  592. 

Period,  Julian,  924.    Of  planets  (App.). 

Periodic  time  of  a  body  revolving  at  the 
earth's  surface,  442.  Of  planets,  how 
ascertained,  486.  Law  of,  48.  Of  a 
disturbed  planet  permanently  altered, 
734... 

Periodical  stars,  820...     List  of,  825. 

Perspective,  celestial,  114. 

Perturbations,  602... 

Peters,  his  researches  on  parallax,  815 

Phases  of  the  moon  explained,  416.  a 
Mercury  and  Venus,  465,  477.  Of 
superior  planets,  484. 

Photometric  scale  of  star  magnitudes,  780. 

Piazzi  discovers  Ceres,  505. 

Pigott.  variable  stars  discovered  by, 
824... 

Places,  mean  and  true,  874.  Qeometrio 
and  heliocentric,  871,  497. 

Planetary  nebultu,  876. 

Planets,  456.  Zodiacal  and  ultra-zodia- 
cal, 457.  Apparent  motions,  459. 
Stations  and  retrogradations,  459. 
Beference  to  sun  as  their  centre,  462. 
Community  of  nature  with  the  earth, 
463.  Apparent  diameters  of,  464. 
Phases  of,  465.  Inferior  and  superior, 
467.  Transits  of  {see  Transit)  Mo- 
tions explained,  468.  Distances,  how 
concluded,  471.  Periods,  how  found, 
472.  Synodical  revolution,  472.  Su- 
perior, their  stations  and  retrograda- 
tions, 485.  Magnitude  of  orbits,  how 
concluded,  485.  Elements  of,  495. 
{See  Appendix  for  Synoptic  Table.) 
Densities,  508.  Physical  peculiarities, 
&c.,  509...  Illustration  of  their  rela- 
tive sizes  and  distances,  526. 

Plantamour,  his  calculations  respecting 
the  double  comet  of  Biela,  683. 


Pleiades,  865.  Assigned  by  M'&dler  as 
the  central  point  uf  the  sidereal  sys- 
tem, 861. 

Plumb-line,  direction  of,  23.  Use  of,  in 
observation,  175. 

Polar  distance,  105.  Point,  on  a  mural 
circle,  170,  172. 

Poles,  83.     Of  ecliptic,  307. 

Pole-star,  69.  Useful  for  finding  the 
latitude,  171.  Not  always  the  same, 
318.  What,  at  epoch  of  the  building 
of  the  pyramids,  319. 

Pores  of  the  sun's  surface,  387. 

Position,  angle  of,  204,     Micr-meter,  ib. 

Precessionof  the  equinoxes,  312.  In  what 
consisting,  314...  Effects,  813.  Phy- 
sical explanation,  642. 

PrcBsepe,  Cancri,  865. 

Priming  and  lagging  of  tides,  753. 

Principle  of  areas,  490.  Of  forced  vibra- 
tions, 650.  Of  repetition,  198.  Of 
conservation  of  vis  viva,  663.  Of  col- 
limation,  178. 

Problem  of  three  bodies,  608. 

Proklems  in  plane  astronomy,  127... 
309... 

Projection  of  a  star  on  the  moon's  limb, 
414,  note. 

Projections  of  the  sphere,  280... 

Proper  motions  of  the  stars,  862.  Of  tho 
sun,  853. 

Pyramids,  819. 

Radial  disturbing  force,  615... 

Radiation,  solar,  on  planets,  508.  On 
comets,  692. 

Rate  of  clock,  how  obtained,  293.     . 

Reading  off,  methods  of,  165. 

Reflexion,  observations  by,  173. 

Refraction,  88.  Astronomical  and  its 
effects,  89,  40.  Measure  of,  and  law 
of  variation,  43.  How  detected  by 
observation,  142.  Terrestrial,  44. 
How  best  investigated,  191. 

Repetition,  principle  of,  198. 

Resistance  of  ether,  577. 

Retrogradations  of  planets,  459.  Of 
nodes.     {See  Nodes.) 

Rhea,  548,  note. 

Right  ascension,  108.  How  determined, 
293. 

Rings  of  Saturn,  dimensions  of,  514. 
Phenomena  of  their  disappearance, 
515...  Equilibrium  of,  518...  Mul- 
tiple, 621,  and  Appendix.     Appear- 


Ml 


656 


INDEX. 


CO 


m 


anoe  of  from  Saturn,  622.     Attraotloo 

of  on  a  point     ithin,  785,  note. 
Ritienhouae,  his  pi  iuciple  of  collimation, 

178. 
Roi^se,  Earl  of,  his  great  reflector,  870, 

882. 
Rotation,  diurnal,  58.     Parallactic,  C8. 

Of  planets,  509...     Of  Jupiter,  512. 

Of  fixed  Btara  on  their  axes,  820. 


S. 


Saros,  426. 

Satellites,  of  Jupiter,  511.  Of  Saturn, 
518,  547.  Discovery  of  an  eighth 
(Appendix).  Of  Uranus,  523,  552. 
Of  Neptune,  524,  558.  Used  to  de- 
termine masses  of  theiv  primaries, 
682.  Obey  Kepler's  laws,  o38.  Eclipses 
of  Jupiter's,  535...  Other  phaenomena 
of,  540.  Their  dimensions  und  masses, 
540.  Discovery,  544.  Velocity  of 
light  ascertained  from,  645. 

Saturn,  remarkable  deficiency  of  density, 
508.  Rings  of,  514.  Physical  descrip- 
tion of,  514.  Satellites  uf,  547,  and 
Appendix.  (See  also  elements  in  Ap- 
pendix.) 

Sea,  proporti;in  of  its  depth  to  radius  of 
the  globe,  ;< ! .  Its  action  in  modelling 
the  exi ■..•lUi'l  irvm  of  the  earth.  227. 

Seasons  (■•■-'hiiiu: A,  3(52...  Temperature 
of,  <i'>\:>. 

Sector,  zeuitb,  192. 

Secular  variatiyns,  C55. 

Selcnoffraphy,  4Z7.  .;     ..'  u 

Sextant,  193... 

Shadow,  dimensions  of  the  earth's,  422, 
428.  Cast  by  Venus,  467.  Of  Jupi- 
ter's satellites  seen  on  disc,  540. 

Shooting  stars  used  for  finding  longi- 
tudes, 265.  Periodical,  900.  (Sec 
Meteors.) 

Sidereal  time,  110,  910.  Year.  (See 
Year.)    Day.     (See  Day.) 

Signs  of  zodiac,  380. 

Sirius,  its  parallax  and  absolute  light, 
818. 

Solar  cycle,  921. 

Sphere,  95.  Projections  of,  280.  Attrac- 
tion of,  735,  note. 

Spheroidal  form  of  Earth  (see  Earth)  pro- 
duces inequalities  in  the  moon's  mo- 
tion, 749. 

^ots  on  Sun,  389... 

Stars  visible  by  day,  61.  Fixed,  777... 
Their    apparent    magnitudes,   778... 


Comparison  by  an  ostromet'  ",  783. 
Law  of  distribution  over  hoavenn, 
785...  alike  in  iiher  hemisiihoro,  71M. 
Parallax  of  vt.aun,   815.     Discs  of, 

816.  Ileal    iaa  and   absolute  light, 

817.  Periodical,  820.  Temporary, 
827.  Irregular,  830.  Missing,  882. 
Double,  838...  Coloured,  851,  and 
note.  Proper  motions  of,  862.  Irre- 
gularities in  motions  not  verified,  859. 
Clusters  of,  864...  Nebulous,  879... 
Nebulous-double,  880. 

Stationary  points  of  planets,  459.  How 
determined,  475.  Of  Mercury  and 
Venus,  476. 

Stcreographic  projection,  281. 

Stones,  meteoric,  898.  Great  shower  of, 
ib. 

Struve,  hia  researches  on  the  law  of  dis- 
tribution of  stars,  793.  Discovery  of 
parallax  of  a  Lyraa,  813.  Catalogue 
and  observation  of  double  stars,  885. 

Struve,  Otto,  his  researches  on  proper 
motions,  854. 

Style,  old  and  new,  932. 

Sun,  oval  shape  nr,d  great  size  on  hori- 
zon explained,  47.  Apparent  motiou 
not  uniform,  34.  Orbit  elliptic,  349. 
Greatest  and  least  distances,  850. 
Actual  distance,  357.  Magnitude, 
358.  Rotation  on  axis,  859,  390. 
Mass,  860.  Physical  constitution, 
886.  Spots,  ib...  Situation  of  its 
equator,  890...  Mncullferous  zones 
of,  898.  Atmosphere,  895.  Tempe- 
rature, 396.  Expenditure  of  heat, 
397.  Eclipses,  420.  Density  of,  417. 
Natural  centre  of  planetary  system, 
462.  Distance,  how  determined,  170. 
Its  size  illustrated,  526.  Action  in 
producing  tides,  751.  Proper  motion 
of,  854...  Absolute  velocity  of  in 
space,  858.  Central,  speculations  on, 
861. 

Sunsets,  two,  witnessed  in  one  day,  26. 

Survey,  trigonometrical,  nature  of,  274. 

Synodic  revolution,  418.  Of  sua  and 
moon,  ib. 


Tangential  force  and  its  effects,  618. 
Momentary  action  on  perihelia,  673. 
Wholly  influential  on  velocity,  660. 
Produces  variations  of  axis,  ib... 
Doubles  the  rate  of  advance  of  lunar 
apsides,  686.  Of  Neptune  on  Uranus, 
and  its  effects,  774. 


vfi 


a  astromot'  •,  788. 
ion  over  hoavenf, 
er  hetnisplicrc,  7VM. 
in,  815.  Discs  of, 
ind  absolute  ligbt, 
820.  Temporury, 
$80.  Missing,  882. 
>cloured,  851,  and 
lions  of,  862.  Irre- 
ins  not  verified,  859. 
.  Nebulous,  879... 
880. 

planets,  459.     How 
Of  Mercury  and 

ion,  281. 

.     Great  shower  of, 

:s  on  the  law  of  dis- 
793.     Discovery  of 
ae,  813.     Catalogue 
f  double  stars,  835. 
learches  on  proper 

132. 

great  size  on  hori- 

Apparent  motion 

Orbit  elliptic,  349. 

ist  distances,   850. 

357.      Magnitude, 

n    axis,   869,   390. 

raical    constitution. 

Situation   of  its 

^Inculifcrous  zones 

ere,  395.     Tempe- 

cnditure   of   heat. 

Density  of,  447. 

)lanetary  system, 

w  determined,  -470. 

626.     Action  in 

Proper  motion 

ite  velocity   of  in 

i[,  speculations  on, 


1 


d  in  one  day,  26. 
al,  nature  of,  274. 
118.     Of  suu  and 


its  effects,  618. 
on  perihelia,  673. 
on  velocity,  660. 

I    of    axis,    ib... 

advance  of  lunar 
»ptune  ou  Urnnus, 


INDEX. 


Teleteope,  164.  Its  application  to  astro- 
nomical instruments,  117. 

Telescopic  tighti,  invention  of,  168,  note. 

Temperature  of  earth's  surface  at  differ- 
ent seasons,  806,  In  South  Africa 
and  Australia,  869.    Of  the  sun,  890. 

Tethys,  r)48,  note. 

Theodolite,  192.  Its  use  in  surveying, 
276. 

T/i  'try  of  instrumental  errors,  141.  Of 
gravitation,  490...  Of  nebulous  sub- 
sidence and  sidereal  aggregation,  872. 

TidcSf  a  system  of  forced  oscillations, 
661.  Explained,  760...  Priming  and 
lagging  of,  753.  Periodical  inequali- 
ties oi,  766.  Instances  of  very  high, 
766. 

Time,  sidereal,  110,  827,  911.  Local, 
129,  162.  Measures  angular  motion, 
149.  How  itself  measured,  150... 
Very  small  intervals  of,  160.  Equi- 
noctial, 257,  926...  Measures,  units, 
and  reckoning  of,  906... 

Titan,  648,  note. 

Titius,  Prof.,  his  law  of  planetaij  dis- 
tances, 506,  note. 

Trade  winda,  239... 

Transit  instrument,  159... 

7Van«iV«  of  stars,  162.  Of  planets  across 
the  sun,  467.  Of  Venus,  479...  Mer- 
cury, 483.  Of  Jupiter's  satellites 
across  disc,  640.  Of  their  shadows, 
549. 

Transparency  of  space,  supposed  by  01- 
bers  imperfect,  798. 

Transversal  disturbing  force,  and  its 
effects,  615... 

Trigonometrical  survey,  274. 

Tropics  98,  380. 

Twilight,  44. 

t. 

Umbra  in  eclipses,  420.  Of  Jupiter,  638. 

Uranography,  111,  800. 

Uranographical  corrections,  842...  Pro- 
blems, 127...  809... 

Uranus,  discovery  of,  605.  Heat  received 
from  sun  by,  608.    Physical  descrip- 


tion of,  6J:i.  Satellites  of,  661. 
turbations  of  by  Neptune,  760... 
observations  of,  760. 


657 

Per- 
Old 


Of 
474 


Vanishing  point  of  parallel  lines,  116. 

Line  of  parallel  planes,  117. 
Variation  of  the  moon  explained,  706... 
Variations  of  elements,  653.     Periodical 

and  Hc     \ar,  666.     Incident  on  the 

V  "•.  of  sun  not  uniform, 

sun  not  uniform,  861. 

jry,  Venus,  and  Earth, 

.1,  .c,   646.      Of  shooting 

stars,  HUy,  904. 

Venus,  synodic  revolution  of,  472.  Sta- 
tionary points,  476.  Velocity  of,  474. 
Phases,  477.  Points  of  greatest 
brightness,  478.  Transits  of,  479. 
Physical  description  and  appearance, 
509.  Inequality  in  earth's  motion 
produced  by,  726.  In  that  of  the 
moon,  743... 

Vernier,  97. 

Vertical,  prime,  102.     Circles,  100. 

Vesta,  discovery  of,  605. 

W. 

Weight  of  bodies  in  different  latitudes, 
322.  Of  a  body  on  the  moon,  508. 
On  the  sun,  4ru. 

Winds,  trade,  240... 

'        Y. 

Year,  sidereal,  806.  Tropical,  388. 
Anomalistic,  384,  and  day  incommen- 
surable, 913.  Leap,  914.  Of  confu- 
sion, 917.  Beginning  of,  in  England, 
change^  982. 

Z. 

Zenith,  99.     Sector,  192. 

Zodiac,  305. 

Zodiacal  light,  899. 

Zones  of  climate  and  latitude,  882. 


THE  END. 


Il 


^'^<,i 


/ 


\ 


^ 

.^^1^ 


IMAGE  EVALUATION 
TEST  TARGET  (MT-3) 


{* 


'4l 


4is 


H 


1.0 


I.I 


«J  Bi    122 


Sf  U&   H2.0 


gi.25  ,u  |;4 

< 

6" 

» 

Photographic 

Sciences 

Corporation 


''^^ 


<> 


V 


23  WBT  MAM  STRUT 

«MnSTiR,N.Y.  i4sao 
(71«)I73-4S03 


v\ 


tn 


59 


* 

V  \ 

■^     m.. 

*>    •■>■ 'T   " 

■-  ■'"^t'-j--" V*"  ,■■■■■  •'■'j-^ ^^r?" 

;;"-ui    '    i'x*  ..v,yf;,^V, ^. 

*      ■\ 

■f' 

\    • 

■'.•■'■                                .i 

,.  •-►«:;  ^_-v.   - 

'.--.■       •••';             *■     ,       ,■      ^ 

1 

A 

\  ■' 

■  ■"'  ' 

1 

i 

• 

'   >v''"'*^' 

! 

■ 

M 

t 

■-'    ''-''- 

1 

i 

\ 

i                 « 

l|>.. 

■    ■'  -     '  '  - 

■     '*• 

'  ' 

;„  ,^  ,^,,  ■..■f."'' 

1  A  ,.■; 

^, 

:     -            .                                 :J~- 

1 

t 

r 

:  4 

-jii.  .*  .\t,;.^-,,..'{,;--Vr  -;. 

■    ^       .      ' 

""■*■.  -■ 

rtV^.'u?-;^'! 


• 

* 

is; 

la?**' 


4  I 


-*4=- 


m 

s 


Ip-M 

"■>■„; 


* 


-:■■/ 


c 

"=1 


i:i 


P.'.iu.  IV 


.\ 


'■i'h'iHI 


/?-7,. 


J^^f2 


T.  Sindoiri  ath.. 


i 


' 

y-' 

\  \ 

»■ 
■lli 

./ 

*^ 

-»- 

it 

» 

i ; 

< 

.  1  ■ 
i 

)     : 

I  i     ■ 

i 
■  i 

'1 

« 

**«. 

*• 

^ 

• 

•    , 

m 

/ 

• 

% 


Si 

§„ 


• 

1- 

« 

* 

V. 

.1 

-    l/v 

* 

i 

•, 

1      „;;. 

» 

1  ■,  ■ 

.— . 

I 


^.j^^li. 


f^.I 


BLANCHARD  &  LEA'S  PUBUCATIONS.— (JTutory  ^  Biog  ^aphy.)    3 
N«W  ANQ  IMPROVED  COITION. 

LIVES  OF  Till  QIiIIns  OF  ENOLANO, 

FROM  fHE  NORMAir  CONCtirEST. 

WITH  ANECDOTES  OF  THEIR  COURTS. 

Now  flnrt  pnldiahad  from  Oflloial  Baeordi,  and  oAor  Anthonttd  Doenmonts,  Frlvatt 

M  wall  u  Pukila. 

HBW  BDinoH,  WITH  AO0ITIOITI  AND  coBmconom. 
BY  AGNES  STRICKLAND. 

In  lix  TolumMy  crown  octavo,  extra  crimaon  cloth,  or  half  morocco,  printed  on 

fine  paper  and  large  type. 

CopUt  of  the  Buodeetmo  EdMmut  in  tttelve  votumet,  nuty  •fill  be  had, 

A  valuable  contribution  to  hiaterical  knowledge^  to  young  persons  especially.  It  con- 
tains a  mass  of  every  kind  of  historical  matter  of  interest,  which  industry  and  resource 
could  collect.  We  have  derived  much  entertainment  and  instruction  from  the  work.— 
Athtnaum. 

The  execution  of  this  work  is  eqnal  Jp  the  conception.  Great  pains  have  been  taken 
to  make  it  both  interesting  and  valuable. — lAurary  Oaxru*. 

A  charminf  worl^ii-f^rof  interest,  at  once  serious  and  p)easing.~JireiujtfWf  p^izot. 


LIVES  or  tHE  qUEENS  Of  lENRT 

AND  OF  mS  MOTHER.  ELIZABETH  OF  YORK. 

BY  MISS  STRICKLAND. 
Complete  in  one  handaome  crown  octavo  volume,  extra  cloth.  ^  (Jvut  btvti.) 


MEMOIRS  OF  BUZABETH, 

SECOND  QUEEN  REGNANT  OF  ENGLAND  AND  IRELAND. 

BY  MISS  STRICKLAND. 

Complete  in  one  handsome  crown  octavo  volume,  extra  doth.    (Jiaf  JMumf.) 


(JUST  READY.) 

MEMORIALS    AMP    P0RCIE6P0NDENCE 

or 
CHARLfiS   ^AMBS  FOX. 

.,,,,-  Edited  BT  LORD  JOHN  RUSSELL. 

.  t  n  la  two  very  handaome  volomea,  royal  ISmo.*  extra  doth. 


THE  GARDENER'S    DICTIONARY. 

A  DICTIONARY  OF  MODEBN  GARDENING.  By  olw.  Johnson, Esq.  With  nu- 
merous additions,  by  David  Landreth.  With  one  hundred  and  eighty  wood>cuis. 
tn  one  very  large  royal  ISmo.  volume,  of  aboat  660  dottUeMMilttmned  pafea. 

This  work  is  now  offered  at  a  very  low  price. 


f  V 


(JUST  READY.) 


WISE  SAWS  AND  MODEBN  IISTAVliBS. 

BY  THE  AUTHOR  OF  SAM  SLICK. 
In  one  royd  12mo.  volume. 


4  BLANCHARD  &  LEA'S  PITBLICATIONS.— (JlfMM//iffi«oiM.) 

THE  ENC7CL0Pffl)IA  AUEiaCANA; 

A  POPULAR  DICTIONARY  OP  ARTS,  SCIENCES,  LITERATURE,  HIS- 
TORY, POLITICS,  AND  BIOGRAPHY. 

In  fourteen  large  octavo  volumes  of  over  600  double-columned  pagea  each. 

,.   .'^  '      For  tale  very  low,  in  various  atylea  of  binding.  .^ 

Some  years  having  elapsed  since  the  original  thirteen  volumes  of  the  ENCY« 
CLOP^DIA  AMERICANA  were  published,  to  bring  it  up  to  the  present  day, 
with  the  history  of  that  period,  at  the  request  of  numerous  subscribers,  the  pub- 
lishers have  issued  a 

SUPPLEMENTARY  VOLUME  (THE  FOURTEENTH),  '*  **  "^ 

jMk*  1)4  i%\\^  t..'  ■««""»0  rUZ  WORK  THOBOVOHLT  OF.  ■  ,  h,^  .,^,^,.^ 

:,<,^-r    yi         Edited  by  HENRY  VETHAKE,  LL.  D. 

.^i'  'one' large  octavo  volume,  of  over  650  double*columned  pages,  which  may  be 
had  separately,  to  complete  sets. 


MURRAY'S  ENCYCLOPEDIA  OF  GEOGRAPHY. 

THE  ENCYCLOPJEDIA  OF  GEOGRAPHY,  comprising  a  Complete  Description 
of  the  Earth,  Physicai,  Statistical,  CWil,  and  Political ;  exhibiting  its  Rela. 
tion  to  the  Heavenly  Bodies,  its  Physical  Structure,  The  Natursl  History  of 

.  each  Country,  and  the  Industry,  Commerce,  Political  Institntions,  and  Civil 
and  Social  State  of  all  Nations.  By  Hvoh  Mokbat,  F.  R.  S.  E.,  &c.  Assisted 
in  Botany,  by  Professor  Hooker— Zoology,  be.,  by  W.  W.  Swainson— Astrono- 
my, ke.,  by  Professor  Wallace— Geology,  be.,  by  Profbssor  Jameson.  Re- 
vised, with  Additions,  by  Thomas  G.  Bradfokd.  The  whole  brought  up,  by 
a  Supplement,  to  1843.  In  three  Urge  ootavo  volumes  various  styles  of 
binding. 

This  great  work,  furnished  at  a  remarkably  eheap  rate,  contains  about  Ninktun 
HiTNDaaD  LABOK  Imperial  Paoks,  and  is  illustrated  by  EUohtt.two small  Maps,  and  a 
colored  Map  or  the  United  States,  after  Tanner's,  together  with  about  Elevem  Hun- 
9RU  Wooo-cuTS  executed  in  the  best  st>  le. 


YOUATT  AND  SKINNER  ON  THE  HORSE. 


30H2aHO.c 


THE    HOaSE. 


.•lOfAg.M, 


BY  WILLIAM  YOUATT. 

J  ««•»  «4fM*is,  fsMA  MMMsroMS  MtUuirmtimmtt  ' 

TOOETHES  WITH  A  OCREBAL  HltroBT  OF  THE  HOME;  A  DNSERTATION  6ir  THE 

AHERICAH  TmOTTlirO  HORSE  {  BOW  TRAWEO  AKD  JOCKEYED  {  AN  ACCOUHT 

OF  HIS  REMARKABLE  PERFORMANCES;   AMD  AN  ESSAY  ON  THE 

AIS  AND  THE  MULE. 


i-i  f. 


wv 


BY  J.  S.  SKINNER, 
Asslstiitt'roStmasier>Oenera],  and  Editor  Of  the  Turf  Register. 

This  editkm  pf  Yonatt's  well-known  and  standard  work  on  the  Management,  Dis- 
esws,  and  Treatment  of  the  Horse,  embodying  the  valuable  additions  of  Mr.  Skinner,  has 
already  obtained  such  a  wide  circuiik.lon  throughout  the  country,  thai  the  Publishers 
need  say  nothing  to  attract  to  it  the  attention  and  confidence  of  all  who  keep  Horses  or 
are  interested  in  their  improvement 


VbOAtt  ANb  LEWIS  ON 


DOG. 


THE  DOO.   By  Willism  Yonati.    Edited  by  E.  J.  Lewis,  M.  D.    With  numerous  and 
beautiful  illustrations.   In  one  very  handsome  vohimot  crown  8vo,  crimson  cloih,  gilt. 


t^latumta.) 

DANA; 

ERATURE,  HIS- 

med  paget  each. 

IS* 

imei  of  the  ENCY- 
to  the  present  day, 
ibicribera,  the  pub« 


;ENTH), 


n  la  a\ 


i«;\ 


D. 

igeii  which  may  be 


iQRAPHY. 

tmplete  Deacription 
nhibitiag  ita  Reiap 
I  Natural  History  of 
itifaitiona,  and  Civil 
3.  E.,  &c.  Assisted 
Iwainson — Astrono- 
sof  Jameson.  Re- 
lole  brought  up,  by 
I  varioua  styles  of 


ins  about  Ninitkin 

0  SMALL  Maps,  and  a 

about  Elkvbm  Hun- 


lORSE. 


'  i<.S 


■EBTATION  6ir  THE 
D  (  AH  ACCOVHT 
T  ON  THE 


tegistar. 

«  Managenentf  Dia- 
ls of  Mr.  Skinnerv  has 
',  thai  the  Publishers 
who  keep  Horses  or 


V^ffi.^iH* 


With  nnmerous  and 
o,  crimson  cloth,  gilt. 


\ 


BLANCHARD  &  LEA'S  PUBLICATI0NS.-(5«»«nM.)  5 

UBIULRT  or  ILLUSTRAnSD  SOIBNTinO  WORKS. 

A  aeries  of  beautifiiUy  printed  volumea  on  varioua  branehea  of  aoienee,  by  the 
most  eminent  men  in  their  respective  departmenta.  The  wh^le  printed  in  the 
handsomest  style,  and  profuaely  embelliahed  in  the  moat  efficient  manner. 

IT^  No  expense  has  been  or  will  be  spared  to  render  this  series  worthy  ofthe  support 
onne  seientiflc  public,  while  at  the  same  time  it  is  one  of  the  handsomest  speoimeus  of 


typographical  and  anistie  exeention  wbieh  have  appeared  in  thia  eoantry. 
DB  JLA  BBOHB*8  OBOI.OOT-(Jiiat  laaued.) 

THE  aEOLOaiOAL  OBSERVER. 

BY  SIR  HENRY  T.  DE  LA  BECHE,  C.B.,F.R.S.,    ^ 

Director-General  of  the  Geological  Survey  of  Great  Britain,  Ac.  '^' 

In  one  very  large  and  handsome  octavo  volume.  ". 

WITH    OVBS    TBRBB    HUITDRBD   WOOD-OXTTS. 

Wa  have  here  prenented  to  us,  by  one  admirably  qualified  for  the  task,  the  most  com- 
plete compendium  of  the  science  of  veology  ever  produced,  in  which  the  different  facts 
which  fall  under  the  cognizance  ofthii  branch  of  natural  science  are  arranged  under 
the  different  causes  by  which  they  are  produced.  From  ihe  style  in  which  the  subject 
is  treated,  the  work  is  calculated  not  only  for  the  use  of  the  professional  geologist,  but 
for  that  of  the  nninidated  reader,  who  will  find  in  it  much  cunons  «nd  interesting  infor- 
mation on  the  changes  which  the  surface  of  our  globe  has  undergone,  and  the  history  of 
the  various  striking  appearances  which  itpresrAts  Vol\iminniM  as  the  work  is,  it  is 
not  rendered  unreadable  from  its  bulk,  owing  tothe  jndieioos  subdivision  of  iu  contents, 
and  the  copious  index  which  is  appeoded.-r-/dAt»  BuU.  ' 

Having  bad  such  abundant  opportunities,  no  one  could  be  found  ao  capable  of  direct- 
ing the  labors  of  the  young  geologist,  or  to  aid  by  his  own  experience  the  studies  of  those 
who  may  not  have  been  able  lO  range  so  extensively  over  the  earth's  siirfhee.  We 
strongly  recommend  Sir  Henry  De  la  Beebe's  book  to  those  who  desire  to  know  what 
haa  been  done,  and  to  learn  something  of  the  wide  examination  which  yet  liea  wailing 
for  the  industrious  observer.— TAs  Aiktnaum. 


KNAPP'S  CHEMICAL  TECHNOLOGY. 

—  '  I  ivis  •irr . 

TECHNOLOGY }  or,  Crem nTBT  Applied  to  the  A»n  Aia>  to  MAmrvACTumss. 
By  Dk.  F.  Khapp,  Profeaaor  at  the  Univeraity  of  Giesaen.  Edited,  with  nu- 
merous Notes  and  Additions,  by  Dk.  Edhtjitd  Robtalm,  and  Dm.  Trokas 
RicHAsoioir.  First  American  Edition,  with  Notes  and  Additiona  by  Pnf. 
Waltek  R.  JoHinoN.  In  two  handsome  octavo  volumea,  printed  end  illus- 
trated in  the  highest  style  of  art,  with  about  600  wood-eiigraviiigp. 

The  style  of  excellence  in  which  the  first  volume  was  sot  up  is  fully  preserved  in  this. 
The  treatises  themselves  aie  admirable,  and  the  editing, both  by  the  English  and  Ameri- 
can editors,  judicious;  so  that  the  work  maintains  itself  as  tl^e  best  of  the  series  to  which 
it  belongs,  and  worthy  the  attendon  of  all  interested  in  the  arts  of  which  it  treata.«» 
FnttMm  ImdhH*  Joumml. 


WEI8BACH'8_MECHANiC8. 

PRINCIPLES  OF  THE  MECHANICS  OF  MACHINERY  AND  ENGINEER- 
ING. By  PBorxHOE  Julius  Weibbach.  Translated  and  Edited  by  Paor. 
Gordon,  of  Glasgow.  First  American  Eidition,  with  Additiojis  by  Psol*.  Wal- 
ter R.  JoHMfoir.  In  two  octavo  volumea,  beautifully  printed,  with  900  illua- 
trationa  on  wood. 

The  most  yaluable  contribution  to  practical  science  that  has  yet  appeared  in  this 
country.— iUA«n«um. 

Unequalled  by  anything  of  the  kind  yet  produced  in  this  conntry— the  most  standard 
book  on  mechanics,  machinery,  and  engineerinK  now  extant.— J\r.  V.  Commtreial 

In  every  way  worthy  of  being  recommended  to  our  readers— i^'ranANM  hxttitutt 
Journal. 


6  BLANCHARD  &  LEA»S  PUBLICATIONS.— (S««««.) 

^,j  ^OABPEMTSR'S  OOBCFABATI^  PST8I0L0OT-(Jmt  Amad.) 

PRINCIPLES  OF  OBNRRAL  ANO~COMPARATIVE  PHYSIOLOGY;  in- 
tended  aa  an  Introduetion  to  the  Study  or  Human  Phyaiologjr,  and  aa  a  Guide 
to  the  Philoaophical  Purauit  of  Natural  Hiatory.  By  William  B.  Cabpbnteb, 
M.  0.,  F.  R.  8.,  author  of  «  Human  Phyaiology,"  «  Vegetable  Phyaiology,*' 
&c.  fto.  Third  improved  and  enlarged  edition.  In  one  very  large  and  hand> 
aome  octavo  volume,  with  aevera)  hundred  beautiful  illuitratioDS. 


I 

5  it 


I 


PRINCIPLES  OF  PHYSICS  AND  METEOROLOGY.  By  Pbofemob  J.  Mvl. 
LCK,  M.  D.  Edited,  with  Additions,  by  R.  EoLRsrELD^GBirFiTH,  M.  D.  In 
one  large  and  handaome  octavo  volume,  with  550  wood-cuta  and  two  colored 
platea. 

The  (tyle  in  whieh  the  volume  it  publiahed  is  in  the  highest  degree  oredilable  to  the 
<>nlerpri*e  of  the  publishers.  It  contains  nearly  four  hundred  engravings  executed  in 
H  style  of  extraordinary  elegance.  We  commend  the  Itook  to  general  lavor.  it  is  the 
l>estof  iia  kind  we  have  everaeeu.— AT.  Y.  Couritr  and  JEnjwtrir.  -i 


IfOHB,  BQDWOOD,  AND  FBOOTER'S  FHABICAOT. 

PRACTICAL  PHARMACY:  Compriaing  the  Arrangements,  Apparatus,  and 

)L^  Manipulationa  of  the  Pharmaoeutieal  Shop  and  Laboratory.     Bv  FBAMCia 

MoHB,  Ph.  D.,  Asseaaor  Pharmacia  of  the  Royal  Pruaeian  College  of  Medicine, 

Cobleats  {  and  TMbraiLtn  Rbdwood,  Professor  of  Pharmacy  in  the  Pharma* 

,.  «entical  Sooiety  of  Great  Britain.  Edited,  with  estenaive  Additiona,  by  PBor. 

h  William  Pboctbb,  of  the  Philadelphia  College  of  Pharmacy.   In  one  hand- 

~:  aomely  printed  octavo  volume,  of  570  pagea,  with  over  600  engravinga  on 

wood. 


r-  'j>  I    TBB  Kp&WBZOaT'S  OUIDB. 
THE  MILLWRIOHrS  AND  MILLER'S  GUIDE.  By  Olivxx  Evans.  Eleventh  Edi- 
tion.    With  4ddiiiona  and  Oorreetions  by  ihe  Professor  ofMeehanics  in  the  Franklin 
Institute,  and  a  description  of  an  improved  Merchant  Flour  Mill.    .By  0.  and  O.  Evans. 
In  one  octavo  volume,  with  numerous  engravings. 

HUMAN  HEALTH ;  or,  the  influence  of  Atmosphere  and  liOcality,  Change  of  Air  and 
Climate,  Seasons,  Fbod.  ChMhhig,  Bathintt,  Mineral  Springs,  Exercise.  Sleep,  Corporeal 
and  Mental  Pursuits,  Ac.  Ac.,  on  Healthy  Man.  cousuiutiog  Elementa  of  Hygiene. 
By  Robley  Dunglison,  M.  D.    In  one  octavo  volume. 


ACTON'S   COOKERY. 

MODERN  COOKERY  IN  ALL  ITS  BRANCHES,  reduced  toaSystemofEasy  Free- 
uce,  for  the  Use  of  Privnie  Families ;  in  a  Series  of  Practical  Receipts,  all  of  which 
are  given  with  the  most  minute  exactncM.  By  Bllza  Acton.  With  numerous  wood- 
cut illustrations;  to  which  is  added  a  Table  of  Weights  and  Measures.  The  whole 
revised,  and  prepared  for  American  housekeepers,  by  Mrs.  Sarah  J.  Hale.    From  the 

r'SceondliondenBdithin.    In  one  large  19mo.  volume. 

THE  DOMESTIC  MANAGEMENT  OF  THE  SICK-ROOM,  necessary,  In  aid  ol 

hiedieal  treatment  for  the  cure  of  diseases.  By  A.  T.  Thomson,  M.  D.  lidited  by  R.  E. 

Griffith,  M .  D.  ■  In  one  volume  royal  ISmo.,  extra  cloth. 
LANGUAGE  OF   FLOWERS,  with  illustrative  poetry.    Eighth  edition.    In 

one  beautiful  volume,  royal  18mo.,  crimson  cloth,  gilt,  with  colored  plates. 
AMERICAN  ORNITHOLOGY.    By  Charles  Bonsparte. Prince  of  Canino.  In  four  folio 

volumes,  half  bonnd,  with  numerous  magnificent  colored  plates. 

LECTURES  ON  THE  PHYSICAL  PHENOMENA  OF  LIVING  BEINGS.  By 
Carlo  Matteucci.  indited  by  Jonathan  Pereira,  M  D.  In  one  royal  19mo.  volume, 
extra  cloth,  v<7ith  illustrations. 


!^. 


ct6nc$»j 


At  Itnitd.) 

[YSIOLOOV;  in- 
y,  and  «■  a  Guide 

lM  B. CAmPBNTCB, 

«ble  Phyiiology,** 
ry  Urge  and  hand« 
Ktioni. 


>BOFEMOm  J.  Mvi> 
IFFITH,  M.  D.     In 

;■  and  two  colored 


ree  oieditable  to  the 
[ravings  executed  in 
eral  iavor.    It  is  the 


ICAOT. 

a,  Apparatua,  and 
>ry.  Bv  Fbancm 
»llege  of  Medicine, 
icy  in  the  Pharma- 
Ldditiona,  by  Pmor. 
^cy.  In  one  hand- 
00  engravinga  on 


rANi.  Eleventh  Edi- 
mica  in  the  Franklin 
By  C.  and  O.  Evani. 

Change  of  Air  and 
ise.  Sleep,  Corporeal 
lementa  of  Mygi^ue. 


T 


jrttem  of  Easy  Prae- 

iceipts.  all  or  which 

ith  numerous  .wood- 

asures.    The  whole 

J.  Hale.    From  the 


ecetsary,  In  aid  ol 
,D.  Edited  by  R.E. 

Ighth  edition.    In 

d  plates. 

3anino.  In  four  folio 


SO  BEINGS.     By 
oyal  13nio.  volume, 


•  -      BLANCHARD  &  LEA'S  PUBLICATIONS.— (S««i«.)  7 

ORAHAM'8  OKBMiaTBT.  NSW  EDITION.    Part  L-<Now  Beady.) 

ELEMENTS  oF  CHEMISTRY; 

INCLUblNO  TUB  APPikl^ATIOHS  OF  THB  SCIENCE  IN  THE  ARTS. 

BY  TH0MA8  QRAHAM,  F.  n.  8.,  &c., 

Professor  of  Chemistry  iu  University  Colleife,  i<oiiden,  &e. 
Second  American,  from  an  entirely  ReTlaed  and  greatly  Enlarged  English  Edition. 

WITH  NUMEROUS  WOOD-ENGRAVINGS. 

•f^'i  EDrtiSj  wim  Noras,  av  ROBERT  BfUDOES.  Vt.D.,  ..  . 

Professor  of  Chemistry  in  the  Philndelphia  College  of  Pharmacy,  ttc. 

To  be  completed  in  Two  Porta,  forming  one  very  large  octavo  volume. 
PART  I,  now  ready,  of  430  large  pages,  with  186  engravings. 
PART  II,  preparing  for  early  publication. 

■"'''*'  ^  '         From  the  Editor's  Preface. 

The  <*  Blementa  of  Chemistry,"  of  which  a  aecond  edition  la  now  presented, 
attnined,  on  its  first  appearance,  an  immediate  and  deserved  reputation.  The 
copious  selection  of  facts  from  all  reliable  sources,  and  their  judicious  an.tnge- 
ment,  render  it  a  safe  guide  for  the  beginner,  while  the  clear  eiposition  of  the- 
oretical pointa,  and  frequent  references  to  apecial  treatises,  make  it  a  valnable 
aasiatant  for  the  more  advanced  student. 

From  this  high  character  the  present  edition  will  in  no  way  detract.  The 
great  changes  which  the  aoience  of  Chemistry  has  undergone  during  the  interval 
nave  rendered  neccasary  a  complete  revision  of  the  work,  and  this  has  been 
most  thoroughly  accompliahed  by  the  author.  Many  portions  will  therefore  be 
found  esaentially  altered,  thereby  increasing  greatly  the  size  of  the  work,  while 
the  aeriea  of  illuatrationa  haa  been  entirely  changed  in  style,  and  nearly  doubled 
in  number. 

Under  these  circumataneea  but  little  has  been  left  for  the  editor.  Owing, 
however,  to  the  appearance  of  the  London  edition  in  parts,  some  years  have 
elapaed  aince  the  first  portions  were  published,  and  he  nna  therefore  found  oe- 
oaaion  to  introduce  the  more  recent  investigationa  and  discoveries  in  some  sub- 
jects, ae  well  aa  to  correct  aueh  inaccuracies  or  miaprints  aa  had  eacaped  the 
author'a  attention,  and  to  make  a  few  additional  referencea. 

INTRODUCTION  TO  PRACTICAL  CHEMISTRY,  including  ^.nalysis.  By 
John  E.  Bowman,  M.  D.  In  one  neut  royal  limo.  volume,  extra  cloth,  with  numer- 
ous illustrations.  

DANA  ON   CORALS. 
ZOOPHYTES  AND  CORALS.    By  Jamea  D.  Dana.    In  one  volume  imperial 

quarto,  extra  cloth,  wilh  wodd-cuts. 
Alto,  an  Atlas  to  the  above,  one  volume  imperial  folio,  wilh  sixiyone  magnificent 
plates,  colored  afwr  nature.    Bound  in  hall'  morocco. 

Thfse  splendid  volumes  form  aportioii  of  the  puolicationi  of  the  United  States  Explor- 
ing Expedition.  As  but  very  few  co|)ieB  have  been  prepared  for  sale,  and  an  ihe>e 
are  nearly  exhausted,  all  who  are  denimus  of  enriching  ilieir  librarirs  with  tht8.  the  uiost 
creditable  specimen  of  American  Art  and  Science  a»  yet  issued,  will  do  well  to  procure 
copies  at  once. 

THE  ETHNOGRAPHY  AND  PHILOLOGY  OF  THE  UNITED  STATES  EX- 
PLORING  EXPEDITION.  Hy  Horatio  Hale.  In  one  large  imperial  quarto  volume, 
beautifully  printed,  and  strongly  bound  in  extra  cloth. 

BARON  HUMBOLDT'S  LAST  WORK. 
ASPECTS    OF    NATURE    IN    DIFFERENT   LANDS   AND   DIFFERENT 
CLIMATES.    Wilh  Scientific  Elucidations.    By  Alexander  Von  Hamtioldt     trans- 
lated  hy  Mrs.  Sabine.    Second  American  edition.    In  one  handsome  volume,  large 
royal  12mo.,  extra  cloth. 

CHEMISTRY  OF  THE  FOUR  SEASONS,  Spring,  Summek,  AtrrvMN,  and 
WiMTSK.  By  Thomas  Orlffiih.  In  one  handsome  volume,  royal  l8mo,  extra  ciotb, 
with  numerous  illustrations. 


8     BLANCHARD  fc  LEA'B  PUBLIC ATIONS.-(J»mm«iVmm/  Viror/ti.) 


i 

^1 


/ 


'-'^      A  Maw  TBXT-BO<«  OW  WATOBAXi  nDLOtOPRT.  ■^■^^^ 

HANDBOOKS  3J3 

OF  HATURAL  PHILOSOPRY  AND  ASTR0N8MY. 

BY  DIONTSIUS  LARDNER,  LL.D.,  ETC. 
Mechanics,  HydroitaUei,  Hydniliei,  PDemniUei,  Solid,  uid  Optics. 

In  one  Urge  royal  12mo.  Tolume  of  750  pagei,  ■tronglr  bound  in  leather,  with 
over  400  wood-euta,  ( Juat  laaued.) 

THB  9B001ID  COVRSB,  embrMlBS  '  i)^-^ 


-.•ni 


HEAT,  HAONETISM,  ElEGTRICITT,  AND  6ALTANI8M. 

.i>m  ■    or  about  400  pageai  and  illuatrated  with  360  outa,  ia  now  ready. 
THB  THIRD  GOVRSB',  •onatltntlny 
A  COMPLETE  TREATISE   ON   ASTRONOMY 

WITH   irUMBKOVa  BTKSL  PLATC8  AWD  WOOD-CUTt,  18  MEABtT  BCAOT. 

The  intention  of  the  author  hai  been  to  prepare  a  worli  whioh  ihoald  eiqbrae«  the 
principleit  of  Natural  Philosophy,  in  iheir  latest  state  of  sciemlfio  develepineni,  divested 
of  the  iihstruwneBs  whieh  renders  them  nnfftied  for  the  yoanger  Modent,  and  at  iho  aanie 
time  illustrated  by  numerous  praciical  applieatioii*  in  every  braiiob  of  art  and  aoience. 
Dr.  Lardner's  extensive  acquireraentf  in  alldepertmenlaor  human  knowledge,  and  hU 
well  known  skill  in  popularizinK  his  subject,  have  thus  enabled  him  to  pre»<;nt  a  text- 
book which,  though  strictly  scientific  in  its  groundwork,  Is  yet  easily  mast<<red  by  the 
student  while  caloulaled  to  interest  the  minu,  and  awaken  th«  aneniion  by  showing  the 
importance  of  thn  principles  diocussed.  and  the  manner  in  whioh  they  may  be  nade 
Mibservient  to  the  practical  purpoaes  or  life.  To  aeeomplish  Ihia  still  further,  tha  editor 
has  added  to  each  section  a  serien  of  exampias>  to  be  worked  out  by  the  learner,  thus 
iinpresaing  upon  him  the  pracdcal  importance  and  variety  of  the  results  to  beobtinned 
from  the  general  laws  of  nature.  The  subject  is  still  fbrther  simpitfled  by  the  very  large 
number  of  illnstrative  wood-eou  whieh  are  seaiiored  throogh  the  volooMi  ntaking'pwin 
to  the  eye  what  might  not  readily  be  grasped  by  the  tmasstated  mind  ;  and  every  eare 
has  been  taken  to  render  the  typojgraptiical  aoctiraoy  of  the  work  what  it  sheotd  M. 

Although  the  first  portion  only  has  been  issued,  and  that  but  for  a  few  months,  yet  it 
has  already  been  adopted  by  many  aoademies  and  colleges  of  the  highest  standing  and 
character.  A  few  of  the  numerous  recommendations  with  which  the  work  haa  been 
favored  are  subjoined. 

Ftom  Pnf.  MOKnglui,  Univ.  tfJUuittlppi^  April  10, 18S9. 

I  am  highly  pleased  with  its  otmtenu  and  arrangement  It  eontalna  a  greater  number 
of  every  day  useful  practical  facts  and  examples  than  I  have  ever  aeen  noticed  in  a 
similar  work,  and  I  do  not  hesitate  to  say  that  as  a  book  for  teachijig  I  prefer  it  to  any 
other  of  the  same  size  and  extent  that  I  am  acquainted  with.  During  the  thirteen  years 
that  I  was  at  William  and  Mary  Collc«e  I  had  to  leaoh  Natural  Philosophy ,And  I  should 
have  been  very  glad  to  have  such  a  text-book. 

*  From  Edmund  Smith,  BaltSmer*,  May  19, 1808. 

I  have  a  class  using  it,  and  think  it  the  best  book  of  the  kind  with  whieh  I  auM* 
qaainted. 

Prom  Prof.  Cltttland,  Philadtlpkia,  October  17, 1891. 

I  feel  prepared  to  say  that  it  is  the  fullest  and  most  valuable  maiiual  upon  the  subject 
that  has  fallen  under  my  notice,  and  I  intend  to  make  it  the  text- book  for  the  first  class 
in  my  school. 

'V';f!;i    'K  From  8.  Stkooltr,  Hanoetr  AeadtmHf  Va.,  '■{'V^,-^ 

The  "  Handboeka^  seem  to  me  the  best  popular  treatises  on  their  respective  nibjeQts 
with  which  I  am  acquainted.  Dr.  Lardner  certainly  popularizes  scienoe  very  well,  and 
a  good  text-book  for  schools  and  colleges  was  not  beiore  in  existence.  „ 

From  Prqf.  J.  S.  Hmderson,  Farmer's  College,  O.,  Feb.  16, 1858.  , ,. --  .5, 

It  is  an  admirable  work,  and  well  worthy  of  public  patronage.  For  clearneaa  end 
fulness  it  is  unequalled  by  any  that  i  have  seen. 


mat  Worii.) 
PRT. 

VONOMY. 

to. 

I,  uid  Optics. 

1  in  leather,  with 


(ISM, 

Bw  fMdy. 
•  NOMY 

U.T  BBAPT.     i  ): 

hoald  embrae^  Hliif 
etopmen't,  dlveat«d 
inf ,  and  ai  tha  aaiiie 
of  an  and  aoieaaa, 
[iiowled||«,  and  hit 
1  to  pref«;nt  a  text- 
iljr  mattcfred  by  the 
ion  by  ehowiny  th« 
ihey  may  ba  nada 
I  further,  the  editor 
y  the  learner,  thus 
lul^  to  be' obtained 
)  by  the  very  large 
aiM^  inaicingipMin 
d  ;  and  every  eare 
at  it  ahaoid  be. 
few  montha,  yet  it 
[beatataudiog  and 
le  Work  haa  been 


a  greater  nninber 

aeen  noticed  in  a 

I  prefer  it  to  any 

the  thirteen  yaart 

ophy»Aad  I  ahould 


hwhiah  I  aniM- 


i  upon  the  iifbicct 
for  the  first  class 


iipeetive  snbjeots 
oe  very  well^jwtd 

1853. 

^or  clearness  pnd 


BLANCHARD  &  LEA'S  VVBIA0A.TlOV3.~(Ed«eationaI  Vft^t.)     9 
maw  AlID  ZMFROTBD  BXIXnOir.—(Now  Ready.) 

OUTLINES    OF^ASTRONOMY. 

BY  SIB  JOHN  F.  W.  HERSCHEL.  F.  R.  S.,  &c. 

A  HKW  AMBMOAir  FBOK  TMB  rOVBTU  LOKOOir  BOITIOIf. 

In  one  very  neat  orowa  oetavo  voiune,  eitra  doth,  with  six  platea  and  na- 

merouB  wood-cuts. 

This  edition  will  be  found  thoroughly  brought  up  to  the  present  state  of  aa- 
tronomical  science,  with  the  nost  recent  inveatigations  and  discoveriea  Ailljr 
discussed  and  explained. 

We  now  talta  leave  of  this  remarkable  work,  which  wa  hold  to  be,  beyond  a  doubt, 
the  greatest  and  most  remarkable  of  the  works  in  which  the  law*  of  astronomy  and  the 
appearance  of  the  heavens  are  described  to  those  who  are  not  mnthematician*  nor  ob- 
servers, and  recalled  to  those  who  are.  It  is  the  reward  of  men  who  can  descend  from 
the  advancement  of  knowledge  to  care  for  its  diffusion,  that  their  works  are  essential 
to  all,  that  they  become  the  manuals  of  the  proficient  as  well  as  the  text-books  of  the 
learner.— illA«M«wffi. 

There  is  perhaps  no  book  In  the  English  language  on  the  snhjeot,  which,  whilst  it  con- 
tains so  many  of  ilie  facta  of  Astronomy  (which  it  attempt*  to  explain  wiih  as  little  tech- 
nical language  as  possible),  is  so  attractive  in  its  style,  and  to  clear  and  forcible  in  its 
illustrations.'— £van(i/iVai  JUmev. 

Probably  no  book  ever  written  upon  any  science,  embraces  within  to  small  a  comnati 
an  entire  epitome  of  everything  Known  within  all  its  various  deparime'nta,  practical, 
theoretical,  and  phytical.— ilzamintr. 


A  TRBATISB  ON  A8TRONOM7. 
BY  SIR  JOHN  F.  W.  HERSCHEL.   Edited  by  8.C.  Walkeb.    In  one  12mo. 
volume,  half  bound,  with  platea  and  wood-cuta. 


A   TRBATIBB    ON   OPTICS. 

BY  SIR  DAVID  BREWSTER,  LL.  D.,  F.  R.  S.,  &o. 
A  NEW  EDITION. 

WITH  AH  AFPBirDIZ,  OORTAIirilTO  AW  BUUKCRTABy  VIZW  OF  THB  APFLICATIOV 
or  AHALTSM  TO  BBrLECTIOIT  AND  BEFBACTION. 

BY  A.  D.  BACHE,  Superintendent  U.  S.  Coast  Survey,  &c. 
In  one  neat  duodecimo  volume,  half  bound,  with  about  200  illustrations. 


BOIiMAR'S  FRENCH  SERIES. 

New  editions  of  the  followiitg  works,  by  A.  Bolmab,  forming,  in  oonneotion 
with  "  Bolmar's  Levixac,*'  a  complete  aeries  for  the  acquiaition  of  the  French 
language  :— 

A  SELECTION  OF  ONE  HUNDRED  PERRIN'S  FABLES,  accompanied  by 
a  Key,  eoniaining  the  text,  a  literal  and  free  translaiion,  arranged  in  such  a  manner  aa 
to  point  out  the  difference  between  the  French  and  English  idiom,  ftc.  In  one  vol.l9mo. 

A  COLLECTION  OF  COLLOQUIAL  PHRASES,  on  every  topic  neceaaary  to 

maintain  conversation.  Arranged  under  dilDsreiit  heada,  with  numerous  remarkt  Oii 
the  peculiar  pronunciation  and  usee  of  various  words ;  the  whole  to  disposed  at  oon- 
aiderably  to  Ausilitato  tho  acquisition  of  a  correct  pronunciation  of  the  French.  In 
one  vol.  18mo. 

LES  AVENTURES  DE  TELEMAQUE,  PAR  FENELON,  in  one  vol.  12mo., 

accompanied  by  a  Key  to  the  first  eight  l>ookt.  In  one  vol.  12nio.,  containing,  like  the 
Fablet,  the  Text, « literal  and  free  tranalation,  intended  at  a  aequel  to  the  Fablea. 
Either  volume  told  teparately. 

ALL  THE  FRENCH  VERBS,  both  regular  and  irregular,  in  a  small  voluma. 


10   BLANCHARU  dfc  LEA'S  PUBLICATIONS.— (£^M«rili<MM/  Wortt.) 


1^ 


ELEMENTS  OF  NATURAL  PHILOSOPHY; 

BEINO 

AN  EXPERIMENTAL  INTRODUCTION  TO  THE  PHYSICAL  SCIENCES. 


Illnitratcd  with  OT«r  Thr««  Handrcd  l¥oo4-««l«> 

BY  OOLDINO  BIRD,  M.D., 
AititiMi  Phjr»iei>n  lo  Ouy*«  Hoipiial. 

Prom  tho  Third  London  edition.    In  one  nett  volume,  royal  12mo. 


«I 


We  era  eatoniihed  to  And  that  Ihrre  !•  room  In  w  imell  e  hook  for  even  the  liare 
recital  of  to  many  tuhjocii.  Where  everything  i*  treated  ■nceineily,  frreai  JuriKmeiit 
and  much  time  are  iieednd  in  inaliiiiK  a  ■election  and  winnowing  the  wheal  frnm  the 
chaff  Dr.  Bird  ha*  no  need  to  plead  the  peculiarity  of  hia  poaiiion  a*  a  iihield  aeaintl 
nritioiam,  m>  lonir  en  hit  liook  coiiiinuea  to  lie  the  l>eat  epiiomn  in  the  Knitlifh  lan- 
guage of  thia  wide  range  of  phyiical  tubjeoia.— JVoriA  Amtrtean  Hteltw,  April  1, 1881. 

From  Prt(f  John  /oAfUlen,  ITw/ayen  UnUt.,  MUilttotfn,  CI. 

For  thoee  deairing  aa  ezienaive  a  woric,  I  think  it  decidedly  auperior  to  anything  of 
the  kind  with  which  I  nm  aoijuaiiiied. 

From  Prtff.  Jt.  O.  Ouiray,  Xmt$  TtHttvnt  Univtrrttif, 

I  am  mueh  graijlled  in  peruaini  a  work  which  fo  well,  »o  fully,  and  m>  clearly  aeia 
forth  thia  branch  of  thn  Natural  Sciencea.  For  aome  time  I  have  been  deairoua  of  oh* 
laiuiiig  a  aubaiiiute  for  the  one  now  uaed— one  which  ahould  embrace  the  recent  dia- 
coveriea  In  the  acieucea,  and  I  can  truly  aay  that  auch  a  one  ia  afforded  in  thia  work  of 
Dr.  Bird'a. 

From  Prof.  W.  F,  Hopkitu,  JUojonVe  Univtrtltjf,  TfHn. 

It  in  JuRt  the  aort  of  book  I  think  needed  In  moat  colleiret.  heinir  flir  above  the  rank  of 
a  mere  poptilur  work,  and  yet  not  beyond  the  eomprrhenaion  of  all  but  the  most  accom- 
pli«hed  matiiematiciana. 


180 


ELEMENTAKY  CHEMISTRY; 

.ti         THEORETICAL  AND  PRACTICAL. 
BY  GEORGE  FOWNES,  Ph.D., 

Chemical  Lecturer  ia  the  Middleaex  Hoapiial  Medical  School,  Ac.  &e. 

WITH  NUMEROUS  ILLUSTRATIONS. 

Third  American,  from  a  late  London  edition.    Edited,  with  Additions, 

BY  ROBERT  BRIDGES,  M.  D., 

i*rofeator  of  General  and  Pharmaeeutieal  Chemlatry  in  the  Philadelphia 
College  of  Pharmacy,  ke.  Ac. 

In  one  large  royal  12mo.  volume,  of  over  five  hundred  pagei,  with  -lUout 
wood-eute»aheep  er  extra  eloth. 

The  work  of  Dr.  Fowne*  hoe  long  been  before  the  public,  and  ita  merit' 
fnily  appreeiatfd  aa  the  beat  text-book  on  Chemiatry  now  in  exi»tence.    V< 
coiirae,  place  it  in  a  rank  nuperior  to  the  worka  of  Braiide,  Graham.  Turner,  (ireitory, 
or  Gmelin.  hut  we  aay  that,  aa  a  work  (or  atudenta,  it  ia  preferable  lo  any  of  them.-<-Lo»> 
donJ^.   ntUof  Mediein*. 

AVe  know  of  io  (reiuiae  ao  well  calculated  to  aid  the  atodent  in  becoming  familiar 
with  the  numer.-)!  a  facta  in  the  aeience  on  whirh  it  treat*,  or  one  better  calculated  aa 
•  text-book  for  li  nse  ettfsndiiig  Chemical  t<ecture».  •  •  •  *  The  beat  text-book  on  Che- 
miatry thathaa  ija.j;*d  rrom  our  pre*  .—American  Mid.  Journal. 

We  know  of  no  -<e  ■ .  '.'Mn  •)*'.  same  li>niia,  which  haa  higher  claims  lo  our  coniidenre 
OS  a  college  ■Tl-!9f-b'H»',  or*'  j^  aeeur'vy  of  detail  and  scientifio  arrangement.— ^lu- 
giwla  Mtd,  Jourtt'tl. 

%  

ELiiMENTS   OF   PHYSICS- 

OR,  NATURAL  PHILOSOPHY,  GENERAL  AND  AflRDICAL  Written  for  uni- 
versal use,  in  plain,  or  non-technical  latiguaire  By  Nku4.  AaxoTT,  M.  D.  In  one 
octavo  volume,  with  about  two  hundred  illusirationa. 


1  )V0  •>«."' 
HOf 


onal  1Ver4:s.) 

isophyT" 

ICAL  SCIENCES. 


.1 

royal  12mo. 

k  for  even  the  Imre 
Btly,  ptreat  juil|cnieiit 
Id*  wh«Bi  frmn  ihs 
I  ••  n  rhiflil  maiiiRi 
In  th«  KiiRlifh  laii- 
(«W,  April  1,  1681. 

im,  Ct. 

erior  to  anything  of 

iiir. 

and  M>  elrnrty  ■«•» 
b«rn  (Ipalrou*  of  ob> 
irace  the  rveritt  dl»- 
trdad  in  thii  work  of 

run. 

»T  nhore  the  rank  of 

bui  the  most  accom- 


itry; 

u. 

lol,  he.  &e. 
ith  Additions, 

Philadelphia 

M,  with  about  180 


la  raaril"  ;i  'v  ;  '..■  ." 
nee.  V. .  11,  i>ui,of 
I.  Turner,  UreKory, 
any  of  thero.-^Lon- 

becominK  familiar 
letter  ealculaictt  a« 
tezt'bookoii  Che- 

I  to  our  roniidenre 
arrangement.— Am- 


Written  for  uni- 
OTT,  M.  D.    In  one 


BLANCHARD  de  LEA'S  TVBUCATIO^^.'  (BitiroHomU  W»rkt.)    11 


■OMaAYZLurs  pbtsical  OEooRAPar. 


PHYSICAL  GBOaR 

BY  MARY  SOMERVILLE. 


APHT. 


A  KBW  AMBRIOAN   FBOM  TBI  LAST  AND  REYISID  LONDON  IDITION, 
Wvm  AMERICAN  NOTEB,  GLOSSARY,  ETC. 

BY  W.  y   W.  RUSCHENBERGER,  M.D.,  U.  S.  N. 
In  one  nai4t  oyu.  V  aio.  folain«,eitra  cloth,  of  over  flTohnndred  and  flfty.paget. 

Ttff  'rren'  ijeeesibt  thia  work,  and  ita  Introduction  into  many  of  ourhinhar  ichoola 
and  be  ^di  >  <  ,  have  induced  the  publiihera  to  prepare  a  new  and  much  improved 
f^iiion.  In  nddiiion  to  the  corrections  and  improvements  of  the  author  bestowed  on 
work  in  its  passan  throuah  the  press  a  second  time  in  London,  notes  have  been 
mdapi  it  more  rally  to  the  phya' 
uomprabensive  glossary  has  baan  nddad,  renaai 
to  aauoauojiAl  parpoaea. 


trodneed  to  (idapi  It  more  rally  to  the  phyaical  ceography  of  this  country  |  and  a 

mring  the  Tolnme  more  particularly  suited 


Our  praise  eomea  lagging  in  the  rear,  and  la  wetlnigh  superfluous.  But  we  are 
anxious  to  recommend  lo  our  youth  the  enlarged  method  of  studying  geofraphy  whii-h 
lier  preaeni  work  demonstrates  to  be  as  captivating  aa  it  is  instructive.  We  hold 
such  presents  aa  Mrs.  Somerville  has  bestowed  upon  the  public,  lo  be  of  incalculable 
value,  disseminating  more  sound  information  than  all  the  literary  and  scieniific  intii* 
tulions  will  accomplish  in  a  whole  eyela  of  their  existence.— UtoeneooiTaJIIagastns. 

From  Thtmmt  Bkirwi>%,  High  School,  Boilon, 
I  hold  it  in  the  highest  estimation,  and  am  confident  that  it  will  prove  a  very  efficient 
aid  in  the  education  of  the  young,  and  a  source  of  much  interest  and  iiisuuciiou  to  the 
adult  reader. 

^roM  j;re«t«M  BvtrHt,  High  Sehoot,  iVsw  Orlmns. 

I  have  examined  it  with  a  good  dealof  eare,and  am  tlad  tolind  that  it  supplies  an  im« 
poriant  desideratum.  The  whole  work  if  a  masterpiece.  Whether  we  examine  the 
importance  of  the  suhiects  trealM,or  the  elegant  and  attractive  style  in  which  ihry  are 
presented,  this  work  leaves  nothing  to  desire.  I  have  introduced  it  into  my  school  for 
the  u*e  of  an  advanced  class  in  geography,  and  they  are  greatly  interested  in  it.  1  have 
no  doubt  that  it  will  be  need  in  meet  of  our  higher  seminariea. 

From  W.  Smyth,  Oiuitgo  Aead0ny. 

So  muck  important,  accurate,  and  general  information  1  have  never  seen  in  a  volume 
of  its  extent,  in  fine,  I  believe  it  to  be  a  work  whica  will  aoon  lake  a  high  place  in  the 
academies  and  colleges  of  America,  as  well  as  in  the  libraries  of  every  individual  de- 
li  rous  of  aecurate  information  respecting  the  planet  on  which  we  dwell.  1  have  recom- 
mended it  to  those  connected  with  the  Uiatriet  School  Libraries,  for  which  1  consider  it 
exceedingly  well  adapted. 


JOHNSTON'S  PHTSICAL  ATLAS. 

THE   PHYSICAL   ATLAS 

OF  NATURAL  PHENOMENA. 

FOR  THE  USE  OF  COLLEGES,  ACADEMIES,  AND  FAMILIES. 

BY  ALEXANDER  K£1TH  JOHNSTON,  F.  R.  G.  S.,  F.  6.  8. 

In  one  large  volume,  imperial  qMirto,  handsomely  and  atrongljr  bound.    With 

twenty-six  platea,  engraved  and  colored  in  the  beat  atyle.    Together 

with  one  hundred  aiHi  twelve  pages  of  Descriptive  Letter-press, 

and  a  very  copioua  Index. 

A  work  which  should  be  in  every  fsmily  and  every  school-room,  for  consultation  and 
reference.  By  the  ingenious  arrangement  adopted  t>y  the  author,  it  makes  clear  to  the 
eye  every  fact  and  obeervaiion  relative  to  the  pr«»,*iii  condition  of  the  enrih  arranged 
under  the  departments  of  Geology,  HydroKrapliv,  Meteorology,  and  Naiural  History. 
The  letterpress  illustrates  this  with  a  liody  of  important  information,  nowhere  else  to 
be  found  condensed  into  the  same  space,  wh\le  a  very  full  Index  retidert  the  whole 
0iMy  of  reference.  -    i  ■  '■■  "-  »"»»"'  .».i,vnwH»»<ti  «»*..««.» 


12   BLANCHARD  &  LEA'S  PUBLICATIONS.— (^rf««B<»o»a/  W0ri*.) 

SCHMITZ  AND  ZUMPT'S  OLASSIOAL  SERIES. 

Under  this  title  BLANCHAmD  St  Lca  are  publishing  ■  Mriet  of  Latin  Sebool- 
Books,  edited  by  thoae  distinguished  scholars  and  critics,  Leonhard  Schmitz 
and  C.  G.  Zumpt.  The  object  of  the  series  is  to  present  a  course  of  accurate 
teits,  revised  in  accordance  with  the  latest  investigations  and  MSS.,  and  the 
mo:/,  approved  principles  of  modern  criticism,  as  well  as  the  necessary  element- 
ary books,  arranged  on  the  best  system  of  modern  instruction.  The  former  are 
accompanied  with  notes  and  illustrations  introduced  sparingly,  avoiding  oit  the 
one  hand  the  error  oroverburdening  the  work  with  commentary,  and  on  the  other 
that  of  leaving  the  student  entirely  to  his  own  resources.  The  main  object  has 
been  to  awaken  the  scholar's  mind  to  a  sense  of  the  beauties  and  peculiarities 
of  his  author,  to  assist  him  where  nsiistance  is  necessary,  and  to  lead  him  to 
think  and  to  investigate  for  himself.  For  this  purpose  maps  and  other  en« 
gravings  are  given  wherever  useful,  and  each  author  is  accompanied  with  a 
biographical  ^nd  critical  sketch.  The  form  in  which  the  volumes  are  printed 
is  neat  and  convenient,  whila  it  admits  of  their  being  sold  at  prices  unpre- 
cedentedly  low,  thus  placing  them  within  the  reach  of  many  to  whom  the  cost 
of  classical  works  has  hitherto  proved  a  bar  to  this  department  of  education ; 
while  the  whole  series  being  arranged  on  one  definite  and  uniform  plan,  enables 
the  teacher  to  carry  forwan)  his  student  from  the  rudiments  of  the  language 
without  the  annoyance  and  interruption  caused  by  the  necessity  of  using  text- 
books founded  on  varying  and  conflicting  systems  of  study. 

CliASSlCAI.  TEXTS  PUBLISHBD  IN  THIS  SERIES. 

I.  CJGSARIS  DE  BELLO  6ALLIC0  LIBRI  IV.,  1  vol.  royal  18mo.,  extrft 

cloth,  232  pages,  with  a  Map,  price  60  cents.  r<j 

II.  C.  C.  SALLUSTII  CATILINA  ET  JU6URTHA,  1  vol.  royal  ISmo.,  extra 

cloth,  168  pages,  with  a  Map,  price  60  cents. 

III.  P.  OVIDII  NASONIS  CARMINA  'SELECTA»  1  vol.  royal  18mo.,^extra 
cloth,  246  pages,  price  60  cents. 

IV.  P.  VIR6ILII  MARONIS  CARMINA,  1  vol.  royal  18mo.,  extra  cloth,  438 
pages,  price  75  cents. 

V.  Q.  HORATII  FLACCI  CARMINA  EXCERPTA,  1  vol.  royal  18mo.,  extra 

cloth,  312  pages,  price  60  cents. 

VI.  Q.  CURTII  RUFI  DE  ALEXANDRI  MA6NI  QU^  6UPER8UNT,  1 
vol.  royal  ISnta.,  extra  cloth,  326  pages,  with  m  Map,  price  70  cents.         » 

Vir.  T.  LIVII  PATAVINI  HISTORIARUM  LIBRI  I.,  II.,  XXI.,  XXII.,  1 
vol.  royal  I8mo.,  ex.  cloth,  350  pages,  with  two  colored  Maps,  price  70  cents. 

VIII.  M.  T.  CICERONIS  ORATIONES  SELECTiB  XII.,  1  vol.  royal  18mo., 
extra  cloth,  300  pages,  price  60  cents.  ^^ 

IX.  CORNELIUS  NEPOS,  1  vol.  royal  18mo.,  price  60  cents.  ^ 
isi.EMENTAHY  WORKS  PUBLISHED  IN  THIS  SERIES. 

I. 
A  SCHOOL  DICTIONARY  OF  THE  LATIN  LANGUAGE.    By  Db.  J.  H. 
Kaltschmidt.    la  two  parts,  Latin-English  and  English-Latin. 
Part  I.,  Latin-English,  of  nearly  500  pages,  strongly  bound,  price  90  cents. 
'    Part  II.,  English-Latin,  of  about  400  pages,  price  75  cents. 
Or  the  whole  complete  in  one  very  thick  royal  18mo.  volume,  of  nearly  900 
closely  printed  double-columned  pages,  strongly  bound  in  leather, 
price  only  $1  25. 
II. 
GRAMMAR  OF  THE  LATIN  LANGUAGE.     Bt  Liovhabd  Schmitz,  Ph. 
D.,  F.  R.  S.  E.,  Rector  of  the  High  School,  Edinburgh,  &c.    In  one  hand- 
some volume,  royal  iSmo.,  of  318  pages,  neatly  halt  bound,  price  60  cents 


lonal  Worit.) 

L  SERIES. 

I  of  Latin  Sebool- 
Jeonhard  Schmitz 
iourse  of  accurate 
id  MSS.,  and  the 
leceasary  element- 
.  The  former  are 
y,  avoiding  ort  the 
r,and  on  the  other 
le  main  object  has 
B  and  pRculinrities 
nd  to  lead  him  to 
ips  and  other  en- 
Bompaniec^  with  a 
lumea  are  printed 
t  at  prices  unpre- 
to  whom  the  cost 
lent  of  education ; 
form  plan,  enables 
Is  of  the  language 
■ity  of  using  tezt- 


S  SERIES. 

oyal  18mo.,  extra 

royal  ISmo.,  estra 

oyal  ISmo.M^extra 

,  extra  cloth,  438 

royal  ISmo.,  extra 

SUPER8UNT,  1 
Be  70  cents. 

XXI.,  XXII.,  i 
ips,  price  70  cents. 

vol.  royal  ISmo., 
IS  SERIES. 


S.    By  Dr.  J.  H. 
Latin. 

,  price  90  cents. 

ne,  of  nearly  900 
in  leather. 


RD  Schmitz,  Ph. 
c.  In  one  hand- 
id,  price  60  cents 


BLANCHARD  &  LEA'S  FXTELICATIONS.— {Educational  Wot/ts.)    13 
SCHMITZ  AND  ZUMPT'8  CLASSICAL  SERIES— Continued. 

III. 

ELEMENTARY  GRAMMAR  AND  EXERCISES.  BtDb.  Lborbard  Schmits, 
F.  R.  S.  E.,  Rector  uf  the  High  School,  Edinburgh,  kc.  In  one  handsome 
royal  18mo.  volume  of  246  pages,  extra  cloth,  price  60  cents.  (Just  Issued.) 

PREPARING    FOR   SPEEDY    PUBLICATION.  ^ 

LATIN  READING  AND  EXERCISE  BOOK,  1  vol.,  royal  ISmo. 
A  SCHOOL  CLASSICAL  DICTIONARY,  1  vol.,  royal  ISmo.  ' 

It  will  thus  be  seen  that  this  series  is  now  very  nearly  complete,  embracing 
eight  prominent  Latin  authors,  and  requiring  but  two  more  elementary  works 
to  render  it  sufficient  in  itself  for  a  thorough  course  of  study,  and  these  latter 
are  now  preparing  for  etrly  publication.  Daring  the  successive  appearance  of 
the  volumes,  the  plan  and  execution  of  the  whole  have  been  received  with 
marked  approbation,  and  the  foot  that  it  supplies  a  want  not  hitherto  provided 
for,  is  evinced  by  the  adoption  of  these  works  in  a  very  large  number  of  the 
best  academies  and  seminaries  throughout  the  country.  From  among  several 
hundred  testimonials  with  which  they  have  been  favored,  and  whiob  they  are 
every  day  receiving,  the  publishers  submit  a  few  of  the  more  recent. 

But  we  cannot  Ibrbear  commendingr  •specially  iMth  to  instructors  and  pupils  the 
whole  of  the  series,  edited  by  those  accomplished  scholars,  Dr«.  Schmitz  and  Zumpi. 
Here  witi  be  found  a  set  of  text-books  that  combine  the  ezcell«nui«g  so  long  desired 
ill  this  class  of  works.  They  will  not  cost  ihe  student,  by  one  half  at  least,  that  which 
he  must  expend  for  some  other  editions.  And  who  will  not  say  that  this  is  a  consider- 
ation worthy  of  attention  !  For  the  cheaper  our  school-books  can  be  made,  ilie  more 
widely  will  they  be  circulated  and  used.  Here  you  will  find,  too,  no  useless  display  of 
notes  and  of  learning,  but  in  foot- notes  on  each  page  you  have  everythiii|[(  necessary  to 
the  understanding  nfthe  text.  The  difhcuji  points  are  sometimes  elucidated,  and  often 
is  the  student  referred  to  the  places  where  he  can  find  light,  but  not  without  some  effon 
of  his  own.  We  think  that  the  punctuation  in  these  uooks  might  be  improved;  but 
taken  as  a  whole,  they  come  nearer  to  the  wants  of  the  times  than  any  wiihiu  our  know- 
ledge. — Southern  ColUg*  Review. 

From  W.  J.  Rolfe,  Wrentham,  Mass.,  March  22, 1852. 
They  seem  to  me  the  best  and  the  cheapest  school  editions  of  the  classics  that  I  have 
yet  seen.  The  notus  are  all  that  a  teacher  could,  and  all  that  a  student  should  desire. 
On  classical  history  and  antiquities  I  think  them  particularly  rich,  and  the  maps  add 
very  much  to  the  merit  of  the  books.  Kaltschmidt's  Dictionary  I  adopted  as  a  matter 
of  course.  It  is  so  much  superior  to  all  the  other  school  dictionaries  that  no  one  who 
has  examined  it  can  hesitate  to  recommend  it. 

From  Prqf.  R.  N.  Netsell,  Masanie  CoUegs,  Tenn.,  June  8, 1852. 
I  can  give  you  no  better  proof  of  the  value  which  I  set  on  them  than  by  making  use 
of  them  in  my  own  classes,  and  recommending  their  use  in  the  preparatory  department 
of  our  institution.  I  have  read  them  through  carefully  that  1  might  not  speak  of  them 
without  due  examination,  and.!  latter  mysMf  that  my  opinion  is  fully  borne  out  by  fact 
when  I  pronounce  them  to  be  the  most  useful  and  the  most  correct,  as  well  as  the  cheap- 
est editions  of  Latin  Classics  ever  introduced  in  this  country.  The  Latin  and  Knrlish 
Dictionary  contains  as  much  as  the  student  can  want  in  the  earlier  years  of  his  course : 
it  coniaiiiB  more  than  I  have  ever  seen  compressed  into  a  book  of  this  kind.  It  ought  to 
be  the  student's  constant  companion  in  his  recitations.  It  has  the  extraordinary  recom- 
mendation of  being  at  once  portable  and  comprehensive. 

From  Prof.  D.  Duncan,  Randolph  Macon  College,  Va.,  May  85, 1852. 
It  is  unnecessary  for  me  to  say  anything  respecting  the  text  of  Schmitz  and  Zumpt's 
series.  The  very  names  of  the  editors  are  a  sufficient  guarantee  of  their  puriiy.  The 
beauty  of  the  typography,  and  the  judicious  selection  of  notes  will  insure  their  use  by 
every  experienced  teacher,  whilst  iheir  cheapness  and  convenient  size  will  be  a  sure 
recommeiidntioii  to  every  parent.  I  think,  gentlemen  that  by  the  republicaiion  of  this 
excellent  series  you  have  laid  the  public  under  strong  obligations  to  you.  We  will  use 
them  as  far  as  they  come  into  our  course,  and  I  will  recommend  them  to  our  numi  reus 
preparatory  schools.  Prom  the  merits  above  mentioned,  they  are  desUned,  in  my  opinion 
to  supersede  most  of  the  editions  now  in  use  in  our  schools.  ' 


14    BLANCHARD  &  LEA'S  PUBLICATIONS.— (Brfwcatiowo/  Woris.) 

_i — 

SCHMTTZ  AND  ZUMPT^S  CLASSICAL  SERIES-ConHnued. 


From  the  Rev.  L.  Van  Bolekdm,  Prineipal  qf  St.  Timothy^  Halt,  Md.,  Feb.  18, 1853. 

Since  you  commenced  the  series  I  have  invariably  adopted  the  different  worlcsin  pre- 
■Mrenee  to  all  others,  and  I  now  use  them  all,  with  the  exception  of  "Q.  Cartios.** 

From  W,  F.  WyiT$,  Ntw  London  Aeadtmy,  Feb.  14, 18S2. 

I  have  u«ed  no  other  editions  but  yours  since  they  made  their  first  appearancis,  and 
•hall  certainly  continue  to  do  so. 

Among  the  various  editions  of  the  Latin  Classics,  Sohmitz  aud  Zumpt's  series,  m  far 

Sa  yet  published,  are  at  all  times  preferred,  and  students  are  requested  to  procure  no 
\)\n.—Announeenunt<if  Bethany  College,  Va. 


mom  with  8CHMITZ  AND  ZUPmiASSICAL  SBUES— (Now  ReadrO 
THB  CLASSICAL  ACANUAL;      ^^ 

AN  BPITOMB  OF  ANCIENT  GEOGBAPHT,  ORBBK  AND  ROMAN 
MTIHOLOaT,  ANTIQUITIES,  AND  GHRONOLOOT. 

CHIEFLY   INTENDED   FOR  THE  USE  OF  SCHOOLS. 

BY  JAMES  S.  S.  BAIRD,  T.  C.  D., 

Assistant  Classical  Master,  King's  SchobI,  Oloucefter. 
In  one  neat  volame,  royal  18mo.,  extra  cloth,  price  Fifty  centl. 

This  little  volume  hat  been  prepared  to  meet  the  recognized  want  oran  Epi- 
tome which,  within  the  compaaa  of  a  single  small  volume,  should  contain  the 
information  requisite  to  elucidate  the  Greek  and  Roman  authors  most  com- 
monly read  in  our  achools.  The  aim  of  the  author  baa  been  to  embody  in  it 
•uch  details  aa  are  important  or  necessary  for  the  junior  student,  in  a  form  and 
■pace  capable  of  rendering  them  easily  mastered  and  retained,  and  he  baa  con- 
aeqoently  not  incumbered  it  with  a  mass  of  learning  which,  though  highly 
valuable  to  the  advanced  student,  is  merely  perplexing  to  the  beginner.  In  the 
amount  of  information  presented,  and  the  manner  in  which  it  is  conveyed,  as 
well  as  its  convenient  size  and  exceedingly  low  price,  it  is  therefore  admirably 
adapted  for  the  younger  classes  of  onr  namerons  cleastcal  schoola. 

From  Mr.  B.  F.  Stem,  Frtdtriebburg,  7m.,  July  30, 1899. 

The  Classical  Manual  T  have  perused  with  delight,  and  shall  at  once  introduce  it  into 
my  school.  It  is  a  book  that  has  long  been  needed,  and  1  know  of  none  where  so  much 
varied  matter  can  be  found  in  lo  smalt  a  space. 

From  ilfr.  C.  Hammond,  Monson,  Matt.,  Aug.  6,  ISSi. 

I  shall  introduce  it  into  my  school  at  once.  It  is  just  what  we  have  needed  for  a  long, 
Song  time. 

From  Fn/.  TrimbU,  Ktnyon  ColUgt,  O.,.  Aug.  30, 1608. 

It  must  recommend  itself  to  the  teachers  in  all  the  classical  institutions  within  the 
■Union,  not  only  on  aocount  of  its  cheapness,  but  also  for  its  excellent  arrangement;  and 
tit  ivili  be  a  tin*  9«a  non  compendious  class-book  for  every  student  wishing  to  enter 
•out  oolleges. 

From  Mr.  J.  H.  Nourte,  Wathin^ton,  Aug.  17, 18S8. 

I  shall  require  every  classical  student  to  possess  a  copy  of  "Baird's  Manual." 

From  Mr,  W.  W.  Clarhi,  Qouvemeur  Wet.  Sem.,  N.  Y.,  Aug.  17, 18SS. 

I  admire  it  very  much  for  lh«  large  amount  of  classical  information  so  concisely  and 
clearly  set  forth.  It  is  just  the  thing  for  students  in  their  early  studies,  and  has  long  been 
a  desideratum. 

From  Mr.  W.  S.  Bogari,  TaUakanu,  Fl,  Aug.  7, 1869. 

It  contains  a  vast  amount  of  geographical  and  classical  information  in  a  most  concise 
rompass,  which  adapu  it  eavally  to  the  pupil  and  the  advanced  student  who  wishes  to 
I  eview  his  classical  knowledge. 


'onal  Worts.) 

Continued. 

«d.,  Feb.  18, 1893. 
rerent  works  in  pre- 
Q.  Cnniu.** 

18S2. 

rtt  appearance,  and 

ampt's  series,  so  fiir 
ested  to  procure  no 


I— (Now  Beady.) 
7AL; 

AND  ROMAN 
)LOaT. 
'  SCHOOLS.^ 

Iter. 

fifty  centl. 

ed  want  oran  Epi- 
ihould  contain  the 
luthora  most  com- 
an  to  embody  in  it 
lent,  in  a  form  and 
d,  and  he  has  con- 
ch, though  highly 
)  beginner.  In  the 
it  is  conveyed,  as 
lererore  admirably 
loola. 

1893. 

ace  introdnee  it  into 

loue  where  so  much 

BSi. 

re  needed  for  a  long) 

399. 

Blitutlons  within  the 
arrangement;  and 
m  wishing  to  enter 

13. 

d's  Manual." 

g.  17, 1868. 

on  so  concisely  and 
s,andhas  long  been 

)93. 

n  in  a  most  concise 
ident  who  wishes  » 


6LANCHARD  &  LEA'S  PUBLICATIONS.— (i?rf«ca«o«a/  Woria.)   15 

SCHOEDLER  &  IEDLOCK'8  BOOI  OF  NATUBB— (Nearly  Ready). 
•  3m  THB  BOOK  OF  NATITRE; 

AN  ELEMENTARY  INTRODUCTION 
TO  THE  BcniircES  or 

PHYSICS.  ASTRONOMY.  CHEMISTRY.  MINERALOGY.  GEOLOGY,  BOTANY. 
-vv  ;  /.     .      PHYSIOLOGY.  AND  ZOOLOGY.  Tiw 

'■  BY  FREDERICK  SCHOEDLER,  Ph.D. 

.^■^■^        TRANSLATBD  EROM   THB  SIXTH  OEBHAN  BOITION,        ,,{ 

..  ..9.  .q  ...1       BY  HENRY  MEDLOCK,  F.  C.  S.,  &c. 

With  irotes  and  Additions  "by  tta«  Auerlean  Bdltor. 

In  one  large  crown  octaTO  rolume,  with  over  six  hundred  handsome  illustrations. 


A  HISTORY  OF  8REEK  CUSSICAL  LITERATORL 

BY  THE  KEY.  B.  W.  BROWNE,  M.  A., 

•Mu  a         Professor  of  Classical  Literatnre  in  King's  College,  London. 

In  one  very  neat  volume,  crown  8vo.,  extra  cloth.  ^ 

To  be  shortly  follo^^ed  by  a  similar  volume  on  Roman  Literatnra 

From  Prq/l  /.  A,  Speneer,  New  York,  March  19, 185'2. 

ft  is  an  admirable  volume,  sufficiently  full  and  copious  in  detail,  clear  and  preciie  in 
style,  very  scholar-like  in  its  execution.  Kcnial  in  its  criticism,  and  alioKether  display- 
ing a  mind  well  stored  with  ibe  learning  genius,  wisdom,  and  exquisite  taste  of  the 
ancient  Greeks.  It  is  in  advance  of  everything  we  have,  and  it  may  be  considered 
indisptnsable  to  the  classical  scholar  and  student. 

to 
From  Prq/:  N.  H.  Griffin,  Williams  College,  Mass.,  March  22, 18iS3. 

A  valuable  compend,  einhracin^  in  a  small  compass  matter  which  the  student  would 
have  to  go  over  much  ground  to  gather  for  himself. 

From  Prof.  M.  F.  Hyde,  Burlington  College,  N.  J.,  Feb.  10, 1859. 

This  book  meets  a  want  that  has  long  been  felt  of  rome  single  work  on  the  subject 
presenting  to  the  student  and  general  reader,  in  a  popular  form,  information  widely  dis- 

Rerted  througti  a  great  variety  of  publications,  and  nowhere  combined  into  one  whole. 
Ir.  Browne's  selection  of  materials  is  Judiciously  made,  and  presented  in  a  perspicu> 
ous,  elegant,  and  agreeable  manner. 

From  Prof.  Gessner  Harrison,  University  of  Va.,  Feb.  28, 1868. 

1  am  very  favorably  impressed  with  the  work  from  what  I  have  seen  of  it,  and  hope 
to  find  in  it  an  important  help  for  my  class  of  history.    Such  a  work  is  very  much  needed. 


QEOQRAPHIA   CLAS8ICA: 

OR.  THE  APPLICATION  OP  ANCIENT  OROGRAPHY  TO  THE  CLASSICS. 
By  Samuel  Bvtlkb,  D  D.,  late  Lord  Bishop  of  Litchfield.  Revised  by  his  Son.  Sixth 
American,  from  the  last  London  Edition,  with  Questions  on  the  Maps,  by  John  Frost, 
LL.  I>.    In  one  neat  volume,  royal  18mo.,  half  bound.  ;  ^^a.y,^yii, 

'   •■  .ihil- 
,1H  u:,      AN   ATLAS  OF  ANCIENT   GEOGRAPHY. 

By  Sanusi.  BrTLTta,  D.  D.,  late  Lord  Bishop  of  Litchfield.  In  one  octavo  volume,  halt 
bound,  couiainiiig  twenty-one  quarto  colored  Maps,  and  an  accentuated  Index. 


16  BLANCHARD  &  LEA'S  VVBUCAT10iiS.—(£dttcatiokal  W0ri$.) 

.  {jnBW  Ain>  ncmo'ViiD  jnuivioif ~Oirow  BmAj.) 
OUTLIMES  OF  ENGLISH 

BY  THOMAS  B.  SHAW, 

ProfeMor  of  English  Literataia  ia  the  Imperial  Alexander  Lyeeum,  St  Peteriburg. 


•■OOffP  AMKBUAir  xstnoR. 


HI 


WITH  A  SKETCH  OF  AMERICAN  LITERATURE. 

BY  HENRY  T.  TUCKERMAN» 
Author  of"  CharaetertMies  of  LiterMnre,'*  "The  dptiaiiit,*' Ac. 

In  one  large  and  handsome  volume,  reyal  ISmo.,  extra  clolh^  of  about  500  page*. 

The  object  of  this  worlt  is  to  present  to  the  atudent  a  history  of  the  progress 
of  English  Literature.  To.  accomplish  this,  the  author  has  followed  its  course 
from  the  earliest  times  to  the  preient  age,  seizing  upon  the  more  prominent 
**  Sebools  of  Writings"  tmcing  their  causes  And  effecls»ai)d  seleeting  the  more 
celebrated  authors  as  subjects  for  brief  biographical  and  critical  sketches,  nna- 

2 sing  their  best  worlis,  and  thus  presenting  to  the  student  a  definite  view  of  the 
iveiopneBt  of  the  laneuage  and  literature,  iritb  socciiiot  descriptions  of  those 
'books  end  men  of  whien  no  edtieatetf  person  should  be  ignorant.  He  has  thus 
not  only  supplied  the  acknowledged  want  of  a  manual  on  this  subject,  but  by 
the  liveliness  and  power  of  his  style,  the  thorough  knowledge  be  displays  of  his 
topic,  and  the  variety  of  his  subjects,  be  has  succeeded  in  pro^qcing  a  most 
agreeable  reading-book,  which  will  captivate  the  mind  of  the  scholar,  and  re- 
lieve the  monotony  of  drier  atudiea. 

This  work  having  attracted  much  attention,  and  been  introduced  into  a  large 
number  of  our  best  academies  and  colleges,  the  publishers,  in  answering  the  call 
for  a  new  edition,  have  endeavored  to  render  it  still  more  appropriate  for  the 
student  of  this  country,  by  adding  to  it  a  sketch  of  American  literature.  This 
has  been  prepared  by  Mr.  Tuokerm,an,  on  the  plan  adopted  by  Mr.  8haw,  and 
the  volume  is  again  presented  with  full  confidence  that  it  will  be  ilMind  of  great 
utility  as  a  text-book,  wherever  this  subject  forms  part  of  the  educational  course; 
or  as  an  introduction  to  a  systematic  plan  of  readmg. 

From  Pr^.  R,  P.  Dunn,  Brown  Univmity,  April  SS,  1852. 

I  had  already  determined  to  adopt  it  as  the  principal  book  of  reference  in  my  depart- 
ment. This  is  the  first  term  in  which  it  has  been  used  here ;  but  froth  the  trial  which  I 
have  now  made  of  it,  I  have  every  reason  to  eongraiulaie  myself  on  my  selection  of  it 
as  a  tiizi-book. 

From  tit  Em.  W.  O,  T.  SKtdd,  Trtfmv^Kntli*^  Uttrmturt  in  tt«  UnhurHtyqf  Ft 

I  take  great  pleasure  in  saying  that  it  supplies  a  want  that  has  long  existed  of  a  brief 
history  of  English  literature,  written  in  the  right  method  and  spirit,  to  sei  v  e  as  an  intro- 
duction to  the  critical  study  of  it    I  shall  recommend  the  book  to  my  classes. 

From  Jama  Shannon,  Prtsidtnt  <ff  Baton  CoUigt,  JK!y. 

I  have  read  about  one-half  of  "  Shaw's  Outlines,"  and  so  fttr  I  am  more  than  pleased 
with  the  work.  I  concur  with  you  fully  in  the  opinion  that  it  supplies  a  want  long  felt 
in  our  higher  educational  institutes  of  a  eriiioal  history  of  English  literature,  ocitupving 
a  reasonable  space,  and  written  in  a  manlier  to  interest  ana  attract  the  attention  of  the 
student.    I  sincerely  desire  that  iUnay  obiainLCa  it  d<<sttrMSi  an  extensive  circulation 


SANDBOOK  OF  nODIRN  SURI 


UTERATURE. 


Britiah,  Danish,  Dutch,  French,  German,  Hungarian,  Italian,  Polish  and  Rus- 
sian, Portoguese,  Spanish,  and  Swedish.  With  a  full  Biographical  and 
Chronologioal  Index.  By  Mrs.  Fobtek.  In  one  large  royal  t2mo.  volume, 
extra  cloth.    Uniform  with  "  Shaw's  Outlines  of  English  Literature.'* 


atiohal  Works.) 

ERUTURE. 

earn,  St  Petersburg. 

ERATURE. 

milt,*' Ac. 

,  of  about  fiOO  pages. 

itory  of  the  progreas 
I  followed  iti  cuurie 
the  more  prominent 
i  aeieoting  the  more 
'itical  sketches,  ana* 
1  definite  view  of  the 
ieaeriptiona  of  those 
orant.  B«  haa  thqa 
this  subject,  but  by 
ge  ha  displays  of  his 
a  producing  a  roost 
the  scholar,  and  re- 

Todueed  into  a  large 
in  answering  the  call 
appropriate  for  the 
lan  liurature.  This 
id  by  Mr.  Shaw,  and 
rill  be  found  of  great 
i  educational  course; 

S2,18S2. 

tferdnce  in  my  depart- 
t  from  the  trial  which  I 
if  on  my  selection  of  it 

«  Ou  Vnieenity'iif  Yt. 
long  existed  of  a  brief 
it,  to  sei  <  e  as  an  imro- 
my  classes. 

r«,  Ky. 

am  more  than  pleased 
pplies  a  want  long  felt 
h  literature,  occupying 
act  the  attention  ot  the 
extensive  circulation 


IT1RAT1JBE. 

an,  Polish  and  Rus- 
ill  Biographical  and 
royal  12ino.  volumei 
\  Literature.** 


